Datasets:
ttlynne
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PhyX_mini_MC_embedding

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int64
0
999
image
stringlengths
4.4k
871k
question
stringlengths
189
2.04k
answer
stringclasses
4 values
category
stringclasses
6 values
subfield
stringclasses
26 values
reasoning_type
stringclasses
20 values
embedding
listlengths
4.1k
4.1k
900
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC+An4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Charge \q_2 is in static equilibrium. What is \q_1?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -12nC B: 20nC C: -20nC D: 5nC
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.037841796875, 0.004058837890625, -0.0242919921875, -0.0086669921875, -0.006744384765625, 0.01513671875, -0.0311279296875, 0.0130615234375, -0.0289306640625, 0.0040283203125, 0.01214599609375, 0.0032806396484375, 0.0025634765625, 0.01177978515625, -0.01385498046875, -0.023193359375, ...
901
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJ+ApADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two point charges on threads repel each other. What is the angle \( heta \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 3^\circ B: 9^\circ C: 4.4^\circ D: 2^\circ
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.02099609375, 0.03173828125, -0.030517578125, 0.00061798095703125, -0.01953125, 0.01531982421875, -0.031494140625, -0.018798828125, -0.0517578125, 0.0096435546875, -0.0177001953125, 0.024169921875, -0.01092529296875, -0.007232666015625, 0.024658203125, -0.01348876953125, -0.02954101...
902
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJsAnQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two point charges on threads repel each other. What is the charge?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.35\mu\{C} B: 0.55\mu\{C} C: 0.75\mu\{C} D: 1.75\mu\{C}
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.031982421875, 0.01324462890625, -0.0150146484375, -0.005096435546875, -0.02880859375, 0.00738525390625, 0.000782012939453125, -0.0224609375, -0.0242919921875, 0.0213623046875, 0.005523681640625, 0.02197265625, 0.0038299560546875, -0.00628662109375, -0.0113525390625, -0.016357421875, ...
903
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHuAhoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
What is the magnitude of the electric fields at point 1? What is the magnitude of the electric fields at point 1?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.25 \times 10^{3}N/C B: 1.35 \times 10^{5}N/C C: 1.8 \times 10^{5}N/C D: 5.33 \times 10^{5}N/C
C
Electromagnetism
Electrostatics
['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning']
[ 0.0361328125, 0.011962890625, -0.03759765625, -0.00506591796875, -0.02587890625, 0.01153564453125, 0.00286865234375, -0.00010395050048828125, -0.0289306640625, 0.01141357421875, -0.01708984375, 0.0196533203125, -0.0032958984375, 0.01397705078125, 0.001556396484375, 0.000074386596679687...
904
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALAAhIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
An electric field \( \vec{E} = 100{,}000\,\hat{i}\,\mathrm{N/C} \) causes the point charge in figure to hang at a angle. What is the charge on the ball?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.35\mu\{C} B: 0.55\mu\{C} C: 0.18\mu\{C} D: 0.75\mu\{C}
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.031494140625, 0.004547119140625, -0.018798828125, -0.00119781494140625, -0.0286865234375, 0.0123291015625, -0.005767822265625, -0.0228271484375, -0.03515625, 0.0115966796875, -0.0020294189453125, 0.017333984375, -0.00119781494140625, -0.00823974609375, -0.00445556640625, -0.006408691...
905
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAK8AgwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
An electric field \( \vec{E} = 200{,}000\,\hat{i}\,\mathrm{N/C} \) causes the point charge in figure to hang at a angle. What is the charge on the ball?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 3^\circ B: 9^\circ C: 14^\circ D: 20^\circ
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0211181640625, 0.0196533203125, -0.0167236328125, -0.003509521484375, -0.02099609375, 0.026611328125, -0.0303955078125, -0.0169677734375, -0.04736328125, 0.02001953125, -0.0115966796875, 0.0181884765625, -0.002838134765625, -0.003631591796875, 0.0242919921875, -0.01080322265625, -0...
906
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHMAbQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
The identical small spheres shown in figure hang as shown in a \( 100{,}000\,\mathrm{N/C} \) electric field. What is the mass of each sphere?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 3g B: 4.4g C: 4.1g D: 5.2g
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.015625, 0.0086669921875, -0.0113525390625, 0.00665283203125, -0.00689697265625, 0.0419921875, -0.016845703125, -0.018310546875, -0.0211181640625, -0.0115966796875, 0.00762939453125, -0.00390625, -0.0203857421875, -0.006866455078125, 0.015380859375, -0.0177001953125, -0.029541015625...
907
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFcAk4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
The force on the -1.0 nC charge is as shown in Figure What is the magnitude of this force?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7.25 \times 10^{-4}N B: 6.35 \times 10^{-4}N C: 1.7 \times 10^{-4}N D: 1.33 \times 10^{-4}N
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.0224609375, 0.0234375, -0.034912109375, 0.01397705078125, -0.0174560546875, 0.03369140625, -0.0146484375, -0.01129150390625, -0.032470703125, 0.0172119140625, -0.0150146484375, 0.023681640625, 0.005126953125, 0.006378173828125, -0.006683349609375, -0.0181884765625, -0.04150390625, ...
908
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAI4A+IDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two electrodes are spaced apart. They are charged by transferring \( 1.0\times10^{11} \) electrons from one electrode to the other. An electron is released from rest at the surface of the negative electrode. Assume the space between the electrodes is a vacuum. What is its speed as it collides with the positive electrod...
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0361328125, -0.006103515625, -0.0157470703125, -0.004638671875, -0.01129150390625, 0.030029296875, -0.01385498046875, 0.025146484375, -0.0274658203125, 0.0198974609375, -0.02392578125, 0.0439453125, -0.009521484375, 0.00860595703125, 0.01275634765625, 0.005615234375, -0.029296875, ...
909
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAI4BNADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
An electron gun creates a beam of electrons moving horizontally with a speed of \( 3.3\times10^{7}\,\mathrm{m/s} \). The electrons enter a gap between two parallel electrodes with a electric field. By what angle, is the electron beam deflected by these electrodes?Please directly answer the question and provide the corr...
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0191650390625, 0.01708984375, -0.0146484375, -0.006072998046875, -0.01397705078125, 0.033935546875, -0.0361328125, 0.0010986328125, -0.041259765625, 0.013916015625, -0.020263671875, 0.03955078125, -0.0069580078125, -0.000743865966796875, 0.035400390625, -0.0028228759765625, -0.0197...
910
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGWA0QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two balls are connected by a \( 2.0\,\mathrm{cm} \)-long insulating rod of negligible mass. The rod is held in a uniform electric field at an angle with respect to the field, then released. What is its initial angular acceleration?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, ...
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.03466796875, 0.0004253387451171875, -0.0260009765625, -0.00014400482177734375, -0.004119873046875, 0.027587890625, -0.02197265625, -0.022216796875, -0.037841796875, 0.021484375, -0.013427734375, 0.0196533203125, -0.00689697265625, 0.0120849609375, 0.0228271484375, -0.001617431640625,...
911
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADWAlQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
The water molecule \(\mathrm{H_2O}\) has a permanent dipole moment of magnitude \(6.2\times10^{-30}\,\mathrm{C\,m}\). A water molecule is located some distance from a \(\mathrm{Na^+}\) ion in a saltwater solution. What force does the ion exert on the water molecule?Please directly answer the question and provide the co...
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0250244140625, 0.005859375, -0.0257568359375, -0.004608154296875, -0.016845703125, 0.035400390625, -0.00775146484375, -0.0050048828125, -0.04052734375, 0.006134033203125, -0.01165771484375, 0.034423828125, -0.00909423828125, -0.0010833740234375, -0.006500244140625, 0.007476806640625,...
912
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHSAfIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
In a vacuum chamber, a proton orbits a \(1.0\,\mathrm{cm}\)-diameter metal ball \(1.0\,\mathrm{mm}\) above the surface with a period of \(1.0\,\mu\mathrm{s}\). What is the charge on the ball?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -1.3 \times 10^{-12}...
C
Electromagnetism
Electrostatics
['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning']
[ 0.0269775390625, 0.0084228515625, -0.013916015625, -0.01263427734375, -0.01080322265625, 0.01300048828125, -0.0091552734375, -0.003936767578125, -0.030517578125, 0.0146484375, -0.0079345703125, 0.0166015625, -0.006011962890625, -0.00909423828125, 0.0038299560546875, 0.0037994384765625,...
913
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFAARoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
What is the strength of the electric field at the position indicated by the dot? What is the strength of the electric field at the position indicated by the dot?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.3 \times 10^{3}N/C B: 5.3 \times 10^{3}N/C C: 7....
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.03662109375, 0.01092529296875, -0.02587890625, -0.0027923583984375, -0.0235595703125, 0.013916015625, -0.0004253387451171875, 0.00946044921875, -0.025634765625, 0.004852294921875, -0.01275634765625, 0.0284423828125, -0.0029754638671875, 0.00142669677734375, -0.0002574920654296875, 0....
914
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE6AOwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
What is the strength of the electric field at the position indicated by the dot? What is the strength of the electric field at the position indicated by the dot?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.3 \times 10^{3}N/C B: 5.3 \times 10^{3}N/C C: 1....
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.036865234375, 0.013916015625, -0.031982421875, -0.007049560546875, -0.0257568359375, 0.019287109375, 0.004669189453125, 0.0076904296875, -0.0283203125, 0.0050048828125, -0.01153564453125, 0.033935546875, -0.00518798828125, 0.00970458984375, 0.00390625, 0.003936767578125, -0.0250244...
915
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFAAP4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
What is the strength of the electric field at the position indicated by the dot? What is the strength of the electric field at the position indicated by the dot?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.3 \times 10^{3}N/C B: 5.3 \times 10^{3}N/C C: 1....
C
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.031494140625, 0.01434326171875, -0.02783203125, -0.01275634765625, -0.02392578125, 0.0224609375, 0.0019683837890625, 0.01324462890625, -0.037353515625, 0.003387451171875, -0.0130615234375, 0.028076171875, -0.00179290771484375, 0.0093994140625, 0.00130462646484375, 0.007659912109375, ...
916
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGtAz4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A copper wire carries a steady current to an electroplating tank. Find the magnetic field due to a 1.0 cm segment of this wire at a point 1.2 m away from it, if the point is point $P_2$, in the $xy$-plane and on a line at $30^\circ$ to the segment.Please directly answer the question and provide the correct OPTION LETTE...
C
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.0274658203125, 0.0081787109375, -0.00058746337890625, 0.0034942626953125, -0.00555419921875, 0.039794921875, -0.0177001953125, 0.0185546875, -0.0196533203125, -0.000339508056640625, -0.0196533203125, 0.040283203125, 0.01806640625, 0.0255126953125, 0.01043701171875, 0.0125732421875, ...
917
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The magnetic field between the poles of the electromagnet in figure is uniform at any time, but its magnitude is increasing at the rate of $0.020 \, \text{T/s}$. Find the induced current in the circuit.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.024mA B...
C
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.02685546875, 0.002532958984375, -0.020263671875, 0.003082275390625, -0.0205078125, 0.00726318359375, -0.01446533203125, -0.006744384765625, -0.037109375, 0.008056640625, -0.0125732421875, 0.0172119140625, -0.000301361083984375, 0.00872802734375, 0.00665283203125, -0.0028533935546875,...
918
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Figure shows a U-shaped conductor in a uniform magnetic field $\vec{B}$ perpendicular to the plane of the figure and directed into the page. We lay a metal rod (the “slidewire”) with length $L$ across the two arms of the conductor, forming a circuit, and move it to the right with constant velocity $\vec{v}$. This induc...
C
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0225830078125, -0.030029296875, 0.00799560546875, -0.0167236328125, -0.0036468505859375, 0.006256103515625, -0.00994873046875, -0.004058837890625, -0.01385498046875, -0.0021209716796875, -0.0159912109375, 0.031005859375, -0.00579833984375, 0.00384521484375, 0.0159912109375, -0.007293...
919
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In the slidewire, energy is dissipated in the circuit owing to its resistance. Let the resistance of the circuit (made up of the moving slidewire and the U-shaped conductor that connects the ends of the slidewire) at a given point in the slidewire's motion be $R$. Find the rate at which energy is dissipated in the circ...
C
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0230712890625, 0.00095367431640625, -0.0103759765625, 0.0045166015625, 0.004913330078125, -0.0030975341796875, -0.00872802734375, -0.0164794921875, -0.0106201171875, 0.0164794921875, -0.0263671875, 0.01031494140625, -0.0184326171875, 0.007232666015625, 0.01495361328125, -0.0023193359...
920
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Figure shows a conducting disk with radius \( R \) that lies in the \( xy \)-plane and rotates with constant angular velocity about the \( z \)-axis. The disk is in a uniform, constant \( \vec{B} \) field in the \( z \)-direction. Find the induced emf between the center and the rim of the disk.Please directly answer th...
C
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.028564453125, -0.00179290771484375, -0.00946044921875, 0.01385498046875, -0.00072479248046875, -0.017578125, -0.03564453125, -0.0177001953125, -0.046142578125, 0.0242919921875, -0.0022735595703125, 0.002410888671875, -0.0262451171875, -0.0062255859375, 0.0029754638671875, -0.01348876...
921
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGlArgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
In one form of Tesla coil (a high-voltage generator popular in science museums), a long solenoid and cross-sectional area is closely wound with turns of wire. A coil with turns surrounds it at its center. Find the mutual inductance \( M \).Please directly answer the question and provide the correct OPTION LETTER ONLY, ...
C
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0458984375, 0.01080322265625, -0.027587890625, -0.002227783203125, -0.003173828125, 0.005157470703125, -0.00726318359375, 0.007415771484375, -0.02587890625, 0.0220947265625, -0.0216064453125, 0.029296875, 0.008544921875, 0.01190185546875, -0.00634765625, -0.00848388671875, -0.01342...
922
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Assume that \( B \) is uniform across a cross section (that is, neglect the variation of \( B \) with distance from the toroid axis). Determine the self-inductance of a toroidal solenoid with cross-sectional area \( A \) and mean radius \( r \), closely wound with \( N \) turns of wire on a nonmagnetic core.Please dire...
C
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.02734375, 0.002105712890625, -0.00159454345703125, -0.01165771484375, -0.01019287109375, 0.021484375, -0.01318359375, -0.0032196044921875, -0.04296875, 0.010986328125, -0.0201416015625, 0.036865234375, 0.004241943359375, -0.0177001953125, 0.01611328125, 0.0023345947265625, -0.02233...
923
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Figure is a hypothetical plot of the recessional speeds \( v \) of galaxies against their distance \( r \) from us; the best-fit straight line through the data points is shown. From this plot determine the age of the universe, assuming that Hubble's law holds and that Hubble's constant has always had the same value.Ple...
C
Electromagnetism
Electromagnetic Waves
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.034912109375, 0.00946044921875, -0.03369140625, -0.0201416015625, 0.00010013580322265625, 0.027099609375, -0.0185546875, 0.0015106201171875, -0.0245361328125, 0.018310546875, -0.004547119140625, 0.03173828125, -0.00091552734375, -0.006072998046875, -0.002349853515625, 0.0030059814453...
924
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJfA4wDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Figure gives the parameter \( eta \) versus the sine of the angle \( heta \) in a two-slit interference experiment using light of wavelength 435\,\text{nm}. The vertical axis scale is set by \( eta_s = 80.0\,\text{rad} \).Assume that none of the interference maxima are completely eliminated by a diffraction minimum....
C
Electromagnetism
Wave Optics
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.0150146484375, 0.0252685546875, -0.00054931640625, -0.03125, -0.017578125, 0.0255126953125, -0.0218505859375, -0.0172119140625, -0.046875, 0.01611328125, -0.0223388671875, 0.0400390625, -0.0019073486328125, 0.0084228515625, 0.01385498046875, 0.0008697509765625, -0.03125, 0.021728...
925
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACiAXgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Figure shows a 2.0-cm-diameter solenoid passing through the center of a 6.0-cm-diameter loop. The magnetic field inside the solenoid is 0.20 T. What is the magnetic flux through the loop when it is tilted at a 60\(^{\circ}\) angle?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.000820159912109375, 0.00150299072265625, -0.0023345947265625, -0.00384521484375, -0.0244140625, 0.016357421875, -0.02783203125, -0.01171875, -0.03125, 0.0142822265625, -0.00994873046875, 0.045166015625, -0.0125732421875, 0.00653076171875, 0.0047607421875, 0.01239013671875, -0.01525...
926
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEKAOoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Figure shows a 10-cm-diameter loop in magnetic fields. The loop's resistance is \( 0.20 \, \Omega \). What are the size of the induced current?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \(16 \text{ mA}\) B: \( 20 \text{ mA}\) C: \(39\text{ mA}\) D: \(15 ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.00732421875, 0.0126953125, -0.0155029296875, -0.0185546875, -0.00537109375, -0.003692626953125, -0.00396728515625, -0.01312255859375, -0.030517578125, 0.003387451171875, -0.018310546875, 0.01611328125, 0.031494140625, 0.006500244140625, -0.01220703125, 0.00408935546875, -0.01782226...
927
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The magnetic field in figure is decreasing at the rate \( 0.10 \text{ T/s} \). What is the acceleration of a proton initially at rest at points c?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 2.9 \times 10^4 \text{ m/s}^2 \) B: \( 4.8 \times 10^4 \text{ ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0012969970703125, -0.006103515625, -0.01806640625, 0.012451171875, 0.0196533203125, 0.0213623046875, -0.020263671875, -0.02197265625, -0.048583984375, 0.01251220703125, -0.02880859375, 0.0228271484375, -0.0172119140625, -0.004974365234375, 0.00787353515625, 0.0005340576171875, -0.0...
928
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEiAZQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
What value of resistor \( R \) gives the circuit in figure a time constant of \( 25 \, \mu\text{s} \)? What value of resistor \( R \) gives the circuit in figure a time constant of \( 25 \, \mu\text{s} \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 100...
B
Electromagnetism
Electric Circuits
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0478515625, 0.002685546875, 0.006561279296875, 0.00026702880859375, -0.00421142578125, 0.0054931640625, -0.0123291015625, -0.00286865234375, -0.0225830078125, 0.011474609375, -0.01092529296875, 0.0234375, 0.01434326171875, 0.021484375, -0.00909423828125, -0.004241943359375, -0.0314...
929
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADwAYYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Figure shows a square bent at a \( 90^\circ \) angle. A uniform \( 0.050 \, \text{T} \) magnetic field points downward at a angle. What is the magnetic flux through the loop?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 4.2 \times 10^{-4} \ \text{Wb} \) ...
B
Electromagnetism
Electromagnetic Induction
['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning']
[ -0.004974365234375, 0.004119873046875, 0.004180908203125, -0.0014495849609375, -0.0223388671875, 0.0185546875, -0.0091552734375, 0.0019683837890625, -0.0224609375, 0.0125732421875, -0.03173828125, 0.036865234375, -0.00396728515625, 0.016845703125, 0.0167236328125, -0.012451171875, -0...
930
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEaAxYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Figure shows a loop with resistance \( 0.10 \, \Omega \) around a solenoid. The solenoid is \( 10 \, \text{cm} \) long, has \( 100 \) turns, and carries the current shown in the graph positive current is cw when seen from the left. Find the current in the loop at \( t = 2.5 \, \text{s} \).Please directly answer the que...
B
Electromagnetism
Electromagnetic Induction
['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning']
[ 0.02392578125, -0.0022125244140625, -0.025390625, -0.01397705078125, -0.017578125, 0.019775390625, -0.00225830078125, -0.01507568359375, -0.041259765625, 0.0087890625, -0.021484375, 0.026123046875, 0.008544921875, -0.0040283203125, 0.00244140625, -0.004608154296875, -0.01953125, 0....
931
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEoAfgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
The square loop shown in figure moves into a magnetic field at a constant speed. The loop has a resistance of \( 0.10 \, \Omega \), and it enters the field at \( t = 0 \, \text{s} \). What is the maximum current?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A:...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0198974609375, 0.0120849609375, -0.013916015625, -0.021240234375, -0.0023651123046875, 0.0023345947265625, -0.015625, 0.01422119140625, -0.040771484375, -0.0032806396484375, -0.027587890625, 0.0137939453125, -0.0029296875, 0.004241943359375, 0.01153564453125, -0.005584716796875, -0...
932
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Your camping buddy has an idea for a light to go inside your tent. He happens to have a powerful (and heavy!) horseshoe magnet that he bought at a surplus store. This magnet creates a field between two pole tips \( 10 \, \text{cm} \) apart. His idea is to build the hand-cranked generator shown in figure. He thinks you ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0068359375, 0.009765625, 0.006256103515625, 0.00909423828125, 0.00162506103515625, 0.0198974609375, -0.016357421875, 0.00106048583984375, -0.0184326171875, -0.00121307373046875, -0.0223388671875, 0.028076171875, 0.000850677490234375, 0.0235595703125, 0.01611328125, 0.011962890625, ...
933
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Experiments to study vision often need to track the movements of a subject's eye. One way of doing so is to have the subject sit in a magnetic field while wearing special contact lenses with a coil of very fine wire circling the edge. A current is induced in the coil each time the subject rotates his eye. Consider the ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0242919921875, 0.0034027099609375, -0.0174560546875, -0.00830078125, -0.035888671875, 0.00139617919921875, -0.010009765625, 0.0093994140625, -0.042236328125, 0.013916015625, -0.01226806640625, 0.03271484375, 0.0013885498046875, 0.00665283203125, 0.0037384033203125, -0.0118408203125, ...
934
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The switch in figure has been in position 1 for a long time. It is changed to position 2 at \( t = 0 \, \text{s} \). What is the first time at which the current is maximum?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 0.20 \, \text{ms} \) B: \( 0.50 \, \...
B
Electromagnetism
Electric Circuits
['Physical Model Grounding Reasoning', 'Numerical Reasoning']
[ 0.019775390625, -0.011474609375, -0.00145721435546875, -0.0106201171875, -0.005401611328125, 0.0118408203125, -0.00531005859375, -0.008056640625, -0.01263427734375, 0.01611328125, -0.01422119140625, 0.0167236328125, -0.027587890625, 0.0164794921875, 0.01129150390625, 0.005584716796875,...
935
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The area of the conducting loop in the field is $120 \, cm^2$. Find the induced emf and the induced current in the circuit.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.45mV B: 0.24mV C: 0.54mV D: 0.23mV
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.039306640625, -0.00457763671875, -0.037109375, -0.00555419921875, -0.0145263671875, 0.00250244140625, 0.004974365234375, -0.0064697265625, -0.03515625, 0.020751953125, -0.01336669921875, 0.021728515625, -0.007232666015625, 0.003326416015625, 0.0133056640625, -0.01068115234375, -0.0...
936
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A 500-loop circular wire coil with radius \( 4.00 \ \mathrm{cm} \) is placed between the poles of a large electromagnet. The magnetic field is uniform; it decreases at \( 0.200 \ \mathrm{T/s} \). What are the magnitude and direction of the induced emf?Please directly answer the question and provide the correct OPTION L...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0205078125, -0.001373291015625, -0.0164794921875, -0.004547119140625, -0.0264892578125, -0.00141143798828125, -0.00714111328125, -0.00860595703125, -0.01953125, 0.01324462890625, -0.0228271484375, 0.022705078125, 0.009521484375, -0.00170135498046875, -0.00179290771484375, 0.009887695...
937
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Suppose the moving rod in figure is \( 0.10 \\ \mathrm{m} \) long, the velocity \( v \) is \( 2.5 \\ \mathrm{m/s} \), the total resistance of the loop is \( 0.030 \\ \Omega \), and \( B \) is \( 0.60 \\ \mathrm{T} \). Find the force acting on the rod.Please directly answer the question and provide the correct OPTION L...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.040283203125, 0.00762939453125, -0.032958984375, 0.00848388671875, -0.0223388671875, 0.0021514892578125, -0.000946044921875, -0.00335693359375, -0.0361328125, -0.0000705718994140625, -0.0291748046875, 0.0286865234375, 0.005645751953125, 0.002777099609375, -0.00286865234375, -0.007141...
938
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Suppose the long solenoid in figure has 500 turns per meter and cross-sectional area \( 4.0 \\ \mathrm{cm}^2 \). The current in its windings is increasing at \( 100 \\ \mathrm{A/s} \). Find the magnitude of the induced electric field within the loop if its radius is \( 2.0 \\ \mathrm{cm} \).Please directly answer the q...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.035888671875, -0.00061798095703125, -0.0260009765625, -0.00201416015625, -0.0172119140625, 0.00872802734375, -0.006378173828125, 0.008544921875, -0.048583984375, 0.01336669921875, -0.0240478515625, 0.032958984375, -0.0018768310546875, 0.0098876953125, 0.0068359375, -0.007476806640625...
939
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In one form of Tesla coil. Find the mutual inductance \( M \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 22\ \mu\mathrm{H} B: 25\ \mu\mathrm{H} C: 75\ \mu\mathrm{H} D: 28\ \mu\mathrm{H}
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.046630859375, 0.0322265625, -0.027099609375, -0.001922607421875, -0.007568359375, 0.00113677978515625, -0.01507568359375, 0.01275634765625, -0.0223388671875, 0.0205078125, -0.00994873046875, 0.01153564453125, 0.00885009765625, -0.00113677978515625, 0.00067138671875, -0.0079345703125,...
940
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Determine the self-inductance of a toroidal solenoid with cross-sectional area \( A \) and mean radius \( r \), closely wound with \( N \) turns of wire on a nonmagnetic core. Assume that \( B \) is uniform across a cross section (that is, neglect the variation of \( B \) with distance from the toroid axis). Determine ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.034423828125, 0.01275634765625, -0.002685546875, -0.005859375, -0.0074462890625, 0.0076904296875, -0.0133056640625, -0.00494384765625, -0.035888671875, 0.0135498046875, -0.02392578125, 0.032958984375, 0.0084228515625, -0.0172119140625, 0.022216796875, 0.005279541015625, -0.02709960...
941
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A sensitive electronic device of resistance \( R = 175\ \Omega \) is to be connected to a source of emf (of negligible internal resistance) by a switch. The device is designed to operate with a 36 mA current, but to avoid damage to the device, the current can rise to no more than 4.9 mA in the first 58 \( \mu\mathrm{s}...
B
Electromagnetism
Electric Circuits
['Multi-Formula Reasoning', 'Numerical Reasoning']
[ 0.03125, 0.0118408203125, -0.0032806396484375, -0.010498046875, -0.007537841796875, 0.01019287109375, -0.025634765625, -0.0130615234375, -0.0164794921875, 0.007476806640625, -0.0252685546875, 0.0078125, 0.002960205078125, -0.01361083984375, 0.030517578125, 0.007568359375, -0.03735351...
942
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Based on the figure. Determine the capacitive reactance of the capacitor.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 20\ \Omega\ B: 80\ \Omega\ C: 100\ \Omega\ D: 200\ \Omega\
B
Electromagnetism
Electric Circuits
['Physical Model Grounding Reasoning', 'Numerical Reasoning']
[ 0.0341796875, 0.0096435546875, -0.01287841796875, 0.0023651123046875, -0.0162353515625, -0.001495361328125, -0.02734375, 0.0052490234375, -0.025390625, 0.002838134765625, 0.00335693359375, 0.00775146484375, -0.01104736328125, 0.01141357421875, -0.00012969970703125, 0.005157470703125, ...
943
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The series circuit in figure is connected to a variable-frequency ac source with an rms terminal voltage of 1.0\ \mathrm{V}. Determine the the inductive reactance \( X_L \), the capacitive reactance \( X_C \), and the impedance \( Z \)Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.,...
B
Electromagnetism
Electric Circuits
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.036376953125, 0.01031494140625, 0.00732421875, -0.006011962890625, -0.0032958984375, 0.01953125, -0.00909423828125, 0.01513671875, -0.036376953125, 0.003570556640625, -0.030517578125, -0.01153564453125, 0.007293701171875, 0.0302734375, -0.002716064453125, 0.0115966796875, -0.03125,...
944
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A radio station on the earth’s surface emits a sinusoidal wave with average total power 50\ \mathrm{kW} Assuming that the transmitter radiates equally in all directions above the ground (which is unlikely in real situations) find the electric-field and magnetic-field amplitudes \( E_\mathrm{max} \) and \( B_\mathrm{max...
B
Electromagnetism
Electromagnetic Waves
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.028076171875, 0.00080108642578125, -0.008544921875, -0.00738525390625, 0.01055908203125, 0.006866455078125, -0.04052734375, -0.009521484375, -0.03466796875, 0.01123046875, -0.00701904296875, 0.04736328125, -0.0189208984375, 0.0023651123046875, 0.01611328125, 0.003448486328125, -0.0...
945
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If the sun’s radiation is perpendicular to the panels and is completely absorbed. find the average solar power absorbed.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 5.5kW B: 5.6kW C: 7.5kW D: 5.9kW
B
Electromagnetism
Electromagnetic Waves
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.018310546875, 0.01239013671875, -0.0296630859375, -0.00102996826171875, 0, 0.006378173828125, -0.01226806640625, -0.019287109375, -0.0294189453125, 0.006256103515625, 0.0140380859375, 0.025390625, 0.0252685546875, -0.002166748046875, -0.0174560546875, 0.001434326171875, -0.04907226...
946
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Earth's magnetic field near the ground has a magnitude of \( 0.50 \times 10^{-4}\text{T} \) and is inclined downward at \( 45^\circ \); consider whether it is feasible to use this field for a levitation device. Suppose we use easily obtainable \( 1.0\,\text{T} \) permanent magnets to supply the horizontal magnetic fiel...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.04296875, 0.01495361328125, -0.03125, 0.0172119140625, -0.0172119140625, 0.0198974609375, -0.018310546875, -0.00116729736328125, -0.041748046875, -0.00958251953125, -0.02001953125, 0.01092529296875, 0.0133056640625, 0.0016937255859375, 0.005645751953125, -0.0164794921875, -0.027221...
947
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A rectangular loop pivots about the \( y \)-axis and carries a current of \( 15.0\text{A} \) in the direction shown. If the loop is in a uniform magnetic field with magnitude \( 0.48\,\text{T} \) in the \( +x \)-direction, find the magnitude and direction of the torque required to hold the loop in the position shown.Pl...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.0072021484375, 0.01202392578125, -0.001617431640625, -0.0072021484375, -0.0128173828125, 0.01177978515625, -0.0252685546875, 0.015380859375, -0.03466796875, 0.0106201171875, -0.01708984375, 0.0245361328125, -0.00555419921875, -0.0024261474609375, 0.0206298828125, 0.00958251953125, ...
948
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFoARoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A rectangular wire loop of mass \( 0.15\text{g/cm} \) is pivoted about side \( ab \) on a frictionless axis, and carries a current of \( 8.2\text{A} \) in the direction shown. Find the magnitude and direction of the magnetic field parallel to the \(y\)-axis that will cause the loop to swing up until its plane makes an ...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.0150146484375, -0.005767822265625, 0.0169677734375, 0.0050048828125, -0.001190185546875, 0.020263671875, -0.01336669921875, -0.0002498626708984375, -0.025634765625, -0.0026092529296875, -0.0137939453125, 0.0299072265625, -0.000457763671875, 0.00274658203125, 0.035888671875, -0.006195...
949
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACYAHsDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A uniform bar of length \( L \) carries a current \( I \) from end \( a \) to \( b \), and lies in a uniform magnetic field directed into the page. Find the torque about an axis perpendicular to the bar at point \( a \). Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. O...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.026123046875, -0.0184326171875, -0.01055908203125, 0.00750732421875, 0.00506591796875, 0.027587890625, -0.0140380859375, -0.01416015625, -0.0283203125, -0.00469970703125, -0.00994873046875, 0.0115966796875, -0.014892578125, 0.00970458984375, -0.000942230224609375, -0.0098876953125, ...
950
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEMATQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A voice coil has 50 turns, diameter \( 1.56\,\text{cm} \), and carries a current of \( 0.950\,\text{A} \). It lies in a magnetic field of magnitude \( 0.220\,\text{T} \) directed at an angle of \( 60.0^\circ \) from the normal to the coil plane. Calculate the magnitude and direction of the net magnetic force on the coi...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0030670166015625, 0.0146484375, -0.00133514404296875, -0.005126953125, -0.0264892578125, 0.01361083984375, -0.03955078125, -0.0015716552734375, -0.0164794921875, 0.005096435546875, -0.0091552734375, 0.0380859375, 0.026123046875, -0.0137939453125, 0.01141357421875, 0.016845703125, -...
951
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADEAIYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
What must be the current \( I \) in the bar for the bar to be in rotational equilibrium when it is at an angle \( heta = 30.0^\circ \) above the horizontal? Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 4.52A B: 2.26A C: 15.1A D: 2.60A
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.01422119140625, 0.0106201171875, -0.00732421875, -0.00408935546875, -0.002288818359375, 0.02099609375, -0.023193359375, 0.0205078125, -0.03466796875, 0.004730224609375, -0.02880859375, 0.03369140625, 0.0235595703125, 0.004974365234375, 0.0177001953125, 0.01190185546875, -0.00811767...
952
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACrALYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A square current loop of side length \( L \), carrying a clockwise current \( I \), lies in the \( xy \)-plane in a nonuniform magnetic field \( \vec{B} = \left( B_0 z/L ight) \hat{j} + \left( B_0 y/L ight) \hat{k} \), where \( B_0 \) is a positive constant. Find the magnitude an direction of the net magnetic force o...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.00531005859375, -0.00101470947265625, -0.00335693359375, -0.00775146484375, 0.0115966796875, 0.00848388671875, -0.007415771484375, -0.0025482177734375, -0.04248046875, -0.005523681640625, -0.0205078125, 0.0005035400390625, -0.00121307373046875, 0.017822265625, 0.00186920166015625, 0....
953
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACQAHMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A thin uniform rod of mass \( 0.0840\text{kg} \) and length \( 18.0\text{cm} \) is fixed to the floor at one end by a frictionless hinge and is held at an angle \( 53.0^\circ \) above the horizontal by a horizontal string attached to the wall. The rod carries a current \( 12.0\text{A} \) toward the hinge and is placed ...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0296630859375, -0.0098876953125, 0.00921630859375, -0.01080322265625, -0.00848388671875, 0.01129150390625, -0.010009765625, -0.01068115234375, -0.031982421875, -0.0142822265625, -0.035400390625, 0.013916015625, -0.01202392578125, 0.001953125, 0.017333984375, 0.0022735595703125, -0....
954
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAETAOkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A cylinder of radius \( R \) and width \( W \) is wrapped \( N \) times by a conducting wire along its diameter, carrying a current \( I \). A uniform magnetic field of magnitude \( B \) points vertically downward. A mass \( M \) is suspended from a cable wound around the rim, and its height above the lowest point is \...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0096435546875, -0.001953125, 0.006195068359375, 0.025146484375, -0.022705078125, 0.0289306640625, -0.0078125, 0.000148773193359375, -0.027099609375, 0.000659942626953125, -0.006500244140625, 0.044921875, -0.0103759765625, -0.029541015625, 0.0279541015625, -0.00048065185546875, -0.0...
955
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADZASkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
To measure the mass of a muon, which has charge equal to that of an electron and initially zero speed, you apply a magnetic field of \( 0.340\text{T} \) and record values of electric field strength corresponding to zero deflection as a function of accelerating voltage \( V \), then plot \( E^2 \) versus \( V \). Use th...
B
Electromagnetism
Electromagnetic Induction
['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning']
[ 0.0390625, 0.0118408203125, -0.00958251953125, 0.00016021728515625, -0.01141357421875, 0.044921875, 0.00372314453125, -0.00118255615234375, -0.0302734375, 0.0213623046875, -0.01153564453125, 0.03662109375, -0.01446533203125, 0.0021514892578125, 0.018798828125, -0.01104736328125, -0.0...
956
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE3AP4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
An alpha particle moves in a circular path in a magnetic field \( \vec{B} \) perpendicular to the motion. The frequency \( f \) of revolution is measured as a function of \( B \), and the data form a straight-line relationship. With \( B = 0.300\,\text{T} \), what are the cyclotron frequencies \( f \) of an electron?Pl...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Predictive Reasoning']
[ 0.04541015625, 0.0177001953125, -0.00885009765625, -0.0172119140625, 0.0078125, 0.03466796875, -0.0277099609375, -0.01025390625, -0.043701171875, 0.004730224609375, -0.0023651123046875, 0.0302734375, -0.0107421875, -0.0189208984375, 0.00148773193359375, 0.005035400390625, -0.02416992...
957
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEsAZMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A particle with charge \( 2.15\mu\text{C} \), mass \( 3.20 \times 10^{-11}\text{kg} \), and initial speed \( 1.45 \times 10^5\text{m/s} \) enters a \( 0.420\text{T} \) magnetic field perpendicular to its velocity. The field region is \( 25.0\text{cm} \) long, followed by a field-free region of \( 50.0\text{cm} \), and ...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.0167236328125, 0.0031280517578125, 0.003814697265625, -0.01513671875, -0.00689697265625, 0.0203857421875, -0.0074462890625, 0.00836181640625, -0.0220947265625, 0.0023651123046875, -0.03662109375, 0.038330078125, -0.0164794921875, 0.005035400390625, 0.0224609375, -0.0166015625, -0.0...
958
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFiAesDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A particle with mass \( m \) and charge \( q \) starts from rest at the origin in uniform fields \( \vec{E} \) along \( +y \) and \( \vec{B} \) out of the page. The particle moves in a cycloidal path with radius of curvature at the top points equal to twice the corresponding \( y \)-coordinate. Applying Newton's second...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Numerical Reasoning']
[ 0.0130615234375, -0.0201416015625, -0.0111083984375, 0.000568389892578125, -0.00897216796875, -0.002044677734375, -0.02587890625, -0.005157470703125, -0.000056743621826171875, -0.001922607421875, -0.01904296875, 0.01806640625, -0.030517578125, -0.002655029296875, 0.031982421875, -0.016...
959
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAENAQYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
An electron and a proton are each moving at \( 735\,\text{km/s} \) in perpendicular paths. At the instant when they are at the positions shown, the magnetic field the electron produces at the location of the proton.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION:...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.018310546875, 0.0172119140625, -0.01434326171875, 0.016357421875, -0.00836181640625, 0.02197265625, -0.029296875, -0.01165771484375, -0.0185546875, 0.01708984375, -0.0091552734375, 0.018310546875, -0.00885009765625, 0.00171661376953125, -0.00133514404296875, -0.007537841796875, -0....
960
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC5AOgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two parallel wires \( 5.00\,\text{cm} \) apart carry currents in opposite directions. Find the magnitude and direction of the magnetic field at point \( P \) due to two \ 1.50\,\text{mm} \) segments of wire that are opposite each other and each \( 8.00\,\text{cm} \) from \( P \).Please directly answer the question and ...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.018798828125, 0.01318359375, -0.01104736328125, 0.00982666015625, -0.0216064453125, 0.022216796875, -0.030517578125, -0.00811767578125, -0.025146484375, 0.006744384765625, -0.0201416015625, 0.031982421875, 0.01092529296875, 0.018310546875, -0.00159454345703125, 0.01202392578125, -0...
961
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADKAQMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A wire carrying a \( 28.0\,\text{A} \) current bends through a right angle. Consider two \( 2.00\,\text{mm} \) segments of wire, each \( 3.00\,\text{cm} \) from the bend. Find the magnitude of the magnetic field these two segments produce at point \( P \), which is midway between them.Please directly answer the questio...
B
Electromagnetism
Magnetism
['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning']
[ 0.01214599609375, 0.01031494140625, -0.0032196044921875, 0.000148773193359375, -0.021240234375, 0.0299072265625, -0.026611328125, -0.0027313232421875, -0.033203125, 0.0093994140625, -0.0262451171875, 0.047607421875, 0.00860595703125, 0.034423828125, 0.0179443359375, -0.0013275146484375...
962
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHTAXsDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A long wire carries a current of \( 8.00\,\text{A} \), and a uniform magnetic field of magnitude \( 1.50 \times 10^{-6}\,\text{T} \) is present in addition to the field from the wire. What is the total field (magnitude) at the following points in the \( xz \)-plane: \( x = 1.00\,\text{m}, z = 0 \)Please directly answer...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.01202392578125, 0.0101318359375, -0.005645751953125, -0.008056640625, -0.002960205078125, 0.0184326171875, -0.01153564453125, -0.00445556640625, -0.052001953125, 0.007415771484375, -0.040771484375, 0.036376953125, 0.006439208984375, 0.00135040283203125, 0.0184326171875, 0.00027275085...
963
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFKAYEDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two charges, \( q = 8.00\,\mu\text{C} \) and \( q' = -5.00\,\mu\text{C} \), move with speeds \( v = 9.00 \times 10^4\,\text{m/s} \) and \( v' = 6.50 \times 10^4\,\text{m/s} \) respectively. When the charges are at the positions shown, find the magnetic force that \( q' \) exerts on \( q \).Please directly answer the qu...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.030029296875, 0.004302978515625, -0.00007200241088867188, -0.0152587890625, -0.017333984375, 0.0198974609375, -0.00640869140625, -0.003204345703125, -0.020263671875, -0.0179443359375, -0.017578125, 0.03076171875, 0, -0.00555419921875, 0.0162353515625, 0.01300048828125, -0.033203125...
964
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEtARQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two long wires perpendicular to the \( xy \)-plane carry currents \( I \) in opposite directions. What is the magnitude of \( \vec{B} \) when \( x \gg a \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \frac{\mu_0 I}{2\pi x} B: \frac{\mu_0 I a}{\pi x^2} C: ...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0019683837890625, -0.001434326171875, -0.01019287109375, -0.01263427734375, -0.0037078857421875, 0.0201416015625, -0.015869140625, -0.0240478515625, -0.032958984375, 0.006988525390625, -0.04052734375, 0.040283203125, 0.0048828125, 0.0031890869140625, 0.02783203125, 0.001617431640625,...
965
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADxAZwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two long, parallel wires hang from a common axis, each with a linear mass density of \( 0.0125\,\text{kg/m} \) and carrying equal but opposite currents. What is the current in each wire if the cords hang at an angle of \( 6.00^\circ \) with the vertical?Please directly answer the question and provide the correct OPTION...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0196533203125, 0.00830078125, 0.006378173828125, -0.003387451171875, -0.005096435546875, 0.0279541015625, -0.0079345703125, 0.0012969970703125, -0.025634765625, -0.0113525390625, -0.034912109375, 0.033935546875, 0.00982666015625, 0.0216064453125, 0.029296875, 0.00433349609375, -0.0...
966
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE4ANcDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
The arc subtends an angle of \( 120^\circ \). Calculate the magnetic field (magnitude) at a point \( P \) due to a current \( I = 12.0\,\text{A} \) in the wire. Segment \( BC \) is an arc of a circle with radius \( 30.0\,\text{cm} \), and point \( P \) is at the center of curvature of the arc.Please directly answer the...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.0150146484375, -0.000614166259765625, -0.0264892578125, -0.020263671875, 0.00750732421875, 0.00579833984375, -0.0184326171875, -0.0218505859375, -0.0289306640625, -0.00014591217041015625, -0.03466796875, 0.0400390625, -0.004913330078125, 0.00081634521484375, 0.0196533203125, 0.003555...
967
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFtAWADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A cylindrical shell with radius \( R_1 \), height \( H \), and charge \( Q_1 \) rotates with angular speed \( \omega_1 \). A small charged disk of radius \( R_2 \), mass \( M \), and charge \( Q_2 \) spins with angular velocity \( \omega_2 \) at an angle \( \theta \) to the axis and precesses with angular velocity \( \...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ -0.00177001953125, 0.00066375732421875, -0.0186767578125, -0.010009765625, -0.0211181640625, 0.031982421875, -0.02099609375, -0.01397705078125, -0.044677734375, -0.002197265625, -0.0244140625, 0.044189453125, -0.0125732421875, 0.00176239013671875, 0.0155029296875, -0.0103759765625, -...
968
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACMANkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two long metal rods of length \( 0.50\text{m} \) lie parallel on a frictionless table, connected by springs of unstretched length \( l_0 \) and force constant \( k \). When current \( I \) flows, the springs stretch by \( x = 0.40\text{cm} \) at \( I = 8.05\text{A} \), and by \( x = 0.80\text{cm} \) at \( I = 13.1\text...
B
Electromagnetism
Magnetism
['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning']
[ 0.0155029296875, 0.0201416015625, -0.00396728515625, -0.027099609375, 0.004302978515625, 0.0164794921875, -0.010986328125, 0.0035247802734375, -0.0299072265625, -0.019287109375, -0.033935546875, 0.04150390625, 0.01171875, 0.018798828125, 0.01806640625, 0.01287841796875, 0.00099182128...
969
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGCAW0DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A cylindrical shell of radius \( R \), length \( W \), and total charge \( Q \) rotates about the \( x \)-axis with angular speed \( \omega \), and is centered at the origin \( O \). Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \frac{\mu_0}{2\pi} \cdot \fr...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ -0.0034027099609375, -0.011474609375, -0.0242919921875, 0.01141357421875, -0.0016021728515625, 0.016845703125, -0.02392578125, -0.01904296875, -0.03759765625, -0.004302978515625, -0.0206298828125, 0.0218505859375, -0.0010833740234375, 0.00067901611328125, 0.007232666015625, 0.010681152...
970
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGnAW4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A spherical shell with total mass \( M \) and charge \( Q \) rotates about the \( z \)-axis with angular speed \( \omega \), and its gyromagnetic ratio is \( \gamma = g\left(\frac{Q}{2M}\right) \). Determine the gyromagnetic ratio \( \gamma \).Please directly answer the question and provide the correct OPTION LETTER ON...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.00836181640625, -0.0172119140625, -0.034423828125, -0.0052490234375, -0.01300048828125, 0.0257568359375, -0.01708984375, -0.02392578125, -0.0303955078125, -0.01385498046875, -0.0126953125, 0.028076171875, -0.0263671875, 0.00531005859375, 0.016845703125, -0.0140380859375, -0.0020751...
971
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Two parallel wires of linear mass density \( \lambda \) are connected to a charged capacitor with initial charge \( Q_0 \), and each wire acquires an initial horizontal velocity \( v_0 \); assume the capacitor discharges instantaneously compared to the wire motion. To what height \( h \) will each wire rise as a result...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0260009765625, 0.002166748046875, -0.021484375, 0.005584716796875, -0.005096435546875, 0.00628662109375, -0.0098876953125, -0.0031585693359375, -0.0279541015625, 0.005523681640625, -0.038330078125, 0.0142822265625, -0.0189208984375, 0.024658203125, 0.0228271484375, -0.005035400390625...
972
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Blood contains positive and negative ions and thus behaves as a conductor. A blood vessel can be modeled as a wire, with blood represented as parallel conducting slabs of thickness \( d \) moving with speed \( v \) through a magnetic field \( \vec{B} \) directed into the page. If you expect that the blood will be flowi...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.033203125, 0.00958251953125, -0.01495361328125, 0.005401611328125, -0.0269775390625, 0.001556396484375, -0.00677490234375, -0.0037994384765625, -0.0203857421875, 0.017578125, -0.0264892578125, 0.023193359375, -0.013671875, -0.002349853515625, -0.00799560546875, 0.0031585693359375, ...
973
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADBAlYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A rectangular circuit with a 12.5\,\Omega\ resistor moves at a constant speed of 3.0\,\text{m/s} perpendicular to a 1.25\,\text{T} magnetic field that is wider than the 50.0\,\text{cm} width of the loop. Find the magnitude of the current induced in the circuit as it is going into the magnetic field.Please directly answ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.015869140625, 0.0126953125, -0.02783203125, -0.01324462890625, -0.0093994140625, 0.00147247314453125, -0.020263671875, -0.01123046875, -0.03173828125, 0.0208740234375, -0.037109375, 0.0201416015625, -0.0008392333984375, 0.0118408203125, 0.01251220703125, -0.0147705078125, -0.023559...
974
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADHARoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A capacitor with \( C = 20.0\mu\text{F} \) is initially charged to \( 100\text{V} \) and then discharges through a resistor \( R_0 = 10.0\Omega \) when the switch is closed at \( t = 0 \); a nearby rectangular loop with dimensions \( a = 10.0\text{cm} \), \( b = 20.0\text{cm} \), placed \( c = 5.0\text{cm} \) from the ...
B
Electromagnetism
Electric Circuits
['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning']
[ 0.0196533203125, 0.0064697265625, -0.002166748046875, -0.023193359375, -0.0194091796875, 0.01312255859375, -0.0036163330078125, 0.0164794921875, -0.037109375, -0.00982666015625, -0.0291748046875, 0.02001953125, 0.002410888671875, 0.01226806640625, 0.0296630859375, -0.00121307373046875,...
975
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC7ATUDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A cylindrical wire of radius \( R \) carries a uniformly distributed current \( I_0 \); calculate the magnetic flux through a rectangle of dimensions \( R \times W \) lying along the axis of the wire. Calculate the magnetic flux through a rectangle that has one side of length \( W \) running down the center of the wire...
B
Electromagnetism
Magnetism
['Physical Model Grounding Reasoning', 'Numerical Reasoning']
[ 0.00970458984375, -0.0004177093505859375, -0.01556396484375, -0.0213623046875, -0.001190185546875, -0.00421142578125, 0.00604248046875, -0.0177001953125, -0.04443359375, 0.00592041015625, -0.020751953125, 0.011474609375, -0.00165557861328125, 0.0026092529296875, 0.01470947265625, 0.005...
976
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADPASMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A bar of length \( L = 0.36\,\text{m} \) and resistance \( 5.0\,\Omega \) slides on frictionless rails in a uniform magnetic field \( B = 2.4\,\text{T} \); with \( \mathcal{E} = 12\,\text{V} \), mass \( 0.90\,\text{kg} \), and switch closed at \( t = 0 \), find the bar's subsequent motion. What is the bar's terminal sp...
B
Electromagnetism
Electromagnetic Induction
['Multi-Formula Reasoning', 'Predictive Reasoning']
[ 0.056396484375, 0.010009765625, -0.031005859375, 0.0032196044921875, 0.0023040771484375, -0.00830078125, -0.006439208984375, 0.000766754150390625, -0.036376953125, 0.0087890625, -0.037109375, 0.0252685546875, -0.000705718994140625, 0.005767822265625, 0.046630859375, 0.032958984375, -...
977
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACnATQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A rectangular loop with width \( L \) and negligible resistance contains a slidewire of resistance \( R \) and mass \( m \); it moves in a uniform magnetic field \( \vec{B} \) directed into the page with initial speed \( v_0 \), then is released to move freely. Show that the distance \( x \) that the wire moves before ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0272216796875, -0.006072998046875, -0.00958251953125, -0.001434326171875, -0.0027923583984375, 0.0057373046875, -0.00982666015625, -0.01318359375, -0.0247802734375, -0.01171875, -0.020751953125, 0.026123046875, -0.006195068359375, 0.00701904296875, 0.0196533203125, -0.0172119140625, ...
978
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAB7ATcDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A circular coil with \( N_1 = 5000 \) turns and radius \( a = 40.0\ \text{cm} \) is connected to a \( 10.00\ \mu\text{F} \) capacitor charged to \( +100\ \mu\text{C} \); a second coil with \( N_2 = 100 \) turns and radius \( b = 4.00\ \text{cm} \) is concentric and parallel to the first, and the switch is closed at \( ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.017822265625, -0.00726318359375, -0.0196533203125, -0.01202392578125, -0.01611328125, 0.0159912109375, -0.0020904541015625, -0.003509521484375, -0.0189208984375, -0.0076904296875, -0.025634765625, 0.032958984375, 0.0076904296875, 0.00555419921875, 0.012939453125, 0.0145263671875, -...
979
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADWARQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
A bar with mass \( M = 1.20\ \text{kg} \) and resistance \( R = 0.500\ \Omega \) slides on a U-shaped rail of width \( W = 40.0\ \text{cm} \), connected to a spring with \( k = 90.0\ \text{N/m} \); it is released from rest at \( x = 10.0\ \text{cm} \) in a \( 1.00\ \text{T} \) magnetic field directed into the page. Wha...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.01708984375, 0.00396728515625, -0.00592041015625, -0.007568359375, 0.00726318359375, 0.0179443359375, -0.01446533203125, 0.005523681640625, -0.032470703125, -0.005584716796875, -0.018310546875, 0.0179443359375, -0.0177001953125, 0.01068115234375, 0.02099609375, 0.00634765625, -0.01...
980
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A coil with 4 turns, radius \( 0.800\ \text{cm} \), and resistance \( 0.250\ \Omega \) is placed between the poles of an electromagnet whose field increases from zero at \( t = 0 \); the current \( i \) induced in the coil as a function of time \( t \) is shown. Calculate the magnetic field at the location of the coil ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0252685546875, 0.01171875, -0.01171875, 0.0091552734375, -0.01422119140625, -0.0086669921875, -0.0191650390625, -0.0036468505859375, -0.02783203125, -0.01141357421875, -0.053955078125, 0.0244140625, 0.003265380859375, -0.0147705078125, 0.020751953125, -0.0031280517578125, -0.039306...
981
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A metal bar with length \( L \), mass \( m \), and resistance \( R \) slides down frictionless inclined rails at angle \( \phi \) in a downward magnetic field \( \vec{B} \); the rails have negligible resistance. After the terminal speed has been reached, at what rate is electrical energy being converted to thermal ener...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0269775390625, -0.0186767578125, -0.006500244140625, -0.004669189453125, 0.007598876953125, 0.00714111328125, -0.00052642822265625, -0.018798828125, -0.0223388671875, -0.0038909912109375, -0.0277099609375, 0.03125, -0.000125885009765625, 0.0191650390625, 0.050048828125, -0.0033569335...
982
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A conducting spherical shell rotates in a vertical magnetic field at 2\,\text{Hz}; two radial rods connect through a 10.0\,\Omega resistor to form a circuit. What is the magnitude of the current in the wire?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.47...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.0087890625, -0.00738525390625, -0.006988525390625, -0.0189208984375, -0.008544921875, 0.02099609375, -0.022216796875, -0.02099609375, -0.02587890625, -0.00701904296875, -0.0186767578125, 0.03271484375, 0.0054931640625, 0.0106201171875, 0.01312255859375, -0.0074462890625, -0.0246582...
983
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A rectangular loop of resistance \( R \), width \( a \), and length \( b \) lies along the axis of a cylinder where the electric field increases as \( \vec{E} = \eta t^2 \hat{k} \). At time \( t = 5.00 \text{ s} \), what is the direction of the induced current as viewed from above?Please directly answer the question an...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.01031494140625, -0.003997802734375, -0.006622314453125, -0.01324462890625, -0.013671875, 0.009765625, -0.0181884765625, -0.000492095947265625, -0.045166015625, 0.0174560546875, -0.018310546875, 0.00823974609375, 0.00154876708984375, -0.0008544921875, 0.01513671875, 0.0009346008300781...
984
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An inductor of inductance \( L = 0.300\,\text{H} \) is connected in a circuit with \( R_1 = 12.0\,\Omega \), \( R_2 = 16.0\,\Omega \), and a \( 96.0\,\text{V} \) battery; the switch \( S \) is closed at \( t = 0 \). When \( i_3 \) has half of its final value, what are \( i_2 \)?Please directly answer the question and p...
B
Electromagnetism
Electric Circuits
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.036865234375, -0.0029144287109375, -0.0228271484375, -0.0206298828125, -0.01324462890625, 0.019775390625, -0.008056640625, 0.01422119140625, -0.045166015625, -0.0101318359375, -0.04931640625, 0.010498046875, 0.015380859375, -0.00018596649169921875, 0.020751953125, 0.0281982421875, ...
985
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACJAPIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
An inductor of inductance \( L = 0.200\,\text{H} \) is connected in a circuit with \( R_1 = 8.00\,\Omega \), \( R_2 = 6.00\,\Omega \), and a \( 48.0\,\text{V} \) battery; the switch \( S \) is closed at \( t = 0 \). When \( i_3 \) has half of its final value, what is \( i_1 \)?sPlease directly answer the question and p...
B
Electromagnetism
Electric Circuits
['Multi-Formula Reasoning', 'Numerical Reasoning']
[ 0.0130615234375, -0.00482177734375, 0.00016021728515625, -0.0289306640625, 0.0078125, 0.0174560546875, -0.0179443359375, -0.00124359130859375, -0.033203125, -0.021484375, -0.040283203125, 0.032470703125, -0.000606536865234375, -0.0086669921875, 0.0242919921875, 0.009765625, -0.033447...
986
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In the circuit, the switch \( S \) has been open for a long time and is suddenly closed. The battery and inductors have negligible resistance. The voltmeter reads a value 0.115\,\text{ms} after \( S \) is closed. What does the voltmeter read 0.115 ms after \( S \) is closed?Please directly answer the question and provi...
B
Electromagnetism
Electric Circuits
['Physical Model Grounding Reasoning', 'Numerical Reasoning']
[ 0.040283203125, 0.005401611328125, -0.0115966796875, -0.031005859375, -0.00921630859375, 0.024169921875, -0.01470947265625, 0.0184326171875, -0.031494140625, 0.0020294189453125, -0.0194091796875, 0.0211181640625, 0.01171875, 0.00860595703125, 0.0211181640625, 0.00311279296875, -0.021...
987
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In the circuit, switch \( S_1 \) has been closed for a long enough time so that the current reads a steady 3.50 A. Suddenly, switch \( S_2 \) is closed and \( S_1 \) is opened at the same instant. What is the maximum charge that the capacitor will receive?Please directly answer the question and provide the correct OPTI...
B
Electromagnetism
Electric Circuits
['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning']
[ 0.03369140625, 0.006195068359375, -0.0189208984375, -0.026611328125, -0.0166015625, 0.01171875, -0.0123291015625, 0.004730224609375, -0.01953125, 0.004852294921875, -0.0238037109375, 0.029052734375, -0.005523681640625, 0.0159912109375, 0.00933837890625, -0.016357421875, -0.0302734375...
988
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During a summer internship as an electronics technician, you are asked to measure the self-inductance \( L \) of a solenoid. You connect the solenoid in series with a 10.0 \( \Omega \) resistor, a battery that has negligible internal resistance, and a switch. Using an ideal voltmeter, you measure and digitally record t...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.037841796875, 0.01226806640625, -0.0255126953125, -0.000637054443359375, 0.0118408203125, 0.0201416015625, -0.026611328125, -0.0030059814453125, -0.035888671875, -0.00130462646484375, -0.0361328125, 0.0269775390625, 0.01348876953125, -0.006256103515625, -0.00007534027099609375, 0.003...
989
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A solenoid of unknown resistance and inductance is connected in series with a \( 50.0\ \Omega \) resistor, a battery with negligible internal resistance, and a switch. Using an ideal voltmeter, the voltage \( v_R \) across the resistor is recorded as a function of time \( t \) after the switch is closed. Your measured ...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Numerical Reasoning']
[ 0.0234375, -0.0037384033203125, 0.0009002685546875, -0.0126953125, -0.01385498046875, 0.01092529296875, -0.01129150390625, 0.0033416748046875, -0.02587890625, 0.019287109375, -0.0390625, 0.013671875, 0.0003147125244140625, 0.004791259765625, 0.0015411376953125, -0.00537109375, -0.023...
990
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At the far end, the outer solenoid is attached to the inner solenoid by a wire, so that current flows down the outer coil and then back through the inner coil as shown. What would be the inductannce if the sense of the inner coil were reversed?Please directly answer the question and provide the correct OPTION LETTER ON...
B
Electromagnetism
Electromagnetic Induction
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.025634765625, 0.035888671875, -0.036865234375, -0.0013885498046875, -0.00897216796875, 0.0203857421875, -0.02197265625, 0.0019073486328125, -0.03759765625, -0.0030517578125, -0.026611328125, 0.0166015625, 0.01446533203125, 0.00885009765625, -0.0010833740234375, 0.003173828125, -0.0...
991
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Consider the circuit shown in figure. Switch \( S \) is closed at time \( t = 0 \), causing a current \( i_1 \) through the inductive branch and a current \( i_2 \) through the capacitive branch. The initial charge on the capacitor is zero, and the charge at time \( t \) is \( q_2 \). The total current through the batt...
B
Electromagnetism
Electric Circuits
['Physical Model Grounding Reasoning', 'Numerical Reasoning']
[ 0.02490234375, 0.009521484375, -0.022705078125, 0.00799560546875, 0.010009765625, 0.0206298828125, -0.02978515625, -0.0040283203125, -0.01123046875, 0.0245361328125, -0.038330078125, 0.02001953125, -0.01434326171875, 0.0033721923828125, 0.0284423828125, 0.011474609375, -0.00933837890...
992
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEUAW8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Two point charges, \( q_1 = +25\,\text{nC} \) and \( q_2 = -75\,\text{nC} \), are separated by a distance \( r = 3.0\,\text{cm} \). Find the magnitude of the electric force that \( q_1 \) exerts on \( q_2 \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.6...
B
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning']
[ 0.03466796875, 0.016357421875, -0.01611328125, -0.01239013671875, -0.00665283203125, 0.0257568359375, -0.0247802734375, -0.0164794921875, -0.029296875, 0.00811767578125, -0.012451171875, 0.0400390625, -0.0120849609375, 0.002197265625, 0.00201416015625, -0.00787353515625, -0.015136718...
993
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF8Ay8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
When the terminals of a battery are connected to two parallel conducting plates with a small gap between them, the resulting charges on the plates produce a nearly uniform electric field between the plates. If the plates are connected to a battery as shown, the field is vertically upward and has magnitude \( 1.00 \time...
B
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning']
[ 0.02294921875, 0.0087890625, -0.00836181640625, -0.003448486328125, -0.008544921875, 0.026611328125, -0.007354736328125, -0.009765625, -0.0166015625, 0.01263427734375, -0.01092529296875, 0.01263427734375, -0.0238037109375, -0.0004215240478515625, 0.007476806640625, -0.007568359375, -...
994
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Point charges \( q_1 \) and \( q_2 \) are separated by a certain distance. (Such pairs of point charges with equal magnitude and opposite sign are called \textit{electric dipoles}.) Compute the total field at point \( c \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D....
B
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
[ 0.034423828125, 0.01458740234375, -0.0159912109375, -0.01495361328125, -0.01348876953125, 0.0245361328125, -0.01470947265625, -0.0023040771484375, -0.03662109375, -0.0040283203125, -0.0213623046875, 0.0189208984375, -0.0045166015625, -0.006072998046875, 0.020263671875, 0.0179443359375,...
995
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGiAyUDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh...
Charge \( Q \) is uniformly distributed around a conducting ring of radius \( a \). Find the electric field at a point \( P \) on the ring axis at a distance \( x \) from its center.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \frac{1}{4\pi\varepsilon_0} \...
B
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
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996
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Figure shows an electric dipole in a uniform electric field of magnitude \( 5.0 \times 10^5\,\text{N/C} \) that is directed parallel to the plane of the figure. The charges are \( \pm 1.6 \times 10^{-19}\,\text{C} \); both lie in the plane and are separated by \( 0.125\,\text{m} \). Find the magnitude of the torque.Ple...
B
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
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997
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An electric dipole is centered at the origin, with \( \vec{p} \) in the direction of the \( +y \)-axis. Derive an approximate expression for the electric field at a point \( P \) on the \( y \)-axis for which \( y \) is much larger than \( d \). To do this, use the binomial expansion \( (1 + x)^n \approx 1 + nx + n(n -...
B
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Numerical Reasoning']
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998
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A disk is oriented with its normal unit vector \( \hat{n} \) at an angle to a uniform electric field \( \vec{E} \). (Since this isn't a closed surface, it has no “inside” or “outside.” That's why we have to specify the direction of \( \hat{n} \) in the figure.) What is the electric flux through the disk?Please directly...
B
Electromagnetism
Electrostatics
['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning']
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999
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An imaginary cubical surface of side \( L \) is in a region of uniform electric field \( E \). Find the electric flux through each face of the cube and the total flux through the cube when the cube is turned by an angle \( heta \) about a vertical axis.Please directly answer the question and provide the correct OPTION...
B
Electromagnetism
Electrostatics
['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning']
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