id int64 1 14M | domain stringclasses 6
values | topic stringclasses 23
values | subtopic stringclasses 37
values | difficulty int64 1 8 | unit_type stringclasses 3
values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
values | learning_objective stringclasses 37
values |
|---|---|---|---|---|---|---|---|---|---|---|
2,301 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.1165e-04 C and 5.5271e-05 C separated by 0.5361 m | Two point charges q1 = -2.1165e-04 C and q2 = 5.5271e-05 C are separated by distance r = 0.5361 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 365.8 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,302 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.3471e-05 C and 3.9935e-04 C separated by 0.6097 m | Two point charges q1 = -5.3471e-05 C and q2 = 3.9935e-04 C are separated by distance r = 0.6097 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 516.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,303 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.8042e-04 C and 4.7511e-04 C separated by 0.2988 m | Two point charges q1 = -3.8042e-04 C and q2 = 4.7511e-04 C are separated by distance r = 0.2988 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.8189e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,304 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.2851e-05 C and 3.8262e-04 C separated by 0.6382 m | Two point charges q1 = 1.2851e-05 C and q2 = 3.8262e-04 C are separated by distance r = 0.6382 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 108.5 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,305 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.8267e-05 C and 9.5623e-04 C separated by 0.8693 m | Two point charges q1 = -9.8267e-05 C and q2 = 9.5623e-04 C are separated by distance r = 0.8693 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1118 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,306 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.3563e-04 C and 8.0251e-04 C separated by 0.5181 m | Two point charges q1 = 3.3563e-04 C and q2 = 8.0251e-04 C are separated by distance r = 0.5181 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9017 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,307 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.6165e-04 C and -7.3458e-04 C separated by 1.182 m | Two point charges q1 = 4.6165e-04 C and q2 = -7.3458e-04 C are separated by distance r = 1.182 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2183 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,308 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.2043e-04 C and -3.1396e-04 C separated by 0.03105 m | Two point charges q1 = -5.2043e-04 C and q2 = -3.1396e-04 C are separated by distance r = 0.03105 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.5232e+06 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,309 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.3186e-04 C and -4.1184e-04 C separated by 1.055 m | Two point charges q1 = -8.3186e-04 C and q2 = -4.1184e-04 C are separated by distance r = 1.055 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2765 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,310 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.5216e-04 C and 2.5264e-04 C separated by 0.07774 m | Two point charges q1 = 3.5216e-04 C and q2 = 2.5264e-04 C are separated by distance r = 0.07774 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.3230e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,311 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.7825e-05 C and -9.5054e-04 C separated by 1.28 m | Two point charges q1 = -5.7825e-05 C and q2 = -9.5054e-04 C are separated by distance r = 1.28 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 301.6 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,312 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.7300e-05 C and -3.7658e-04 C separated by 1.53 m | Two point charges q1 = -8.7300e-05 C and q2 = -3.7658e-04 C are separated by distance r = 1.53 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 126.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,313 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.9611e-04 C and -2.5408e-04 C separated by 0.9392 m | Two point charges q1 = -8.9611e-04 C and q2 = -2.5408e-04 C are separated by distance r = 0.9392 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2320 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,314 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.3914e-04 C and 7.6959e-04 C separated by 1.388 m | Two point charges q1 = -6.3914e-04 C and q2 = 7.6959e-04 C are separated by distance r = 1.388 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2296 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,315 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.5808e-04 C and -2.7801e-04 C separated by 0.1342 m | Two point charges q1 = 2.5808e-04 C and q2 = -2.7801e-04 C are separated by distance r = 0.1342 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.5832e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,316 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.3332e-04 C and -2.5898e-04 C separated by 1.627 m | Two point charges q1 = 3.3332e-04 C and q2 = -2.5898e-04 C are separated by distance r = 1.627 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 292.9 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,317 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.4113e-04 C and 9.7944e-04 C separated by 0.4093 m | Two point charges q1 = -4.4113e-04 C and q2 = 9.7944e-04 C are separated by distance r = 0.4093 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.3176e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,318 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.7926e-04 C and 1.0932e-04 C separated by 1.086 m | Two point charges q1 = 1.7926e-04 C and q2 = 1.0932e-04 C are separated by distance r = 1.086 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 149.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,319 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.1917e-04 C and -9.1270e-04 C separated by 1.434 m | Two point charges q1 = 2.1917e-04 C and q2 = -9.1270e-04 C are separated by distance r = 1.434 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 874.7 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,320 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.5826e-05 C and -5.7177e-04 C separated by 0.5087 m | Two point charges q1 = -3.5826e-05 C and q2 = -5.7177e-04 C are separated by distance r = 0.5087 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 711.5 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,321 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.9746e-05 C and 1.4971e-04 C separated by 1.284 m | Two point charges q1 = 1.9746e-05 C and q2 = 1.4971e-04 C are separated by distance r = 1.284 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 16.11 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,322 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.6494e-04 C and 1.5246e-04 C separated by 0.6664 m | Two point charges q1 = -6.6494e-04 C and q2 = 1.5246e-04 C are separated by distance r = 0.6664 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2052 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,323 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.7507e-04 C and 4.7866e-04 C separated by 0.8138 m | Two point charges q1 = 5.7507e-04 C and q2 = 4.7866e-04 C are separated by distance r = 0.8138 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3736 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,324 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.4059e-04 C and -3.8504e-04 C separated by 1.382 m | Two point charges q1 = -5.4059e-04 C and q2 = -3.8504e-04 C are separated by distance r = 1.382 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 980 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,325 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.2208e-04 C and 3.3411e-04 C separated by 0.6126 m | Two point charges q1 = 1.2208e-04 C and q2 = 3.3411e-04 C are separated by distance r = 0.6126 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 976.8 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,326 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.3264e-04 C and -3.6599e-04 C separated by 1.708 m | Two point charges q1 = -6.3264e-04 C and q2 = -3.6599e-04 C are separated by distance r = 1.708 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 713.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,327 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.1376e-05 C and 7.6069e-04 C separated by 0.587 m | Two point charges q1 = 8.1376e-05 C and q2 = 7.6069e-04 C are separated by distance r = 0.587 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1615 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,328 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.7744e-04 C and -9.6755e-04 C separated by 1.325 m | Two point charges q1 = -1.7744e-04 C and q2 = -9.6755e-04 C are separated by distance r = 1.325 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 879.1 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,329 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.9619e-04 C and -6.3099e-04 C separated by 0.7249 m | Two point charges q1 = 6.9619e-04 C and q2 = -6.3099e-04 C are separated by distance r = 0.7249 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7513 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,330 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.8533e-04 C and 7.3559e-04 C separated by 0.2885 m | Two point charges q1 = -8.8533e-04 C and q2 = 7.3559e-04 C are separated by distance r = 0.2885 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7.0328e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,331 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.6339e-05 C and -4.8974e-04 C separated by 0.1354 m | Two point charges q1 = -2.6339e-05 C and q2 = -4.8974e-04 C are separated by distance r = 0.1354 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6328 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,332 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.0018e-04 C and 9.6661e-04 C separated by 0.04267 m | Two point charges q1 = 5.0018e-04 C and q2 = 9.6661e-04 C are separated by distance r = 0.04267 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.3863e+06 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,333 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.6998e-05 C and -4.0610e-04 C separated by 0.4312 m | Two point charges q1 = 5.6998e-05 C and q2 = -4.0610e-04 C are separated by distance r = 0.4312 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1119 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,334 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.4015e-04 C and -7.4131e-04 C separated by 0.4736 m | Two point charges q1 = 9.4015e-04 C and q2 = -7.4131e-04 C are separated by distance r = 0.4736 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.7922e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,335 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.7841e-05 C and -4.8941e-04 C separated by 0.04794 m | Two point charges q1 = -3.7841e-05 C and q2 = -4.8941e-04 C are separated by distance r = 0.04794 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7.2437e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,336 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.4344e-04 C and -1.5351e-05 C separated by 1.269 m | Two point charges q1 = -2.4344e-04 C and q2 = -1.5351e-05 C are separated by distance r = 1.269 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 20.86 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,337 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.2092e-04 C and -4.5673e-04 C separated by 0.3497 m | Two point charges q1 = 8.2092e-04 C and q2 = -4.5673e-04 C are separated by distance r = 0.3497 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.7560e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,338 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.1798e-04 C and -1.1507e-04 C separated by 1.194 m | Two point charges q1 = -8.1798e-04 C and q2 = -1.1507e-04 C are separated by distance r = 1.194 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 593.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,339 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.4047e-05 C and -4.2679e-04 C separated by 1.625 m | Two point charges q1 = -6.4047e-05 C and q2 = -4.2679e-04 C are separated by distance r = 1.625 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 93.04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,340 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.2491e-04 C and -3.2227e-04 C separated by 1.93 m | Two point charges q1 = 3.2491e-04 C and q2 = -3.2227e-04 C are separated by distance r = 1.93 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 252.7 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,341 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.6446e-04 C and -3.3617e-04 C separated by 0.2503 m | Two point charges q1 = -7.6446e-04 C and q2 = -3.3617e-04 C are separated by distance r = 0.2503 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.6871e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,342 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.5779e-04 C and -6.9660e-04 C separated by 1.111 m | Two point charges q1 = -7.5779e-04 C and q2 = -6.9660e-04 C are separated by distance r = 1.111 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3842 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,343 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.4440e-04 C and -1.3424e-04 C separated by 1.584 m | Two point charges q1 = 2.4440e-04 C and q2 = -1.3424e-04 C are separated by distance r = 1.584 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 117.5 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,344 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.7788e-04 C and -8.7975e-04 C separated by 0.1706 m | Two point charges q1 = 7.7788e-04 C and q2 = -8.7975e-04 C are separated by distance r = 0.1706 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.1123e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,345 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.8023e-04 C and -7.0703e-04 C separated by 1.192 m | Two point charges q1 = -1.8023e-04 C and q2 = -7.0703e-04 C are separated by distance r = 1.192 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 806.7 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,346 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.1681e-04 C and 6.9267e-04 C separated by 0.4203 m | Two point charges q1 = 4.1681e-04 C and q2 = 6.9267e-04 C are separated by distance r = 0.4203 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.4691e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,347 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.2356e-04 C and 2.4001e-04 C separated by 0.3574 m | Two point charges q1 = 5.2356e-04 C and q2 = 2.4001e-04 C are separated by distance r = 0.3574 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8844 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,348 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.9668e-04 C and 6.1244e-04 C separated by 0.1852 m | Two point charges q1 = -5.9668e-04 C and q2 = 6.1244e-04 C are separated by distance r = 0.1852 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9.5794e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,349 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.4851e-04 C and -5.5815e-04 C separated by 0.3919 m | Two point charges q1 = 3.4851e-04 C and q2 = -5.5815e-04 C are separated by distance r = 0.3919 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.1384e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,350 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.1930e-04 C and -4.6475e-04 C separated by 1.257 m | Two point charges q1 = -6.1930e-04 C and q2 = -4.6475e-04 C are separated by distance r = 1.257 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1638 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,351 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.7715e-04 C and -1.1357e-04 C separated by 0.3069 m | Two point charges q1 = -2.7715e-04 C and q2 = -1.1357e-04 C are separated by distance r = 0.3069 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3003 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,352 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.9802e-04 C and -6.7047e-04 C separated by 0.0958 m | Two point charges q1 = 4.9802e-04 C and q2 = -6.7047e-04 C are separated by distance r = 0.0958 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.2699e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,353 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.8578e-04 C and 2.5213e-04 C separated by 1.237 m | Two point charges q1 = 2.8578e-04 C and q2 = 2.5213e-04 C are separated by distance r = 1.237 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 422.9 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,354 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.4274e-05 C and -9.2494e-04 C separated by 0.36 m | Two point charges q1 = 4.4274e-05 C and q2 = -9.2494e-04 C are separated by distance r = 0.36 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2840 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,355 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.8558e-04 C and -7.1789e-05 C separated by 0.4782 m | Two point charges q1 = -4.8558e-04 C and q2 = -7.1789e-05 C are separated by distance r = 0.4782 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1370 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,356 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.9311e-04 C and 4.1965e-04 C separated by 1.497 m | Two point charges q1 = 5.9311e-04 C and q2 = 4.1965e-04 C are separated by distance r = 1.497 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 998.6 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,357 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.3083e-04 C and -3.2681e-04 C separated by 0.2051 m | Two point charges q1 = 2.3083e-04 C and q2 = -3.2681e-04 C are separated by distance r = 0.2051 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.6110e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,358 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.7002e-04 C and 8.9147e-04 C separated by 0.1563 m | Two point charges q1 = 8.7002e-04 C and q2 = 8.9147e-04 C are separated by distance r = 0.1563 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.8525e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,359 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.5285e-05 C and 1.4580e-04 C separated by 1.856 m | Two point charges q1 = 5.5285e-05 C and q2 = 1.4580e-04 C are separated by distance r = 1.856 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 21.02 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,360 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.7888e-04 C and 1.3727e-04 C separated by 1.442 m | Two point charges q1 = 1.7888e-04 C and q2 = 1.3727e-04 C are separated by distance r = 1.442 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 106.1 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,361 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.7558e-04 C and -3.3656e-04 C separated by 0.07387 m | Two point charges q1 = 9.7558e-04 C and q2 = -3.3656e-04 C are separated by distance r = 0.07387 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5.4081e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,362 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.8132e-04 C and -8.5180e-04 C separated by 0.9226 m | Two point charges q1 = -2.8132e-04 C and q2 = -8.5180e-04 C are separated by distance r = 0.9226 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2530 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,363 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.6058e-04 C and -8.8652e-04 C separated by 1.211 m | Two point charges q1 = -7.6058e-04 C and q2 = -8.8652e-04 C are separated by distance r = 1.211 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4131 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,364 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.7854e-04 C and -8.7388e-05 C separated by 1.715 m | Two point charges q1 = -5.7854e-04 C and q2 = -8.7388e-05 C are separated by distance r = 1.715 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 154.4 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,365 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.6234e-04 C and -5.9199e-04 C separated by 1.676 m | Two point charges q1 = 8.6234e-04 C and q2 = -5.9199e-04 C are separated by distance r = 1.676 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1634 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,366 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.5489e-05 C and 7.3644e-04 C separated by 0.5008 m | Two point charges q1 = 1.5489e-05 C and q2 = 7.3644e-04 C are separated by distance r = 0.5008 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 408.7 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,367 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.3481e-04 C and -8.9193e-04 C separated by 1.188 m | Two point charges q1 = 4.3481e-04 C and q2 = -8.9193e-04 C are separated by distance r = 1.188 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2471 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,368 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.1384e-04 C and -4.1835e-04 C separated by 0.09801 m | Two point charges q1 = -9.1384e-04 C and q2 = -4.1835e-04 C are separated by distance r = 0.09801 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.5773e+05 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,369 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.3374e-04 C and -4.2627e-04 C separated by 0.7947 m | Two point charges q1 = 7.3374e-04 C and q2 = -4.2627e-04 C are separated by distance r = 0.7947 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4451 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,370 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.5299e-04 C and -8.4008e-05 C separated by 1.509 m | Two point charges q1 = -4.5299e-04 C and q2 = -8.4008e-05 C are separated by distance r = 1.509 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 150.3 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,371 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.4998e-04 C and -3.5905e-04 C separated by 0.4857 m | Two point charges q1 = 9.4998e-04 C and q2 = -3.5905e-04 C are separated by distance r = 0.4857 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.2993e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,372 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.6914e-05 C and 1.6264e-04 C separated by 0.924 m | Two point charges q1 = -1.6914e-05 C and q2 = 1.6264e-04 C are separated by distance r = 0.924 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 28.96 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,373 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.7644e-04 C and 7.7206e-04 C separated by 1.75 m | Two point charges q1 = -9.7644e-04 C and q2 = 7.7206e-04 C are separated by distance r = 1.75 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2213 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,374 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.8576e-04 C and 6.2718e-04 C separated by 1.411 m | Two point charges q1 = 1.8576e-04 C and q2 = 6.2718e-04 C are separated by distance r = 1.411 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 526.1 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,375 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.6052e-04 C and -3.8549e-04 C separated by 1.385 m | Two point charges q1 = -8.6052e-04 C and q2 = -3.8549e-04 C are separated by distance r = 1.385 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1555 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,376 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.9729e-04 C and 6.9836e-04 C separated by 1.229 m | Two point charges q1 = -2.9729e-04 C and q2 = 6.9836e-04 C are separated by distance r = 1.229 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1236 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,377 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.8790e-04 C and -6.2083e-04 C separated by 0.678 m | Two point charges q1 = -7.8790e-04 C and q2 = -6.2083e-04 C are separated by distance r = 0.678 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9563 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,378 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.1522e-04 C and 8.8809e-04 C separated by 0.2308 m | Two point charges q1 = -5.1522e-04 C and q2 = 8.8809e-04 C are separated by distance r = 0.2308 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7.7185e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,379 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.6589e-04 C and -3.6621e-04 C separated by 0.3588 m | Two point charges q1 = 4.6589e-04 C and q2 = -3.6621e-04 C are separated by distance r = 0.3588 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.1912e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,380 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.6120e-04 C and -1.3927e-04 C separated by 0.6765 m | Two point charges q1 = -5.6120e-04 C and q2 = -1.3927e-04 C are separated by distance r = 0.6765 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1535 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,381 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.4939e-04 C and -7.5342e-04 C separated by 1.524 m | Two point charges q1 = -6.4939e-04 C and q2 = -7.5342e-04 C are separated by distance r = 1.524 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1893 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,382 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.5336e-04 C and 5.0406e-04 C separated by 0.8516 m | Two point charges q1 = 3.5336e-04 C and q2 = 5.0406e-04 C are separated by distance r = 0.8516 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2207 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,383 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.4306e-05 C and 4.5296e-04 C separated by 1.008 m | Two point charges q1 = -6.4306e-05 C and q2 = 4.5296e-04 C are separated by distance r = 1.008 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 257.7 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,384 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.7069e-04 C and 4.5253e-04 C separated by 0.7426 m | Two point charges q1 = -4.7069e-04 C and q2 = 4.5253e-04 C are separated by distance r = 0.7426 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3471 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,385 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.8917e-04 C and 8.8221e-05 C separated by 0.7875 m | Two point charges q1 = -1.8917e-04 C and q2 = 8.8221e-05 C are separated by distance r = 0.7875 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 241.9 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,386 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.8908e-04 C and -1.1026e-04 C separated by 0.5591 m | Two point charges q1 = -2.8908e-04 C and q2 = -1.1026e-04 C are separated by distance r = 0.5591 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 916.3 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,387 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.9683e-04 C and -5.2117e-04 C separated by 1.258 m | Two point charges q1 = -4.9683e-04 C and q2 = -5.2117e-04 C are separated by distance r = 1.258 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1470 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,388 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.1712e-04 C and -4.7443e-04 C separated by 0.8461 m | Two point charges q1 = 4.1712e-04 C and q2 = -4.7443e-04 C are separated by distance r = 0.8461 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2485 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,389 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.9223e-04 C and -2.3015e-05 C separated by 1.606 m | Two point charges q1 = -2.9223e-04 C and q2 = -2.3015e-05 C are separated by distance r = 1.606 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 23.44 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,390 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.1228e-04 C and 6.5610e-04 C separated by 1.576 m | Two point charges q1 = 4.1228e-04 C and q2 = 6.5610e-04 C are separated by distance r = 1.576 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 979.1 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,391 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.9376e-04 C and 4.5855e-04 C separated by 1.139 m | Two point charges q1 = 5.9376e-04 C and q2 = 4.5855e-04 C are separated by distance r = 1.139 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1887 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,392 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.7257e-04 C and 2.2756e-04 C separated by 0.7501 m | Two point charges q1 = 1.7257e-04 C and q2 = 2.2756e-04 C are separated by distance r = 0.7501 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 627.3 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,393 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5777 Hz, speed 1315 m/s | A periodic wave travels at speed v = 1315 m/s with frequency f = 5777 Hz. The wavelength is λ = v / f = 0.2276 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
2,394 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2984 Hz, speed 641.3 m/s | A periodic wave travels at speed v = 641.3 m/s with frequency f = 2984 Hz. The wavelength is λ = v / f = 0.2149 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
2,395 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9125e+04 Hz, speed 1042 m/s | A periodic wave travels at speed v = 1042 m/s with frequency f = 1.9125e+04 Hz. The wavelength is λ = v / f = 0.0545 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
2,396 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3233 Hz, speed 942.4 m/s | A periodic wave travels at speed v = 942.4 m/s with frequency f = 3233 Hz. The wavelength is λ = v / f = 0.2915 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
2,397 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3662 Hz, speed 510.4 m/s | A periodic wave travels at speed v = 510.4 m/s with frequency f = 3662 Hz. The wavelength is λ = v / f = 0.1394 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
2,398 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4168e+04 Hz, speed 1386 m/s | A periodic wave travels at speed v = 1386 m/s with frequency f = 1.4168e+04 Hz. The wavelength is λ = v / f = 0.0978 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
2,399 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5893e+04 Hz, speed 493.5 m/s | A periodic wave travels at speed v = 493.5 m/s with frequency f = 1.5893e+04 Hz. The wavelength is λ = v / f = 0.03105 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
2,400 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2356 Hz, speed 1493 m/s | A periodic wave travels at speed v = 1493 m/s with frequency f = 2356 Hz. The wavelength is λ = v / f = 0.6335 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.