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 |
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7,501 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 23.09 m, speed 11.42 m/s | An object moves in a circle of radius 23.09 m at constant speed 11.42 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.644 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
7,502 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.05 m, speed 35.72 m/s | An object moves in a circle of radius 34.05 m at constant speed 35.72 m/s. The centripetal acceleration has magnitude a_c = v² / r = 37.48 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
7,503 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 24.95 m, speed 5.385 m/s | An object moves in a circle of radius 24.95 m at constant speed 5.385 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1.162 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
7,504 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.4317e-04 C and -8.6982e-04 C separated by 1.868 m | Two point charges q1 = -6.4317e-04 C and q2 = -8.6982e-04 C are separated by distance r = 1.868 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1441 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. |
7,505 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.9181e-04 C and 7.9684e-04 C separated by 1.752 m | Two point charges q1 = -6.9181e-04 C and q2 = 7.9684e-04 C are separated by distance r = 1.752 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1614 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. |
7,506 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.2334e-04 C and 4.6334e-04 C separated by 0.2728 m | Two point charges q1 = -2.2334e-04 C and q2 = 4.6334e-04 C are separated by distance r = 0.2728 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.2498e+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. |
7,507 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.0090e-04 C and 4.0733e-04 C separated by 0.398 m | Two point charges q1 = 4.0090e-04 C and q2 = 4.0733e-04 C are separated by distance r = 0.398 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9265 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. |
7,508 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.1236e-04 C and -6.4606e-04 C separated by 0.1028 m | Two point charges q1 = -1.1236e-04 C and q2 = -6.4606e-04 C are separated by distance r = 0.1028 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6.1719e+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. |
7,509 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.1548e-04 C and 9.3250e-04 C separated by 0.1351 m | Two point charges q1 = 8.1548e-04 C and q2 = 9.3250e-04 C are separated by distance r = 0.1351 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.7425e+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. |
7,510 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.2616e-04 C and -3.7330e-05 C separated by 1.842 m | Two point charges q1 = 3.2616e-04 C and q2 = -3.7330e-05 C are separated by distance r = 1.842 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 32.24 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. |
7,511 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.5648e-04 C and -7.2976e-04 C separated by 0.1408 m | Two point charges q1 = 8.5648e-04 C and q2 = -7.2976e-04 C are separated by distance r = 0.1408 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.8348e+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. |
7,512 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.2047e-04 C and -1.2080e-04 C separated by 0.06267 m | Two point charges q1 = -3.2047e-04 C and q2 = -1.2080e-04 C are separated by distance r = 0.06267 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8.8571e+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. |
7,513 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.2748e-04 C and -7.6947e-04 C separated by 0.4431 m | Two point charges q1 = 2.2748e-04 C and q2 = -7.6947e-04 C are separated by distance r = 0.4431 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8014 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. |
7,514 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.2956e-04 C and -4.9488e-04 C separated by 0.3373 m | Two point charges q1 = 5.2956e-04 C and q2 = -4.9488e-04 C are separated by distance r = 0.3373 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.0701e+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. |
7,515 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.9926e-04 C and -3.7871e-04 C separated by 0.6983 m | Two point charges q1 = -1.9926e-04 C and q2 = -3.7871e-04 C are separated by distance r = 0.6983 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1391 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. |
7,516 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.1858e-04 C and 1.7683e-04 C separated by 1.444 m | Two point charges q1 = -5.1858e-04 C and q2 = 1.7683e-04 C are separated by distance r = 1.444 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 395 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. |
7,517 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.7604e-04 C and 7.8431e-04 C separated by 0.6945 m | Two point charges q1 = -5.7604e-04 C and q2 = 7.8431e-04 C are separated by distance r = 0.6945 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8419 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. |
7,518 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.6639e-04 C and 8.2742e-04 C separated by 1.721 m | Two point charges q1 = 9.6639e-04 C and q2 = 8.2742e-04 C are separated by distance r = 1.721 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2426 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. |
7,519 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.0964e-04 C and -1.6981e-04 C separated by 1.283 m | Two point charges q1 = -9.0964e-04 C and q2 = -1.6981e-04 C are separated by distance r = 1.283 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 842.7 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. |
7,520 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.2761e-04 C and -8.9373e-04 C separated by 1.211 m | Two point charges q1 = 2.2761e-04 C and q2 = -8.9373e-04 C are separated by distance r = 1.211 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1247 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. |
7,521 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.4227e-06 C and 8.5301e-04 C separated by 1.385 m | Two point charges q1 = -2.4227e-06 C and q2 = 8.5301e-04 C are separated by distance r = 1.385 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9.676 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. |
7,522 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.8208e-04 C and -1.3007e-04 C separated by 0.8522 m | Two point charges q1 = -7.8208e-04 C and q2 = -1.3007e-04 C are separated by distance r = 0.8522 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1259 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. |
7,523 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.0777e-04 C and -4.7007e-04 C separated by 0.1924 m | Two point charges q1 = -5.0777e-04 C and q2 = -4.7007e-04 C are separated by distance r = 0.1924 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5.7975e+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. |
7,524 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.5168e-04 C and 4.6516e-05 C separated by 0.383 m | Two point charges q1 = -5.5168e-04 C and q2 = 4.6516e-05 C are separated by distance r = 0.383 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1572 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. |
7,525 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.8812e-04 C and -7.6473e-04 C separated by 1.616 m | Two point charges q1 = 7.8812e-04 C and q2 = -7.6473e-04 C are separated by distance r = 1.616 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2075 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. |
7,526 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.8175e-04 C and -1.5145e-05 C separated by 0.2581 m | Two point charges q1 = -3.8175e-04 C and q2 = -1.5145e-05 C are separated by distance r = 0.2581 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 780 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. |
7,527 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.0068e-04 C and -8.9306e-04 C separated by 1.121 m | Two point charges q1 = 1.0068e-04 C and q2 = -8.9306e-04 C are separated by distance r = 1.121 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 643.1 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. |
7,528 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.0638e-04 C and 6.6655e-04 C separated by 1.685 m | Two point charges q1 = -7.0638e-04 C and q2 = 6.6655e-04 C are separated by distance r = 1.685 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1490 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. |
7,529 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.2312e-04 C and 5.3460e-04 C separated by 0.524 m | Two point charges q1 = 9.2312e-04 C and q2 = 5.3460e-04 C are separated by distance r = 0.524 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.6156e+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. |
7,530 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.7900e-04 C and 4.4317e-04 C separated by 0.5327 m | Two point charges q1 = 4.7900e-04 C and q2 = 4.4317e-04 C are separated by distance r = 0.5327 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6724 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. |
7,531 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.1061e-04 C and -9.8217e-04 C separated by 1.965 m | Two point charges q1 = -2.1061e-04 C and q2 = -9.8217e-04 C are separated by distance r = 1.965 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 481.4 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. |
7,532 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.5233e-04 C and -6.3511e-04 C separated by 1.511 m | Two point charges q1 = -9.5233e-04 C and q2 = -6.3511e-04 C are separated by distance r = 1.511 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2380 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. |
7,533 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.5450e-04 C and -3.4676e-04 C separated by 1.981 m | Two point charges q1 = 2.5450e-04 C and q2 = -3.4676e-04 C are separated by distance r = 1.981 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 202.1 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. |
7,534 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.1764e-04 C and -1.7946e-04 C separated by 1.917 m | Two point charges q1 = -7.1764e-04 C and q2 = -1.7946e-04 C are separated by distance r = 1.917 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 314.9 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. |
7,535 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.8103e-05 C and -8.2123e-04 C separated by 1.24 m | Two point charges q1 = 5.8103e-05 C and q2 = -8.2123e-04 C are separated by distance r = 1.24 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 279 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. |
7,536 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.1185e-04 C and -9.0032e-04 C separated by 0.4921 m | Two point charges q1 = 2.1185e-04 C and q2 = -9.0032e-04 C are separated by distance r = 0.4921 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7080 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. |
7,537 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.6463e-04 C and -6.7602e-05 C separated by 1.299 m | Two point charges q1 = 8.6463e-04 C and q2 = -6.7602e-05 C are separated by distance r = 1.299 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 311.3 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. |
7,538 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.7228e-04 C and 2.7650e-04 C separated by 1.657 m | Two point charges q1 = -2.7228e-04 C and q2 = 2.7650e-04 C are separated by distance r = 1.657 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 246.4 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. |
7,539 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.8608e-04 C and 2.2989e-04 C separated by 1.122 m | Two point charges q1 = -4.8608e-04 C and q2 = 2.2989e-04 C are separated by distance r = 1.122 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 797.5 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. |
7,540 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.7240e-04 C and 1.4935e-04 C separated by 1.778 m | Two point charges q1 = 7.7240e-04 C and q2 = 1.4935e-04 C are separated by distance r = 1.778 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 327.9 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. |
7,541 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.2053e-04 C and 1.7534e-04 C separated by 1.326 m | Two point charges q1 = -2.2053e-04 C and q2 = 1.7534e-04 C are separated by distance r = 1.326 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 197.8 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. |
7,542 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.6431e-04 C and -5.7134e-04 C separated by 1.443 m | Two point charges q1 = 6.6431e-04 C and q2 = -5.7134e-04 C are separated by distance r = 1.443 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. |
7,543 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.8673e-04 C and 7.3077e-04 C separated by 1.584 m | Two point charges q1 = 3.8673e-04 C and q2 = 7.3077e-04 C are separated by distance r = 1.584 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1013 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. |
7,544 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.6217e-04 C and 5.6911e-04 C separated by 1.601 m | Two point charges q1 = -3.6217e-04 C and q2 = 5.6911e-04 C are separated by distance r = 1.601 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 723.1 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. |
7,545 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.6892e-04 C and 9.7738e-04 C separated by 0.5427 m | Two point charges q1 = -3.6892e-04 C and q2 = 9.7738e-04 C are separated by distance r = 0.5427 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.1005e+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. |
7,546 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.6666e-04 C and 3.3062e-04 C separated by 0.5505 m | Two point charges q1 = -5.6666e-04 C and q2 = 3.3062e-04 C are separated by distance r = 0.5505 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5556 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. |
7,547 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.7666e-04 C and 5.9283e-04 C separated by 0.4309 m | Two point charges q1 = -5.7666e-04 C and q2 = 5.9283e-04 C are separated by distance r = 0.4309 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.6546e+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. |
7,548 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.5141e-04 C and 3.5839e-04 C separated by 0.3779 m | Two point charges q1 = 4.5141e-04 C and q2 = 3.5839e-04 C are separated by distance r = 0.3779 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.0183e+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. |
7,549 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.0362e-04 C and -1.9142e-05 C separated by 0.3458 m | Two point charges q1 = 8.0362e-04 C and q2 = -1.9142e-05 C are separated by distance r = 0.3458 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1156 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. |
7,550 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.6700e-04 C and -6.2313e-04 C separated by 1.308 m | Two point charges q1 = -6.6700e-04 C and q2 = -6.2313e-04 C are separated by distance r = 1.308 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2185 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. |
7,551 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.3682e-04 C and -1.5052e-04 C separated by 0.1559 m | Two point charges q1 = -1.3682e-04 C and q2 = -1.5052e-04 C are separated by distance r = 0.1559 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7620 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. |
7,552 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.7200e-04 C and 9.0603e-04 C separated by 1.244 m | Two point charges q1 = -5.7200e-04 C and q2 = 9.0603e-04 C are separated by distance r = 1.244 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3008 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. |
7,553 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.3245e-04 C and 4.0658e-04 C separated by 1.137 m | Two point charges q1 = 5.3245e-04 C and q2 = 4.0658e-04 C are separated by distance r = 1.137 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1505 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. |
7,554 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.1640e-04 C and -4.2694e-04 C separated by 1.787 m | Two point charges q1 = 2.1640e-04 C and q2 = -4.2694e-04 C are separated by distance r = 1.787 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 259.9 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. |
7,555 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.0823e-05 C and -1.3272e-04 C separated by 1.308 m | Two point charges q1 = -8.0823e-05 C and q2 = -1.3272e-04 C are separated by distance r = 1.308 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 56.39 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. |
7,556 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.6092e-04 C and 6.9576e-04 C separated by 1.928 m | Two point charges q1 = -4.6092e-04 C and q2 = 6.9576e-04 C are separated by distance r = 1.928 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 775.4 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. |
7,557 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.4910e-04 C and 3.5306e-04 C separated by 1.683 m | Two point charges q1 = 6.4910e-04 C and q2 = 3.5306e-04 C are separated by distance r = 1.683 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 727.2 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. |
7,558 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.4076e-04 C and 2.0381e-04 C separated by 1.209 m | Two point charges q1 = -9.4076e-04 C and q2 = 2.0381e-04 C are separated by distance r = 1.209 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1179 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. |
7,559 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.2949e-04 C and -3.1846e-05 C separated by 1.03 m | Two point charges q1 = 3.2949e-04 C and q2 = -3.1846e-05 C are separated by distance r = 1.03 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 88.92 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. |
7,560 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.8251e-04 C and -1.4559e-04 C separated by 0.3255 m | Two point charges q1 = 1.8251e-04 C and q2 = -1.4559e-04 C are separated by distance r = 0.3255 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2254 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. |
7,561 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.5262e-04 C and -7.7482e-04 C separated by 0.9777 m | Two point charges q1 = -3.5262e-04 C and q2 = -7.7482e-04 C are separated by distance r = 0.9777 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2569 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. |
7,562 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.7302e-04 C and 5.6348e-04 C separated by 0.9176 m | Two point charges q1 = 2.7302e-04 C and q2 = 5.6348e-04 C are separated by distance r = 0.9176 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1642 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. |
7,563 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.8046e-04 C and -2.1894e-06 C separated by 0.8475 m | Two point charges q1 = 4.8046e-04 C and q2 = -2.1894e-06 C are separated by distance r = 0.8475 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 13.16 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. |
7,564 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.9625e-04 C and 5.4521e-04 C separated by 1.527 m | Two point charges q1 = 3.9625e-04 C and q2 = 5.4521e-04 C are separated by distance r = 1.527 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 832.3 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. |
7,565 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.0151e-04 C and 5.9349e-04 C separated by 1.847 m | Two point charges q1 = 4.0151e-04 C and q2 = 5.9349e-04 C are separated by distance r = 1.847 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 627.5 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. |
7,566 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.2037e-04 C and -3.8627e-04 C separated by 0.7016 m | Two point charges q1 = -4.2037e-04 C and q2 = -3.8627e-04 C are separated by distance r = 0.7016 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2964 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. |
7,567 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.5767e-04 C and 3.3993e-05 C separated by 0.8193 m | Two point charges q1 = -2.5767e-04 C and q2 = 3.3993e-05 C are separated by distance r = 0.8193 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 117.3 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. |
7,568 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.1542e-04 C and -4.7079e-04 C separated by 0.08489 m | Two point charges q1 = 3.1542e-04 C and q2 = -4.7079e-04 C are separated by distance r = 0.08489 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.8519e+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. |
7,569 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.7508e-04 C and 6.1684e-04 C separated by 1.926 m | Two point charges q1 = 9.7508e-04 C and q2 = 6.1684e-04 C are separated by distance r = 1.926 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1457 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. |
7,570 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.9999e-05 C and 1.3822e-04 C separated by 1.395 m | Two point charges q1 = 7.9999e-05 C and q2 = 1.3822e-04 C are separated by distance r = 1.395 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 51.07 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. |
7,571 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.2178e-04 C and -6.9503e-04 C separated by 1.191 m | Two point charges q1 = -3.2178e-04 C and q2 = -6.9503e-04 C are separated by distance r = 1.191 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1417 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. |
7,572 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.8007e-04 C and 1.1101e-04 C separated by 1.063 m | Two point charges q1 = -1.8007e-04 C and q2 = 1.1101e-04 C are separated by distance r = 1.063 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 159.1 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. |
7,573 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.1411e-04 C and -4.2714e-04 C separated by 0.4772 m | Two point charges q1 = 4.1411e-04 C and q2 = -4.2714e-04 C are separated by distance r = 0.4772 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6981 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. |
7,574 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.5347e-04 C and 9.1625e-04 C separated by 1.245 m | Two point charges q1 = -8.5347e-04 C and q2 = 9.1625e-04 C are separated by distance r = 1.245 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4532 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. |
7,575 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.1211e-04 C and 9.2268e-04 C separated by 0.8338 m | Two point charges q1 = 6.1211e-04 C and q2 = 9.2268e-04 C are separated by distance r = 0.8338 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7302 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. |
7,576 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.4877e-04 C and 7.5397e-04 C separated by 1.751 m | Two point charges q1 = 2.4877e-04 C and q2 = 7.5397e-04 C are separated by distance r = 1.751 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 550.1 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. |
7,577 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.4558e-04 C and 7.0933e-04 C separated by 1.573 m | Two point charges q1 = 7.4558e-04 C and q2 = 7.0933e-04 C are separated by distance r = 1.573 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1920 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. |
7,578 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.1237e-04 C and 5.6982e-04 C separated by 1.211 m | Two point charges q1 = 6.1237e-04 C and q2 = 5.6982e-04 C are separated by distance r = 1.211 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2139 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. |
7,579 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.5323e-04 C and -8.3395e-04 C separated by 1.89 m | Two point charges q1 = -7.5323e-04 C and q2 = -8.3395e-04 C are separated by distance r = 1.89 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1580 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. |
7,580 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.7651e-04 C and 2.8580e-04 C separated by 1.154 m | Two point charges q1 = 2.7651e-04 C and q2 = 2.8580e-04 C are separated by distance r = 1.154 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 533.3 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. |
7,581 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.7720e-04 C and 1.8159e-05 C separated by 1.521 m | Two point charges q1 = 8.7720e-04 C and q2 = 1.8159e-05 C are separated by distance r = 1.521 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 61.92 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. |
7,582 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.4696e-04 C and -5.9373e-04 C separated by 1.006 m | Two point charges q1 = -1.4696e-04 C and q2 = -5.9373e-04 C are separated by distance r = 1.006 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 774.9 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. |
7,583 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.0583e-04 C and 7.2382e-04 C separated by 0.4449 m | Two point charges q1 = -6.0583e-04 C and q2 = 7.2382e-04 C are separated by distance r = 0.4449 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.9914e+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. |
7,584 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.0066e-04 C and -1.0451e-04 C separated by 0.02587 m | Two point charges q1 = 1.0066e-04 C and q2 = -1.0451e-04 C are separated by distance r = 0.02587 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.4124e+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. |
7,585 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.2996e-04 C and -1.1603e-04 C separated by 0.9627 m | Two point charges q1 = 1.2996e-04 C and q2 = -1.1603e-04 C are separated by distance r = 0.9627 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 146.2 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. |
7,586 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.7945e-04 C and 8.9934e-04 C separated by 1.042 m | Two point charges q1 = -4.7945e-04 C and q2 = 8.9934e-04 C are separated by distance r = 1.042 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3570 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. |
7,587 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.8778e-04 C and 3.7117e-04 C separated by 0.9505 m | Two point charges q1 = -2.8778e-04 C and q2 = 3.7117e-04 C are separated by distance r = 0.9505 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1063 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. |
7,588 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.5928e-04 C and -3.8255e-05 C separated by 0.03022 m | Two point charges q1 = -8.5928e-04 C and q2 = -3.8255e-05 C are separated by distance r = 0.03022 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.2351e+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. |
7,589 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.7886e-04 C and 8.4841e-04 C separated by 0.7692 m | Two point charges q1 = 2.7886e-04 C and q2 = 8.4841e-04 C are separated by distance r = 0.7692 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3594 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. |
7,590 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.4923e-04 C and -5.6701e-04 C separated by 1.648 m | Two point charges q1 = -1.4923e-04 C and q2 = -5.6701e-04 C are separated by distance r = 1.648 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 280.1 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. |
7,591 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.9734e-04 C and 1.0753e-04 C separated by 1.56 m | Two point charges q1 = -8.9734e-04 C and q2 = 1.0753e-04 C are separated by distance r = 1.56 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 356.4 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. |
7,592 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.3411e-04 C and 3.3399e-04 C separated by 0.793 m | Two point charges q1 = -7.3411e-04 C and q2 = 3.3399e-04 C are separated by distance r = 0.793 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3504 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. |
7,593 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.2924e-04 C and 1.9112e-04 C separated by 1.169 m | Two point charges q1 = 5.2924e-04 C and q2 = 1.9112e-04 C are separated by distance r = 1.169 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 665.4 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. |
7,594 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.6388e-04 C and 9.7088e-04 C separated by 0.167 m | Two point charges q1 = 9.6388e-04 C and q2 = 9.7088e-04 C are separated by distance r = 0.167 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.0167e+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. |
7,595 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.4444e-04 C and 7.0611e-04 C separated by 1.11 m | Two point charges q1 = -9.4444e-04 C and q2 = 7.0611e-04 C are separated by distance r = 1.11 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4868 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. |
7,596 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.6012e-04 C and 3.9715e-04 C separated by 0.4504 m | Two point charges q1 = -2.6012e-04 C and q2 = 3.9715e-04 C are separated by distance r = 0.4504 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4578 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. |
7,597 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.2360e-04 C and 4.9010e-05 C separated by 0.4174 m | Two point charges q1 = -2.2360e-04 C and q2 = 4.9010e-05 C are separated by distance r = 0.4174 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 565.4 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. |
7,598 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.9130e-04 C and 1.5841e-04 C separated by 1.345 m | Two point charges q1 = -1.9130e-04 C and q2 = 1.5841e-04 C are separated by distance r = 1.345 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 150.6 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. |
7,599 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.4452e-05 C and -1.9571e-04 C separated by 0.9205 m | Two point charges q1 = -3.4452e-05 C and q2 = -1.9571e-04 C are separated by distance r = 0.9205 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 71.52 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. |
7,600 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.6586e-04 C and -6.5637e-04 C separated by 0.04725 m | Two point charges q1 = -2.6586e-04 C and q2 = -6.5637e-04 C are separated by distance r = 0.04725 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7.0260e+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. |
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