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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4,001 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.11 m, speed 37.14 m/s | An object moves in a circle of radius 37.11 m at constant speed 37.14 m/s. The centripetal acceleration has magnitude a_c = v² / r = 37.16 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. |
4,002 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 9.723 m, speed 2.153 m/s | An object moves in a circle of radius 9.723 m at constant speed 2.153 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.4766 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. |
4,003 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 1.25 m, speed 20.96 m/s | An object moves in a circle of radius 1.25 m at constant speed 20.96 m/s. The centripetal acceleration has magnitude a_c = v² / r = 351.5 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. |
4,004 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.702 m, speed 34.81 m/s | An object moves in a circle of radius 7.702 m at constant speed 34.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 157.3 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. |
4,005 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.828 m, speed 9.461 m/s | An object moves in a circle of radius 5.828 m at constant speed 9.461 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.36 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. |
4,006 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 16.44 m, speed 9.571 m/s | An object moves in a circle of radius 16.44 m at constant speed 9.571 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.57 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. |
4,007 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 36.41 m, speed 37.65 m/s | An object moves in a circle of radius 36.41 m at constant speed 37.65 m/s. The centripetal acceleration has magnitude a_c = v² / r = 38.94 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. |
4,008 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 13.45 m, speed 19.78 m/s | An object moves in a circle of radius 13.45 m at constant speed 19.78 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.09 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. |
4,009 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 47.67 m, speed 14.59 m/s | An object moves in a circle of radius 47.67 m at constant speed 14.59 m/s. The centripetal acceleration has magnitude a_c = v² / r = 4.468 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. |
4,010 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 27.62 m, speed 12.48 m/s | An object moves in a circle of radius 27.62 m at constant speed 12.48 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.638 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. |
4,011 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.29 m, speed 20.34 m/s | An object moves in a circle of radius 37.29 m at constant speed 20.34 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.09 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. |
4,012 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 25.68 m, speed 16.6 m/s | An object moves in a circle of radius 25.68 m at constant speed 16.6 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.73 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. |
4,013 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 9.733 m, speed 7.745 m/s | An object moves in a circle of radius 9.733 m at constant speed 7.745 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.163 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. |
4,014 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.38 m, speed 35.61 m/s | An object moves in a circle of radius 34.38 m at constant speed 35.61 m/s. The centripetal acceleration has magnitude a_c = v² / r = 36.87 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. |
4,015 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 14.13 m, speed 16.32 m/s | An object moves in a circle of radius 14.13 m at constant speed 16.32 m/s. The centripetal acceleration has magnitude a_c = v² / r = 18.86 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. |
4,016 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.22 m, speed 30.89 m/s | An object moves in a circle of radius 29.22 m at constant speed 30.89 m/s. The centripetal acceleration has magnitude a_c = v² / r = 32.65 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. |
4,017 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 15.65 m, speed 31.97 m/s | An object moves in a circle of radius 15.65 m at constant speed 31.97 m/s. The centripetal acceleration has magnitude a_c = v² / r = 65.32 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. |
4,018 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 47.69 m, speed 20.03 m/s | An object moves in a circle of radius 47.69 m at constant speed 20.03 m/s. The centripetal acceleration has magnitude a_c = v² / r = 8.408 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. |
4,019 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 44.15 m, speed 17.53 m/s | An object moves in a circle of radius 44.15 m at constant speed 17.53 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.956 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. |
4,020 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.38 m, speed 32.82 m/s | An object moves in a circle of radius 37.38 m at constant speed 32.82 m/s. The centripetal acceleration has magnitude a_c = v² / r = 28.82 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. |
4,021 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 31.18 m, speed 24.68 m/s | An object moves in a circle of radius 31.18 m at constant speed 24.68 m/s. The centripetal acceleration has magnitude a_c = v² / r = 19.54 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. |
4,022 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 21.52 m, speed 23.12 m/s | An object moves in a circle of radius 21.52 m at constant speed 23.12 m/s. The centripetal acceleration has magnitude a_c = v² / r = 24.83 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. |
4,023 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 18.76 m, speed 25.68 m/s | An object moves in a circle of radius 18.76 m at constant speed 25.68 m/s. The centripetal acceleration has magnitude a_c = v² / r = 35.14 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. |
4,024 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.307 m, speed 7.523 m/s | An object moves in a circle of radius 3.307 m at constant speed 7.523 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.11 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. |
4,025 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 1.785 m, speed 20.94 m/s | An object moves in a circle of radius 1.785 m at constant speed 20.94 m/s. The centripetal acceleration has magnitude a_c = v² / r = 245.8 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. |
4,026 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.38 m, speed 12.45 m/s | An object moves in a circle of radius 29.38 m at constant speed 12.45 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.271 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. |
4,027 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 41.35 m, speed 26.16 m/s | An object moves in a circle of radius 41.35 m at constant speed 26.16 m/s. The centripetal acceleration has magnitude a_c = v² / r = 16.55 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. |
4,028 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 48.26 m, speed 14.74 m/s | An object moves in a circle of radius 48.26 m at constant speed 14.74 m/s. The centripetal acceleration has magnitude a_c = v² / r = 4.501 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. |
4,029 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 1.594 m, speed 8.016 m/s | An object moves in a circle of radius 1.594 m at constant speed 8.016 m/s. The centripetal acceleration has magnitude a_c = v² / r = 40.31 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. |
4,030 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.2996e-04 C and -3.5839e-04 C separated by 0.1546 m | Two point charges q1 = 4.2996e-04 C and q2 = -3.5839e-04 C are separated by distance r = 0.1546 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5.7977e+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. |
4,031 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.7259e-04 C and 1.2318e-04 C separated by 0.644 m | Two point charges q1 = 3.7259e-04 C and q2 = 1.2318e-04 C are separated by distance r = 0.644 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 994.6 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. |
4,032 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.1709e-04 C and -4.6591e-04 C separated by 1.593 m | Two point charges q1 = -7.1709e-04 C and q2 = -4.6591e-04 C are separated by distance r = 1.593 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1184 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. |
4,033 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.6208e-04 C and 2.8433e-04 C separated by 0.4322 m | Two point charges q1 = -5.6208e-04 C and q2 = 2.8433e-04 C are separated by distance r = 0.4322 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7688 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. |
4,034 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.0382e-04 C and 7.1655e-04 C separated by 1.893 m | Two point charges q1 = -1.0382e-04 C and q2 = 7.1655e-04 C are separated by distance r = 1.893 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 186.6 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. |
4,035 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.7437e-04 C and 6.8245e-04 C separated by 0.8761 m | Two point charges q1 = -5.7437e-04 C and q2 = 6.8245e-04 C are separated by distance r = 0.8761 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4590 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. |
4,036 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.9895e-04 C and -8.0292e-04 C separated by 1.002 m | Two point charges q1 = 1.9895e-04 C and q2 = -8.0292e-04 C are separated by distance r = 1.002 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1429 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. |
4,037 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.2182e-04 C and -4.5333e-04 C separated by 1.207 m | Two point charges q1 = 4.2182e-04 C and q2 = -4.5333e-04 C are separated by distance r = 1.207 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1180 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. |
4,038 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.3719e-04 C and -2.8575e-04 C separated by 1.291 m | Two point charges q1 = 2.3719e-04 C and q2 = -2.8575e-04 C are separated by distance r = 1.291 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 365.5 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. |
4,039 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.1173e-04 C and 1.3193e-04 C separated by 1.934 m | Two point charges q1 = -9.1173e-04 C and q2 = 1.3193e-04 C are separated by distance r = 1.934 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 289 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. |
4,040 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.9593e-04 C and -3.3805e-04 C separated by 0.04238 m | Two point charges q1 = -8.9593e-04 C and q2 = -3.3805e-04 C are separated by distance r = 0.04238 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.5154e+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. |
4,041 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.6025e-05 C and 7.2353e-04 C separated by 0.5566 m | Two point charges q1 = 9.6025e-05 C and q2 = 7.2353e-04 C are separated by distance r = 0.5566 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2016 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. |
4,042 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.0094e-04 C and 4.9432e-04 C separated by 0.1037 m | Two point charges q1 = 4.0094e-04 C and q2 = 4.9432e-04 C are separated by distance r = 0.1037 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.6573e+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. |
4,043 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.9676e-04 C and 4.9384e-04 C separated by 1.286 m | Two point charges q1 = 6.9676e-04 C and q2 = 4.9384e-04 C are separated by distance r = 1.286 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1871 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. |
4,044 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.4323e-04 C and -3.0259e-05 C separated by 0.1052 m | Two point charges q1 = -8.4323e-04 C and q2 = -3.0259e-05 C are separated by distance r = 0.1052 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.0725e+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. |
4,045 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.3960e-04 C and 8.6153e-04 C separated by 1.451 m | Two point charges q1 = -1.3960e-04 C and q2 = 8.6153e-04 C are separated by distance r = 1.451 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 513.2 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. |
4,046 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.7102e-04 C and -7.2438e-04 C separated by 1.626 m | Two point charges q1 = -1.7102e-04 C and q2 = -7.2438e-04 C are separated by distance r = 1.626 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 420.9 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. |
4,047 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.3418e-04 C and -2.6043e-04 C separated by 1.572 m | Two point charges q1 = -9.3418e-04 C and q2 = -2.6043e-04 C are separated by distance r = 1.572 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 884.8 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. |
4,048 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.8955e-05 C and 7.5967e-05 C separated by 0.6654 m | Two point charges q1 = -4.8955e-05 C and q2 = 7.5967e-05 C are separated by distance r = 0.6654 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 75.5 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. |
4,049 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.7064e-04 C and -9.2493e-04 C separated by 1.171 m | Two point charges q1 = 2.7064e-04 C and q2 = -9.2493e-04 C are separated by distance r = 1.171 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1641 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. |
4,050 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.2716e-04 C and -7.5328e-04 C separated by 1.777 m | Two point charges q1 = -1.2716e-04 C and q2 = -7.5328e-04 C are separated by distance r = 1.777 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 272.7 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. |
4,051 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.3727e-04 C and -5.2224e-04 C separated by 0.4886 m | Two point charges q1 = 6.3727e-04 C and q2 = -5.2224e-04 C are separated by distance r = 0.4886 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.2527e+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. |
4,052 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.6161e-04 C and 3.2259e-04 C separated by 1.464 m | Two point charges q1 = 6.6161e-04 C and q2 = 3.2259e-04 C are separated by distance r = 1.464 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 894.5 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. |
4,053 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.2708e-05 C and 7.1167e-04 C separated by 0.7125 m | Two point charges q1 = -9.2708e-05 C and q2 = 7.1167e-04 C are separated by distance r = 0.7125 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1168 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. |
4,054 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.5982e-04 C and -6.9527e-04 C separated by 0.1595 m | Two point charges q1 = -6.5982e-04 C and q2 = -6.9527e-04 C are separated by distance r = 0.1595 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.6199e+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. |
4,055 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.1207e-05 C and -6.7083e-04 C separated by 0.9416 m | Two point charges q1 = 6.1207e-05 C and q2 = -6.7083e-04 C are separated by distance r = 0.9416 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 416.2 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. |
4,056 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.8873e-04 C and -3.4111e-04 C separated by 1.63 m | Two point charges q1 = 1.8873e-04 C and q2 = -3.4111e-04 C are separated by distance r = 1.63 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 217.8 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. |
4,057 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.6073e-04 C and 7.0880e-04 C separated by 1.314 m | Two point charges q1 = 7.6073e-04 C and q2 = 7.0880e-04 C are separated by distance r = 1.314 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2807 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. |
4,058 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.1421e-04 C and -9.1678e-04 C separated by 0.7773 m | Two point charges q1 = -9.1421e-04 C and q2 = -9.1678e-04 C are separated by distance r = 0.7773 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.2468e+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. |
4,059 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.6799e-04 C and -7.8024e-04 C separated by 0.384 m | Two point charges q1 = 8.6799e-04 C and q2 = -7.8024e-04 C are separated by distance r = 0.384 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4.1273e+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. |
4,060 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.2367e-04 C and 9.5154e-04 C separated by 1.159 m | Two point charges q1 = 4.2367e-04 C and q2 = 9.5154e-04 C are separated by distance r = 1.159 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2699 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. |
4,061 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.4814e-04 C and -7.4528e-04 C separated by 0.4887 m | Two point charges q1 = -1.4814e-04 C and q2 = -7.4528e-04 C are separated by distance r = 0.4887 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4155 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. |
4,062 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.8784e-04 C and -4.7676e-04 C separated by 1.066 m | Two point charges q1 = 1.8784e-04 C and q2 = -4.7676e-04 C are separated by distance r = 1.066 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 707.7 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. |
4,063 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.6631e-04 C and -3.5507e-04 C separated by 0.432 m | Two point charges q1 = 2.6631e-04 C and q2 = -3.5507e-04 C are separated by distance r = 0.432 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4554 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. |
4,064 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.0269e-04 C and 5.4104e-05 C separated by 0.5525 m | Two point charges q1 = 5.0269e-04 C and q2 = 5.4104e-05 C are separated by distance r = 0.5525 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 800.9 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. |
4,065 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.0085e-05 C and 7.3227e-04 C separated by 0.851 m | Two point charges q1 = -5.0085e-05 C and q2 = 7.3227e-04 C are separated by distance r = 0.851 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 455.2 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. |
4,066 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.9026e-04 C and -5.9446e-04 C separated by 1.064 m | Two point charges q1 = 1.9026e-04 C and q2 = -5.9446e-04 C are separated by distance r = 1.064 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 898.2 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. |
4,067 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.1910e-04 C and -6.8148e-04 C separated by 1.296 m | Two point charges q1 = 5.1910e-04 C and q2 = -6.8148e-04 C are separated by distance r = 1.296 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1892 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. |
4,068 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.2036e-04 C and -8.9516e-04 C separated by 1.155 m | Two point charges q1 = -2.2036e-04 C and q2 = -8.9516e-04 C are separated by distance r = 1.155 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1330 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. |
4,069 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.6782e-05 C and -2.7618e-04 C separated by 1.766 m | Two point charges q1 = -6.6782e-05 C and q2 = -2.7618e-04 C are separated by distance r = 1.766 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 53.13 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. |
4,070 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.9252e-04 C and -2.2067e-04 C separated by 1.65 m | Two point charges q1 = 3.9252e-04 C and q2 = -2.2067e-04 C are separated by distance r = 1.65 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 286 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. |
4,071 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.9568e-04 C and -7.8594e-04 C separated by 0.7018 m | Two point charges q1 = 4.9568e-04 C and q2 = -7.8594e-04 C are separated by distance r = 0.7018 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7109 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. |
4,072 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.0615e-04 C and 7.3415e-04 C separated by 0.1975 m | Two point charges q1 = 7.0615e-04 C and q2 = 7.3415e-04 C are separated by distance r = 0.1975 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.1940e+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. |
4,073 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.3935e-04 C and -1.7106e-04 C separated by 1.366 m | Two point charges q1 = 7.3935e-04 C and q2 = -1.7106e-04 C are separated by distance r = 1.366 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 609.1 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. |
4,074 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.8816e-04 C and 1.4269e-04 C separated by 0.03534 m | Two point charges q1 = -1.8816e-04 C and q2 = 1.4269e-04 C are separated by distance r = 0.03534 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.9318e+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. |
4,075 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.2849e-04 C and -1.7834e-04 C separated by 0.535 m | Two point charges q1 = 4.2849e-04 C and q2 = -1.7834e-04 C are separated by distance r = 0.535 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2399 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. |
4,076 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.7155e-04 C and -5.9441e-04 C separated by 1.939 m | Two point charges q1 = -1.7155e-04 C and q2 = -5.9441e-04 C are separated by distance r = 1.939 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 243.7 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. |
4,077 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.8882e-04 C and -4.7310e-04 C separated by 0.0999 m | Two point charges q1 = -4.8882e-04 C and q2 = -4.7310e-04 C are separated by distance r = 0.0999 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.0826e+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. |
4,078 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.6770e-04 C and 8.3552e-04 C separated by 1.055 m | Two point charges q1 = -5.6770e-04 C and q2 = 8.3552e-04 C are separated by distance r = 1.055 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3828 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. |
4,079 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.5524e-04 C and -1.0089e-04 C separated by 1.61 m | Two point charges q1 = -7.5524e-04 C and q2 = -1.0089e-04 C are separated by distance r = 1.61 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 264.3 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. |
4,080 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.5316e-04 C and 9.8980e-04 C separated by 0.5221 m | Two point charges q1 = 4.5316e-04 C and q2 = 9.8980e-04 C are separated by distance r = 0.5221 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.4789e+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. |
4,081 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.5428e-04 C and 1.4547e-05 C separated by 0.7117 m | Two point charges q1 = 2.5428e-04 C and q2 = 1.4547e-05 C are separated by distance r = 0.7117 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 65.63 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. |
4,082 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.9148e-04 C and 1.1365e-04 C separated by 1.375 m | Two point charges q1 = 8.9148e-04 C and q2 = 1.1365e-04 C are separated by distance r = 1.375 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 481.8 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. |
4,083 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.4875e-04 C and 8.5641e-04 C separated by 1.322 m | Two point charges q1 = -1.4875e-04 C and q2 = 8.5641e-04 C are separated by distance r = 1.322 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 655 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. |
4,084 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.5784e-04 C and -2.4512e-04 C separated by 1.485 m | Two point charges q1 = -3.5784e-04 C and q2 = -2.4512e-04 C are separated by distance r = 1.485 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 357.7 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. |
4,085 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.6006e-04 C and -1.9465e-04 C separated by 1.91 m | Two point charges q1 = 3.6006e-04 C and q2 = -1.9465e-04 C are separated by distance r = 1.91 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 172.6 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. |
4,086 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.6549e-04 C and 9.8734e-04 C separated by 1.753 m | Two point charges q1 = -9.6549e-04 C and q2 = 9.8734e-04 C are separated by distance r = 1.753 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2787 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. |
4,087 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.6604e-04 C and 8.8811e-04 C separated by 0.7881 m | Two point charges q1 = -2.6604e-04 C and q2 = 8.8811e-04 C are separated by distance r = 0.7881 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3419 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. |
4,088 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.4532e-04 C and 3.1001e-04 C separated by 0.09179 m | Two point charges q1 = 9.4532e-04 C and q2 = 3.1001e-04 C are separated by distance r = 0.09179 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3.1262e+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. |
4,089 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.3434e-04 C and -4.3403e-04 C separated by 0.9155 m | Two point charges q1 = 8.3434e-04 C and q2 = -4.3403e-04 C are separated by distance r = 0.9155 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3883 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. |
4,090 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.8912e-04 C and -4.9943e-04 C separated by 1.374 m | Two point charges q1 = 2.8912e-04 C and q2 = -4.9943e-04 C are separated by distance r = 1.374 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 687.2 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. |
4,091 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.8124e-04 C and 6.2417e-04 C separated by 1.332 m | Two point charges q1 = 6.8124e-04 C and q2 = 6.2417e-04 C are separated by distance r = 1.332 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2154 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. |
4,092 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.8734e-04 C and -7.9999e-04 C separated by 0.04103 m | Two point charges q1 = 4.8734e-04 C and q2 = -7.9999e-04 C are separated by distance r = 0.04103 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.0815e+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. |
4,093 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.1811e-04 C and -5.4140e-05 C separated by 0.6186 m | Two point charges q1 = -2.1811e-04 C and q2 = -5.4140e-05 C are separated by distance r = 0.6186 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 277.4 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. |
4,094 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.5290e-04 C and -5.0852e-05 C separated by 0.2841 m | Two point charges q1 = 3.5290e-04 C and q2 = -5.0852e-05 C are separated by distance r = 0.2841 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1999 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. |
4,095 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.8548e-04 C and -9.5373e-04 C separated by 1.429 m | Two point charges q1 = 7.8548e-04 C and q2 = -9.5373e-04 C are separated by distance r = 1.429 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3296 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. |
4,096 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.9592e-04 C and -4.3262e-04 C separated by 1.837 m | Two point charges q1 = -9.9592e-04 C and q2 = -4.3262e-04 C are separated by distance r = 1.837 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1147 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. |
4,097 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.1964e-04 C and 9.3300e-04 C separated by 0.505 m | Two point charges q1 = 2.1964e-04 C and q2 = 9.3300e-04 C are separated by distance r = 0.505 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7223 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. |
4,098 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.2314e-04 C and -8.9314e-04 C separated by 1.841 m | Two point charges q1 = 4.2314e-04 C and q2 = -8.9314e-04 C are separated by distance r = 1.841 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1002 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. |
4,099 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.7413e-04 C and 6.7924e-04 C separated by 0.6517 m | Two point charges q1 = 1.7413e-04 C and q2 = 6.7924e-04 C are separated by distance r = 0.6517 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2503 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. |
4,100 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.8364e-04 C and -2.5077e-04 C separated by 0.8385 m | Two point charges q1 = -6.8364e-04 C and q2 = -2.5077e-04 C are separated by distance r = 0.8385 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2192 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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