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 |
|---|---|---|---|---|---|---|---|---|---|---|
5,801 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.6985e-04 C and 4.7905e-04 C separated by 0.3454 m | Two point charges q1 = -2.6985e-04 C and q2 = 4.7905e-04 C are separated by distance r = 0.3454 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9739 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,802 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.4606e-04 C and 3.6521e-04 C separated by 1.524 m | Two point charges q1 = -8.4606e-04 C and q2 = 3.6521e-04 C are separated by distance r = 1.524 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1196 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,803 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.0740e-04 C and -9.3284e-05 C separated by 1.394 m | Two point charges q1 = -7.0740e-04 C and q2 = -9.3284e-05 C are separated by distance r = 1.394 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 305.3 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. |
5,804 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.5114e-04 C and 4.5365e-04 C separated by 0.5934 m | Two point charges q1 = -2.5114e-04 C and q2 = 4.5365e-04 C are separated by distance r = 0.5934 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2908 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,805 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.7923e-04 C and -2.2986e-04 C separated by 0.6301 m | Two point charges q1 = 2.7923e-04 C and q2 = -2.2986e-04 C are separated by distance r = 0.6301 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1453 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,806 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.3258e-04 C and -6.2132e-04 C separated by 1.149 m | Two point charges q1 = -2.3258e-04 C and q2 = -6.2132e-04 C are separated by distance r = 1.149 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 982.9 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. |
5,807 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.8895e-04 C and 9.4207e-04 C separated by 1.791 m | Two point charges q1 = -2.8895e-04 C and q2 = 9.4207e-04 C are separated by distance r = 1.791 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 762.8 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. |
5,808 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.8165e-05 C and -6.0303e-04 C separated by 0.1633 m | Two point charges q1 = -1.8165e-05 C and q2 = -6.0303e-04 C are separated by distance r = 0.1633 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3691 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,809 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.6978e-04 C and -5.3442e-04 C separated by 1.56 m | Two point charges q1 = -2.6978e-04 C and q2 = -5.3442e-04 C are separated by distance r = 1.56 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 532.2 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. |
5,810 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.2349e-04 C and -5.3412e-04 C separated by 0.3817 m | Two point charges q1 = 7.2349e-04 C and q2 = -5.3412e-04 C are separated by distance r = 0.3817 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.3832e+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. |
5,811 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.2615e-04 C and -7.6658e-04 C separated by 1.031 m | Two point charges q1 = -3.2615e-04 C and q2 = -7.6658e-04 C are separated by distance r = 1.031 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2113 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,812 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.0141e-04 C and -3.9441e-04 C separated by 0.3423 m | Two point charges q1 = -5.0141e-04 C and q2 = -3.9441e-04 C are separated by distance r = 0.3423 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.5167e+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. |
5,813 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.5675e-04 C and -2.4268e-04 C separated by 1.222 m | Two point charges q1 = 1.5675e-04 C and q2 = -2.4268e-04 C are separated by distance r = 1.222 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 229 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,814 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.7429e-04 C and 4.6294e-04 C separated by 0.9153 m | Two point charges q1 = 5.7429e-04 C and q2 = 4.6294e-04 C are separated by distance r = 0.9153 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2852 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,815 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.1372e-04 C and -6.4050e-04 C separated by 1.511 m | Two point charges q1 = -7.1372e-04 C and q2 = -6.4050e-04 C are separated by distance r = 1.511 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1798 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,816 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.8287e-04 C and -1.5728e-06 C separated by 0.9269 m | Two point charges q1 = -9.8287e-04 C and q2 = -1.5728e-06 C are separated by distance r = 0.9269 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 16.17 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,817 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.7785e-04 C and 5.5077e-04 C separated by 1.455 m | Two point charges q1 = 6.7785e-04 C and q2 = 5.5077e-04 C are separated by distance r = 1.455 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1584 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,818 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.6214e-04 C and 7.8660e-04 C separated by 1.159 m | Two point charges q1 = 9.6214e-04 C and q2 = 7.8660e-04 C are separated by distance r = 1.159 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5062 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,819 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.5188e-04 C and 1.6773e-04 C separated by 1.717 m | Two point charges q1 = 7.5188e-04 C and q2 = 1.6773e-04 C are separated by distance r = 1.717 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 384.3 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. |
5,820 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.0503e-04 C and -7.4344e-05 C separated by 1.989 m | Two point charges q1 = -8.0503e-04 C and q2 = -7.4344e-05 C are separated by distance r = 1.989 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 135.9 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. |
5,821 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.1642e-04 C and 3.8319e-04 C separated by 0.606 m | Two point charges q1 = 1.1642e-04 C and q2 = 3.8319e-04 C are separated by distance r = 0.606 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1092 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,822 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.1523e-04 C and -7.5056e-04 C separated by 0.439 m | Two point charges q1 = -3.1523e-04 C and q2 = -7.5056e-04 C are separated by distance r = 0.439 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.1035e+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. |
5,823 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.5049e-04 C and -6.4942e-04 C separated by 0.6109 m | Two point charges q1 = -4.5049e-04 C and q2 = -6.4942e-04 C are separated by distance r = 0.6109 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7045 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,824 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.4317e-04 C and -9.0376e-04 C separated by 0.5133 m | Two point charges q1 = -1.4317e-04 C and q2 = -9.0376e-04 C are separated by distance r = 0.5133 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4414 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,825 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.6688e-04 C and 3.7220e-04 C separated by 0.4173 m | Two point charges q1 = 4.6688e-04 C and q2 = 3.7220e-04 C are separated by distance r = 0.4173 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8967 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,826 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.1638e-04 C and -2.4612e-04 C separated by 0.2996 m | Two point charges q1 = -4.1638e-04 C and q2 = -2.4612e-04 C are separated by distance r = 0.2996 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.0260e+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. |
5,827 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.9612e-04 C and -3.5120e-04 C separated by 1.82 m | Two point charges q1 = -2.9612e-04 C and q2 = -3.5120e-04 C are separated by distance r = 1.82 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 282.3 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. |
5,828 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.9045e-05 C and 3.5542e-04 C separated by 1.03 m | Two point charges q1 = 7.9045e-05 C and q2 = 3.5542e-04 C are separated by distance r = 1.03 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 238 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,829 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.1484e-05 C and 6.8688e-05 C separated by 0.6696 m | Two point charges q1 = 4.1484e-05 C and q2 = 6.8688e-05 C are separated by distance r = 0.6696 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 57.12 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,830 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.2206e-04 C and -1.2045e-05 C separated by 0.2116 m | Two point charges q1 = 9.2206e-04 C and q2 = -1.2045e-05 C are separated by distance r = 0.2116 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2230 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,831 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.0827e-05 C and -6.3104e-04 C separated by 0.7488 m | Two point charges q1 = 6.0827e-05 C and q2 = -6.3104e-04 C are separated by distance r = 0.7488 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 615.2 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. |
5,832 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.0401e-04 C and 3.4758e-04 C separated by 0.6598 m | Two point charges q1 = 4.0401e-04 C and q2 = 3.4758e-04 C are separated by distance r = 0.6598 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2899 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,833 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.1865e-05 C and -8.8365e-04 C separated by 1.519 m | Two point charges q1 = 5.1865e-05 C and q2 = -8.8365e-04 C are separated by distance r = 1.519 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 178.4 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. |
5,834 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.6388e-04 C and -6.6665e-04 C separated by 1.1 m | Two point charges q1 = 7.6388e-04 C and q2 = -6.6665e-04 C are separated by distance r = 1.1 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3779 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,835 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.9865e-04 C and -9.3301e-04 C separated by 0.7621 m | Two point charges q1 = -9.9865e-04 C and q2 = -9.3301e-04 C are separated by distance r = 0.7621 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.4420e+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. |
5,836 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.3172e-04 C and 1.4481e-04 C separated by 1.527 m | Two point charges q1 = 7.3172e-04 C and q2 = 1.4481e-04 C are separated by distance r = 1.527 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 408.6 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. |
5,837 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.4096e-05 C and 2.7648e-04 C separated by 0.4483 m | Two point charges q1 = -9.4096e-05 C and q2 = 2.7648e-04 C are separated by distance r = 0.4483 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1164 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,838 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.0361e-04 C and -1.9530e-04 C separated by 1.143 m | Two point charges q1 = -3.0361e-04 C and q2 = -1.9530e-04 C are separated by distance r = 1.143 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 408 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,839 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.9967e-04 C and -4.2748e-04 C separated by 1.141 m | Two point charges q1 = 7.9967e-04 C and q2 = -4.2748e-04 C are separated by distance r = 1.141 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2361 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,840 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.5664e-06 C and -1.6423e-04 C separated by 0.08455 m | Two point charges q1 = -1.5664e-06 C and q2 = -1.6423e-04 C are separated by distance r = 0.08455 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 323.4 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. |
5,841 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.8723e-04 C and -4.6884e-04 C separated by 1.963 m | Two point charges q1 = 7.8723e-04 C and q2 = -4.6884e-04 C are separated by distance r = 1.963 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 861.2 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. |
5,842 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.1512e-04 C and 8.1188e-04 C separated by 0.692 m | Two point charges q1 = 1.1512e-04 C and q2 = 8.1188e-04 C are separated by distance r = 0.692 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1754 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,843 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.5074e-04 C and 5.7747e-04 C separated by 1.1 m | Two point charges q1 = 8.5074e-04 C and q2 = 5.7747e-04 C are separated by distance r = 1.1 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3647 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,844 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.3189e-04 C and 5.2718e-04 C separated by 1.339 m | Two point charges q1 = 6.3189e-04 C and q2 = 5.2718e-04 C are separated by distance r = 1.339 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1670 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,845 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.0638e-04 C and -2.2697e-04 C separated by 0.05423 m | Two point charges q1 = 8.0638e-04 C and q2 = -2.2697e-04 C are separated by distance r = 0.05423 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5.5938e+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. |
5,846 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.7292e-04 C and 4.9938e-04 C separated by 1.451 m | Two point charges q1 = 2.7292e-04 C and q2 = 4.9938e-04 C are separated by distance r = 1.451 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 581.5 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. |
5,847 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.2235e-05 C and 8.0187e-04 C separated by 0.5227 m | Two point charges q1 = 5.2235e-05 C and q2 = 8.0187e-04 C are separated by distance r = 0.5227 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1378 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,848 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.5546e-04 C and -8.8087e-04 C separated by 0.505 m | Two point charges q1 = -5.5546e-04 C and q2 = -8.8087e-04 C are separated by distance r = 0.505 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.7244e+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. |
5,849 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.2613e-04 C and 4.1323e-04 C separated by 0.8057 m | Two point charges q1 = -9.2613e-04 C and q2 = 4.1323e-04 C are separated by distance r = 0.8057 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5299 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,850 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.9979e-04 C and -1.6328e-04 C separated by 0.9675 m | Two point charges q1 = 2.9979e-04 C and q2 = -1.6328e-04 C are separated by distance r = 0.9675 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 470 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,851 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.7519e-04 C and -4.3619e-04 C separated by 1.632 m | Two point charges q1 = -7.7519e-04 C and q2 = -4.3619e-04 C are separated by distance r = 1.632 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1141 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,852 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.1481e-04 C and -3.3445e-04 C separated by 0.7471 m | Two point charges q1 = -4.1481e-04 C and q2 = -3.3445e-04 C are separated by distance r = 0.7471 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2234 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,853 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.3645e-04 C and 9.2791e-04 C separated by 0.7987 m | Two point charges q1 = 2.3645e-04 C and q2 = 9.2791e-04 C are separated by distance r = 0.7987 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3091 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,854 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.0591e-04 C and -2.8718e-04 C separated by 1.225 m | Two point charges q1 = -4.0591e-04 C and q2 = -2.8718e-04 C are separated by distance r = 1.225 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 698.1 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. |
5,855 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.3678e-04 C and 5.9385e-04 C separated by 1.708 m | Two point charges q1 = -3.3678e-04 C and q2 = 5.9385e-04 C are separated by distance r = 1.708 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 616.2 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. |
5,856 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.3013e-05 C and -1.5090e-04 C separated by 0.8628 m | Two point charges q1 = -8.3013e-05 C and q2 = -1.5090e-04 C are separated by distance r = 0.8628 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 151.2 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. |
5,857 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.3444e-04 C and -9.9185e-04 C separated by 0.01415 m | Two point charges q1 = -9.3444e-04 C and q2 = -9.9185e-04 C are separated by distance r = 0.01415 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4.1581e+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. |
5,858 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.3652e-05 C and 9.8372e-04 C separated by 0.7399 m | Two point charges q1 = -3.3652e-05 C and q2 = 9.8372e-04 C are separated by distance r = 0.7399 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 543.5 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. |
5,859 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.6639e-04 C and -4.1389e-05 C separated by 1.787 m | Two point charges q1 = 6.6639e-04 C and q2 = -4.1389e-05 C are separated by distance r = 1.787 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 77.64 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,860 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.0087e-04 C and -9.8820e-04 C separated by 1.233 m | Two point charges q1 = 1.0087e-04 C and q2 = -9.8820e-04 C are separated by distance r = 1.233 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 589.7 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. |
5,861 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.8975e-04 C and 8.2437e-04 C separated by 0.9858 m | Two point charges q1 = -7.8975e-04 C and q2 = 8.2437e-04 C are separated by distance r = 0.9858 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6021 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,862 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.9378e-04 C and -8.3197e-04 C separated by 0.576 m | Two point charges q1 = 5.9378e-04 C and q2 = -8.3197e-04 C are separated by distance r = 0.576 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.3380e+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. |
5,863 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.6287e-04 C and 1.5824e-04 C separated by 1.554 m | Two point charges q1 = -4.6287e-04 C and q2 = 1.5824e-04 C are separated by distance r = 1.554 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 272.5 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. |
5,864 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.9692e-04 C and -6.8934e-04 C separated by 0.07375 m | Two point charges q1 = -4.9692e-04 C and q2 = -6.8934e-04 C are separated by distance r = 0.07375 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5.6607e+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. |
5,865 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.6534e-04 C and 8.1046e-04 C separated by 0.7239 m | Two point charges q1 = 6.6534e-04 C and q2 = 8.1046e-04 C are separated by distance r = 0.7239 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 9248 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
5,866 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.9436e-04 C and 4.1855e-04 C separated by 1.862 m | Two point charges q1 = 2.9436e-04 C and q2 = 4.1855e-04 C are separated by distance r = 1.862 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 319.5 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. |
5,867 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.5889e+04 Hz, speed 1317 m/s | A periodic wave travels at speed v = 1317 m/s with frequency f = 1.5889e+04 Hz. The wavelength is λ = v / f = 0.08286 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,868 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3332e+04 Hz, speed 552.7 m/s | A periodic wave travels at speed v = 552.7 m/s with frequency f = 1.3332e+04 Hz. The wavelength is λ = v / f = 0.04145 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,869 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9237 Hz, speed 1144 m/s | A periodic wave travels at speed v = 1144 m/s with frequency f = 9237 Hz. The wavelength is λ = v / f = 0.1238 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,870 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 755.2 Hz, speed 370.5 m/s | A periodic wave travels at speed v = 370.5 m/s with frequency f = 755.2 Hz. The wavelength is λ = v / f = 0.4906 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,871 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7505e+04 Hz, speed 477.2 m/s | A periodic wave travels at speed v = 477.2 m/s with frequency f = 1.7505e+04 Hz. The wavelength is λ = v / f = 0.02726 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,872 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9965e+04 Hz, speed 451.3 m/s | A periodic wave travels at speed v = 451.3 m/s with frequency f = 1.9965e+04 Hz. The wavelength is λ = v / f = 0.02261 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,873 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4461e+04 Hz, speed 639 m/s | A periodic wave travels at speed v = 639 m/s with frequency f = 1.4461e+04 Hz. The wavelength is λ = v / f = 0.04419 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,874 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6668 Hz, speed 683.9 m/s | A periodic wave travels at speed v = 683.9 m/s with frequency f = 6668 Hz. The wavelength is λ = v / f = 0.1026 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,875 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4800 Hz, speed 877.9 m/s | A periodic wave travels at speed v = 877.9 m/s with frequency f = 4800 Hz. The wavelength is λ = v / f = 0.1829 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,876 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 8209 Hz, speed 1416 m/s | A periodic wave travels at speed v = 1416 m/s with frequency f = 8209 Hz. The wavelength is λ = v / f = 0.1725 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,877 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3372e+04 Hz, speed 1106 m/s | A periodic wave travels at speed v = 1106 m/s with frequency f = 1.3372e+04 Hz. The wavelength is λ = v / f = 0.08271 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,878 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4593e+04 Hz, speed 663.1 m/s | A periodic wave travels at speed v = 663.1 m/s with frequency f = 1.4593e+04 Hz. The wavelength is λ = v / f = 0.04544 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,879 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4188e+04 Hz, speed 1375 m/s | A periodic wave travels at speed v = 1375 m/s with frequency f = 1.4188e+04 Hz. The wavelength is λ = v / f = 0.09689 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,880 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3131e+04 Hz, speed 737.1 m/s | A periodic wave travels at speed v = 737.1 m/s with frequency f = 1.3131e+04 Hz. The wavelength is λ = v / f = 0.05613 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,881 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 7828 Hz, speed 714.1 m/s | A periodic wave travels at speed v = 714.1 m/s with frequency f = 7828 Hz. The wavelength is λ = v / f = 0.09122 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,882 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 997.3 Hz, speed 1309 m/s | A periodic wave travels at speed v = 1309 m/s with frequency f = 997.3 Hz. The wavelength is λ = v / f = 1.313 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,883 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6076e+04 Hz, speed 767.5 m/s | A periodic wave travels at speed v = 767.5 m/s with frequency f = 1.6076e+04 Hz. The wavelength is λ = v / f = 0.04774 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,884 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6254e+04 Hz, speed 856.2 m/s | A periodic wave travels at speed v = 856.2 m/s with frequency f = 1.6254e+04 Hz. The wavelength is λ = v / f = 0.05268 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,885 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9332e+04 Hz, speed 1240 m/s | A periodic wave travels at speed v = 1240 m/s with frequency f = 1.9332e+04 Hz. The wavelength is λ = v / f = 0.06417 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,886 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7254e+04 Hz, speed 839.5 m/s | A periodic wave travels at speed v = 839.5 m/s with frequency f = 1.7254e+04 Hz. The wavelength is λ = v / f = 0.04866 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,887 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.6319e+04 Hz, speed 1194 m/s | A periodic wave travels at speed v = 1194 m/s with frequency f = 1.6319e+04 Hz. The wavelength is λ = v / f = 0.07319 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,888 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4154e+04 Hz, speed 1090 m/s | A periodic wave travels at speed v = 1090 m/s with frequency f = 1.4154e+04 Hz. The wavelength is λ = v / f = 0.07702 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,889 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9162e+04 Hz, speed 1202 m/s | A periodic wave travels at speed v = 1202 m/s with frequency f = 1.9162e+04 Hz. The wavelength is λ = v / f = 0.06272 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,890 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7365e+04 Hz, speed 520.8 m/s | A periodic wave travels at speed v = 520.8 m/s with frequency f = 1.7365e+04 Hz. The wavelength is λ = v / f = 0.02999 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,891 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7386e+04 Hz, speed 497 m/s | A periodic wave travels at speed v = 497 m/s with frequency f = 1.7386e+04 Hz. The wavelength is λ = v / f = 0.02859 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,892 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5027 Hz, speed 411.9 m/s | A periodic wave travels at speed v = 411.9 m/s with frequency f = 5027 Hz. The wavelength is λ = v / f = 0.08193 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,893 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7513e+04 Hz, speed 701.5 m/s | A periodic wave travels at speed v = 701.5 m/s with frequency f = 1.7513e+04 Hz. The wavelength is λ = v / f = 0.04005 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,894 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 859.7 Hz, speed 468.4 m/s | A periodic wave travels at speed v = 468.4 m/s with frequency f = 859.7 Hz. The wavelength is λ = v / f = 0.5449 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,895 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0265e+04 Hz, speed 894.4 m/s | A periodic wave travels at speed v = 894.4 m/s with frequency f = 1.0265e+04 Hz. The wavelength is λ = v / f = 0.08713 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,896 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5572 Hz, speed 542.7 m/s | A periodic wave travels at speed v = 542.7 m/s with frequency f = 5572 Hz. The wavelength is λ = v / f = 0.0974 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,897 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3627 Hz, speed 346.1 m/s | A periodic wave travels at speed v = 346.1 m/s with frequency f = 3627 Hz. The wavelength is λ = v / f = 0.09544 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,898 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 204.3 Hz, speed 732.9 m/s | A periodic wave travels at speed v = 732.9 m/s with frequency f = 204.3 Hz. The wavelength is λ = v / f = 3.587 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,899 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6872 Hz, speed 1038 m/s | A periodic wave travels at speed v = 1038 m/s with frequency f = 6872 Hz. The wavelength is λ = v / f = 0.151 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
5,900 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6757 Hz, speed 425.5 m/s | A periodic wave travels at speed v = 425.5 m/s with frequency f = 6757 Hz. The wavelength is λ = v / f = 0.06298 m. This relation follows from the definition of frequency as the number of cycles per unit time and wavelength as the spatial period. | v = f λ | basic kinematics | Relate wave speed, frequency, and wavelength. |
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