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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601 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.1507e-04 C and 2.5036e-04 C separated by 0.2358 m | Two point charges q1 = 3.1507e-04 C and q2 = 2.5036e-04 C are separated by distance r = 0.2358 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.2755e+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. |
602 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.9954e-04 C and 9.1363e-04 C separated by 0.2443 m | Two point charges q1 = -4.9954e-04 C and q2 = 9.1363e-04 C are separated by distance r = 0.2443 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6.8704e+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. |
603 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.0433e-04 C and -9.9637e-04 C separated by 0.5783 m | Two point charges q1 = 7.0433e-04 C and q2 = -9.9637e-04 C are separated by distance r = 0.5783 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.8860e+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. |
604 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.0098e-04 C and -8.5297e-04 C separated by 0.9096 m | Two point charges q1 = 2.0098e-04 C and q2 = -8.5297e-04 C are separated by distance r = 0.9096 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1862 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
605 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.9727e-04 C and 6.6817e-04 C separated by 1.422 m | Two point charges q1 = 9.9727e-04 C and q2 = 6.6817e-04 C are separated by distance r = 1.422 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2962 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
606 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.9144e-04 C and -7.1210e-04 C separated by 1.855 m | Two point charges q1 = 8.9144e-04 C and q2 = -7.1210e-04 C are separated by distance r = 1.855 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1657 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
607 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.9390e-04 C and -1.2224e-04 C separated by 0.41 m | Two point charges q1 = -7.9390e-04 C and q2 = -1.2224e-04 C are separated by distance r = 0.41 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5190 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
608 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.3750e-04 C and 2.7258e-05 C separated by 1.113 m | Two point charges q1 = -2.3750e-04 C and q2 = 2.7258e-05 C are separated by distance r = 1.113 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 47.01 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
609 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.6794e-04 C and -6.1234e-04 C separated by 0.1816 m | Two point charges q1 = 4.6794e-04 C and q2 = -6.1234e-04 C are separated by distance r = 0.1816 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 7.8116e+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. |
610 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.9876e-04 C and 5.2617e-04 C separated by 1.541 m | Two point charges q1 = 3.9876e-04 C and q2 = 5.2617e-04 C are separated by distance r = 1.541 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 794.5 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. |
611 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.2620e-04 C and 6.4270e-04 C separated by 0.9054 m | Two point charges q1 = -1.2620e-04 C and q2 = 6.4270e-04 C are separated by distance r = 0.9054 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 889.2 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. |
612 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.2921e-04 C and -7.6801e-04 C separated by 0.2668 m | Two point charges q1 = 1.2921e-04 C and q2 = -7.6801e-04 C are separated by distance r = 0.2668 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.2531e+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. |
613 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.3156e-04 C and -3.0482e-04 C separated by 0.3323 m | Two point charges q1 = -8.3156e-04 C and q2 = -3.0482e-04 C are separated by distance r = 0.3323 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.0629e+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. |
614 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.4668e-04 C and 8.4609e-04 C separated by 0.5087 m | Two point charges q1 = -3.4668e-04 C and q2 = 8.4609e-04 C are separated by distance r = 0.5087 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.0187e+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. |
615 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.2605e-04 C and 6.1481e-04 C separated by 0.1959 m | Two point charges q1 = 1.2605e-04 C and q2 = 6.1481e-04 C are separated by distance r = 0.1959 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.8144e+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. |
616 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.9222e-04 C and -1.7203e-04 C separated by 1.253 m | Two point charges q1 = -5.9222e-04 C and q2 = -1.7203e-04 C are separated by distance r = 1.253 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 583.5 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. |
617 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.4269e-04 C and -8.2541e-04 C separated by 0.06646 m | Two point charges q1 = 8.4269e-04 C and q2 = -8.2541e-04 C are separated by distance r = 0.06646 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.4152e+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. |
618 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -9.4860e-04 C and 6.5148e-04 C separated by 1.536 m | Two point charges q1 = -9.4860e-04 C and q2 = 6.5148e-04 C are separated by distance r = 1.536 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2353 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
619 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.1849e-04 C and -4.9854e-04 C separated by 1.258 m | Two point charges q1 = 6.1849e-04 C and q2 = -4.9854e-04 C are separated by distance r = 1.258 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1751 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
620 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.4227e-04 C and 4.8346e-04 C separated by 1.611 m | Two point charges q1 = 6.4227e-04 C and q2 = 4.8346e-04 C are separated by distance r = 1.611 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1075 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
621 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 2.9814e-04 C and -6.8892e-04 C separated by 0.3246 m | Two point charges q1 = 2.9814e-04 C and q2 = -6.8892e-04 C are separated by distance r = 0.3246 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.7522e+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. |
622 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.8477e-04 C and -3.4085e-04 C separated by 0.2959 m | Two point charges q1 = 4.8477e-04 C and q2 = -3.4085e-04 C are separated by distance r = 0.2959 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.6961e+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. |
623 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.3447e-04 C and 9.7540e-04 C separated by 0.2702 m | Two point charges q1 = 7.3447e-04 C and q2 = 9.7540e-04 C are separated by distance r = 0.2702 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8.8175e+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. |
624 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.1547e-04 C and -3.1980e-04 C separated by 0.9383 m | Two point charges q1 = 5.1547e-04 C and q2 = -3.1980e-04 C are separated by distance r = 0.9383 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1683 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
625 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.5015e-04 C and -9.7715e-05 C separated by 0.5875 m | Two point charges q1 = 4.5015e-04 C and q2 = -9.7715e-05 C are separated by distance r = 0.5875 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1145 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
626 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.6430e-04 C and 2.4902e-04 C separated by 1.732 m | Two point charges q1 = 8.6430e-04 C and q2 = 2.4902e-04 C are separated by distance r = 1.732 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 644.9 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. |
627 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.1366e-04 C and 1.9064e-04 C separated by 0.3271 m | Two point charges q1 = -8.1366e-04 C and q2 = 1.9064e-04 C are separated by distance r = 0.3271 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.3031e+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. |
628 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.9926e-04 C and 4.9787e-04 C separated by 0.1892 m | Two point charges q1 = 4.9926e-04 C and q2 = 4.9787e-04 C are separated by distance r = 0.1892 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6.2410e+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. |
629 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.0594e-04 C and -2.1593e-04 C separated by 0.7123 m | Two point charges q1 = 5.0594e-04 C and q2 = -2.1593e-04 C are separated by distance r = 0.7123 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1935 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
630 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.8207e-04 C and 2.8646e-04 C separated by 0.02627 m | Two point charges q1 = -2.8207e-04 C and q2 = 2.8646e-04 C are separated by distance r = 0.02627 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.0521e+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. |
631 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.3150e-04 C and 7.2778e-04 C separated by 1.53 m | Two point charges q1 = -4.3150e-04 C and q2 = 7.2778e-04 C are separated by distance r = 1.53 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1206 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
632 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 4.6197e-05 C and -5.7071e-04 C separated by 0.3974 m | Two point charges q1 = 4.6197e-05 C and q2 = -5.7071e-04 C are separated by distance r = 0.3974 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1501 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
633 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.4458e-05 C and 7.6464e-04 C separated by 0.5666 m | Two point charges q1 = 7.4458e-05 C and q2 = 7.6464e-04 C are separated by distance r = 0.5666 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1594 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
634 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.2953e-04 C and -3.9451e-04 C separated by 1.592 m | Two point charges q1 = -1.2953e-04 C and q2 = -3.9451e-04 C are separated by distance r = 1.592 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 181.3 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. |
635 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.5827e-04 C and 7.5521e-04 C separated by 0.4061 m | Two point charges q1 = 5.5827e-04 C and q2 = 7.5521e-04 C are separated by distance r = 0.4061 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2.2974e+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. |
636 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.0058e-04 C and -3.9875e-05 C separated by 1.43 m | Two point charges q1 = 5.0058e-04 C and q2 = -3.9875e-05 C are separated by distance r = 1.43 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 87.72 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
637 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.1981e-04 C and -6.0665e-04 C separated by 1.036 m | Two point charges q1 = 5.1981e-04 C and q2 = -6.0665e-04 C are separated by distance r = 1.036 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2641 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
638 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.3144e-04 C and 1.6334e-04 C separated by 1.981 m | Two point charges q1 = 9.3144e-04 C and q2 = 1.6334e-04 C are separated by distance r = 1.981 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 348.3 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. |
639 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.9413e-04 C and 7.0903e-04 C separated by 0.6066 m | Two point charges q1 = 5.9413e-04 C and q2 = 7.0903e-04 C are separated by distance r = 0.6066 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.0290e+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. |
640 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -3.6899e-04 C and -9.7992e-04 C separated by 1.172 m | Two point charges q1 = -3.6899e-04 C and q2 = -9.7992e-04 C are separated by distance r = 1.172 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2368 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
641 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.9731e-04 C and 9.6710e-04 C separated by 1.568 m | Two point charges q1 = -5.9731e-04 C and q2 = 9.6710e-04 C are separated by distance r = 1.568 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2112 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
642 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.2168e-04 C and 1.7134e-04 C separated by 1.262 m | Two point charges q1 = -7.2168e-04 C and q2 = 1.7134e-04 C are separated by distance r = 1.262 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. |
643 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 1.4863e-04 C and -3.2539e-05 C separated by 1.897 m | Two point charges q1 = 1.4863e-04 C and q2 = -3.2539e-05 C are separated by distance r = 1.897 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 12.08 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
644 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -1.9159e-04 C and 3.1438e-04 C separated by 0.3113 m | Two point charges q1 = -1.9159e-04 C and q2 = 3.1438e-04 C are separated by distance r = 0.3113 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5584 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
645 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.1097e-04 C and 8.7294e-04 C separated by 1.474 m | Two point charges q1 = -4.1097e-04 C and q2 = 8.7294e-04 C are separated by distance r = 1.474 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1483 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
646 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -7.0607e-04 C and -5.6133e-04 C separated by 1.996 m | Two point charges q1 = -7.0607e-04 C and q2 = -5.6133e-04 C are separated by distance r = 1.996 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 893.9 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. |
647 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.2595e-04 C and 9.5673e-04 C separated by 0.9247 m | Two point charges q1 = 5.2595e-04 C and q2 = 9.5673e-04 C are separated by distance r = 0.9247 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 5289 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
648 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 5.4673e-04 C and 6.1047e-04 C separated by 0.3926 m | Two point charges q1 = 5.4673e-04 C and q2 = 6.1047e-04 C are separated by distance r = 0.3926 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.9461e+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. |
649 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.7973e-04 C and 2.2564e-04 C separated by 1.946 m | Two point charges q1 = -2.7973e-04 C and q2 = 2.2564e-04 C are separated by distance r = 1.946 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 149.8 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. |
650 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.7140e-04 C and -6.9055e-04 C separated by 0.9831 m | Two point charges q1 = 7.7140e-04 C and q2 = -6.9055e-04 C are separated by distance r = 0.9831 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4953 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
651 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 3.4945e-04 C and 2.8850e-04 C separated by 1.151 m | Two point charges q1 = 3.4945e-04 C and q2 = 2.8850e-04 C are separated by distance r = 1.151 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 683.7 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. |
652 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.9586e-04 C and 8.1856e-04 C separated by 1.91 m | Two point charges q1 = 8.9586e-04 C and q2 = 8.1856e-04 C are separated by distance r = 1.91 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1807 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
653 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -2.9116e-04 C and 9.5536e-04 C separated by 0.1673 m | Two point charges q1 = -2.9116e-04 C and q2 = 9.5536e-04 C are separated by distance r = 0.1673 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 8.9354e+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. |
654 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.5632e-04 C and 2.1477e-04 C separated by 1.658 m | Two point charges q1 = 6.5632e-04 C and q2 = 2.1477e-04 C are separated by distance r = 1.658 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 461.1 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. |
655 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 9.3309e-04 C and 1.3814e-04 C separated by 1.235 m | Two point charges q1 = 9.3309e-04 C and q2 = 1.3814e-04 C are separated by distance r = 1.235 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 759.3 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. |
656 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1745e+04 Hz, speed 590.9 m/s | A periodic wave travels at speed v = 590.9 m/s with frequency f = 1.1745e+04 Hz. The wavelength is λ = v / f = 0.05032 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. |
657 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3403e+04 Hz, speed 937.2 m/s | A periodic wave travels at speed v = 937.2 m/s with frequency f = 1.3403e+04 Hz. The wavelength is λ = v / f = 0.06993 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. |
658 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.2766e+04 Hz, speed 363 m/s | A periodic wave travels at speed v = 363 m/s with frequency f = 1.2766e+04 Hz. The wavelength is λ = v / f = 0.02843 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. |
659 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 8278 Hz, speed 1161 m/s | A periodic wave travels at speed v = 1161 m/s with frequency f = 8278 Hz. The wavelength is λ = v / f = 0.1402 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. |
660 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2029 Hz, speed 1225 m/s | A periodic wave travels at speed v = 1225 m/s with frequency f = 2029 Hz. The wavelength is λ = v / f = 0.6037 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. |
661 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 123.5 Hz, speed 960.4 m/s | A periodic wave travels at speed v = 960.4 m/s with frequency f = 123.5 Hz. The wavelength is λ = v / f = 7.775 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. |
662 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8583e+04 Hz, speed 788.3 m/s | A periodic wave travels at speed v = 788.3 m/s with frequency f = 1.8583e+04 Hz. The wavelength is λ = v / f = 0.04242 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. |
663 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8702e+04 Hz, speed 1354 m/s | A periodic wave travels at speed v = 1354 m/s with frequency f = 1.8702e+04 Hz. The wavelength is λ = v / f = 0.0724 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. |
664 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9559 Hz, speed 539.3 m/s | A periodic wave travels at speed v = 539.3 m/s with frequency f = 9559 Hz. The wavelength is λ = v / f = 0.05642 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. |
665 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9279e+04 Hz, speed 685.4 m/s | A periodic wave travels at speed v = 685.4 m/s with frequency f = 1.9279e+04 Hz. The wavelength is λ = v / f = 0.03555 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. |
666 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.2925e+04 Hz, speed 1390 m/s | A periodic wave travels at speed v = 1390 m/s with frequency f = 1.2925e+04 Hz. The wavelength is λ = v / f = 0.1075 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. |
667 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1807 Hz, speed 989 m/s | A periodic wave travels at speed v = 989 m/s with frequency f = 1807 Hz. The wavelength is λ = v / f = 0.5472 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. |
668 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0712e+04 Hz, speed 1168 m/s | A periodic wave travels at speed v = 1168 m/s with frequency f = 1.0712e+04 Hz. The wavelength is λ = v / f = 0.109 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. |
669 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.8735e+04 Hz, speed 1396 m/s | A periodic wave travels at speed v = 1396 m/s with frequency f = 1.8735e+04 Hz. The wavelength is λ = v / f = 0.07451 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. |
670 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3518 Hz, speed 1359 m/s | A periodic wave travels at speed v = 1359 m/s with frequency f = 3518 Hz. The wavelength is λ = v / f = 0.3862 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. |
671 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3532 Hz, speed 1404 m/s | A periodic wave travels at speed v = 1404 m/s with frequency f = 3532 Hz. The wavelength is λ = v / f = 0.3974 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. |
672 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9943e+04 Hz, speed 776.4 m/s | A periodic wave travels at speed v = 776.4 m/s with frequency f = 1.9943e+04 Hz. The wavelength is λ = v / f = 0.03893 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. |
673 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9918 Hz, speed 1424 m/s | A periodic wave travels at speed v = 1424 m/s with frequency f = 9918 Hz. The wavelength is λ = v / f = 0.1436 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. |
674 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9243e+04 Hz, speed 1411 m/s | A periodic wave travels at speed v = 1411 m/s with frequency f = 1.9243e+04 Hz. The wavelength is λ = v / f = 0.07334 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. |
675 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7537e+04 Hz, speed 311.1 m/s | A periodic wave travels at speed v = 311.1 m/s with frequency f = 1.7537e+04 Hz. The wavelength is λ = v / f = 0.01774 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. |
676 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1368e+04 Hz, speed 428.8 m/s | A periodic wave travels at speed v = 428.8 m/s with frequency f = 1.1368e+04 Hz. The wavelength is λ = v / f = 0.03772 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. |
677 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9660e+04 Hz, speed 641.5 m/s | A periodic wave travels at speed v = 641.5 m/s with frequency f = 1.9660e+04 Hz. The wavelength is λ = v / f = 0.03263 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. |
678 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9782e+04 Hz, speed 952 m/s | A periodic wave travels at speed v = 952 m/s with frequency f = 1.9782e+04 Hz. The wavelength is λ = v / f = 0.04812 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. |
679 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 9888 Hz, speed 1426 m/s | A periodic wave travels at speed v = 1426 m/s with frequency f = 9888 Hz. The wavelength is λ = v / f = 0.1442 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. |
680 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7024e+04 Hz, speed 861.6 m/s | A periodic wave travels at speed v = 861.6 m/s with frequency f = 1.7024e+04 Hz. The wavelength is λ = v / f = 0.05061 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. |
681 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3872 Hz, speed 435.2 m/s | A periodic wave travels at speed v = 435.2 m/s with frequency f = 3872 Hz. The wavelength is λ = v / f = 0.1124 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. |
682 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3267 Hz, speed 850.7 m/s | A periodic wave travels at speed v = 850.7 m/s with frequency f = 3267 Hz. The wavelength is λ = v / f = 0.2604 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. |
683 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 5160 Hz, speed 523.4 m/s | A periodic wave travels at speed v = 523.4 m/s with frequency f = 5160 Hz. The wavelength is λ = v / f = 0.1014 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. |
684 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4738e+04 Hz, speed 1249 m/s | A periodic wave travels at speed v = 1249 m/s with frequency f = 1.4738e+04 Hz. The wavelength is λ = v / f = 0.08474 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. |
685 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.1364e+04 Hz, speed 1209 m/s | A periodic wave travels at speed v = 1209 m/s with frequency f = 1.1364e+04 Hz. The wavelength is λ = v / f = 0.1064 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. |
686 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 3526 Hz, speed 1327 m/s | A periodic wave travels at speed v = 1327 m/s with frequency f = 3526 Hz. The wavelength is λ = v / f = 0.3764 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. |
687 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.7943e+04 Hz, speed 1292 m/s | A periodic wave travels at speed v = 1292 m/s with frequency f = 1.7943e+04 Hz. The wavelength is λ = v / f = 0.07203 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. |
688 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0315e+04 Hz, speed 404.1 m/s | A periodic wave travels at speed v = 404.1 m/s with frequency f = 1.0315e+04 Hz. The wavelength is λ = v / f = 0.03917 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. |
689 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3392e+04 Hz, speed 521.7 m/s | A periodic wave travels at speed v = 521.7 m/s with frequency f = 1.3392e+04 Hz. The wavelength is λ = v / f = 0.03896 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. |
690 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2829 Hz, speed 688.3 m/s | A periodic wave travels at speed v = 688.3 m/s with frequency f = 2829 Hz. The wavelength is λ = v / f = 0.2433 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. |
691 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4976 Hz, speed 612.9 m/s | A periodic wave travels at speed v = 612.9 m/s with frequency f = 4976 Hz. The wavelength is λ = v / f = 0.1232 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. |
692 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 4726 Hz, speed 1205 m/s | A periodic wave travels at speed v = 1205 m/s with frequency f = 4726 Hz. The wavelength is λ = v / f = 0.2549 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. |
693 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.9082e+04 Hz, speed 662.3 m/s | A periodic wave travels at speed v = 662.3 m/s with frequency f = 1.9082e+04 Hz. The wavelength is λ = v / f = 0.03471 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. |
694 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4463e+04 Hz, speed 313.7 m/s | A periodic wave travels at speed v = 313.7 m/s with frequency f = 1.4463e+04 Hz. The wavelength is λ = v / f = 0.02169 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. |
695 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.3081e+04 Hz, speed 1131 m/s | A periodic wave travels at speed v = 1131 m/s with frequency f = 1.3081e+04 Hz. The wavelength is λ = v / f = 0.08649 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. |
696 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1261 Hz, speed 441.9 m/s | A periodic wave travels at speed v = 441.9 m/s with frequency f = 1261 Hz. The wavelength is λ = v / f = 0.3503 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. |
697 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 6150 Hz, speed 786.5 m/s | A periodic wave travels at speed v = 786.5 m/s with frequency f = 6150 Hz. The wavelength is λ = v / f = 0.1279 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. |
698 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.0060e+04 Hz, speed 1374 m/s | A periodic wave travels at speed v = 1374 m/s with frequency f = 1.0060e+04 Hz. The wavelength is λ = v / f = 0.1366 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. |
699 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 1.4077e+04 Hz, speed 673.2 m/s | A periodic wave travels at speed v = 673.2 m/s with frequency f = 1.4077e+04 Hz. The wavelength is λ = v / f = 0.04782 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. |
700 | physics | waves | wave_speed | 4 | worked_example | Wave relation: frequency 2366 Hz, speed 1399 m/s | A periodic wave travels at speed v = 1399 m/s with frequency f = 2366 Hz. The wavelength is λ = v / f = 0.5915 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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