Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

24. Electric Force & Field; Gauss' Law

Coulomb's Law (Electric Force)

Physics

24. Electric Force & Field; Gauss' Law

Coulomb's Law (Electric Force)

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Multiple Choice

There is a $- 4.00 nC$ charge at the origin. A $9.00 nC$ charge is on the x-axis at $x = 2.00 m$ . A $5.00 nC$ charge is on the y-axis at $y = - 1.00 m$ . What is the total force on the $- 4.00 nC$ charge at the origin? Give your answer as a magnitude and an angle counterclockwise from the positive x-axis.

1.97 \times 10^{- 7} N, 66 .3 °

1.80 \times 10^{- 7} N, 294 °

1.80 \times 10^{- 7} N, 66 .3 °

8.12 \times 10^{- 8} N, 294 °

8.12 \times 10^{- 8} N, 66 .3 °

1.97 \times 10^{- 7} N, 294 °

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Verified step by step guidance

First, identify the charges involved and their positions: a -4.00 nC charge at the origin, a 9.00 nC charge at x = 2.00 m, and a 5.00 nC charge at y = -1.00 m.

Use Coulomb's Law to calculate the force between the -4.00 nC charge at the origin and the 9.00 nC charge on the x-axis. The formula is:

F = \frac{k q q'}{r^{2}}

, where k is Coulomb's constant, q and q' are the charges, and r is the distance between them.

Calculate the force between the -4.00 nC charge at the origin and the 5.00 nC charge on the y-axis using the same Coulomb's Law formula. Note the direction of the force vectors: the force due to the 9.00 nC charge is along the x-axis, and the force due to the 5.00 nC charge is along the y-axis.

Determine the net force on the -4.00 nC charge by vector addition of the forces calculated in the previous steps. Use the Pythagorean theorem to find the magnitude of the resultant force: