Exercises: Coulomb's Law

Two small charged spheres, $q_1 = 2.0 \times 10^{-6}\ \text{C}$ and $q_2 = 3.0 \times 10^{-6}\ \text{C}$, are placed $0.30\ \text{m}$ apart in air. Use $k = 8.99 \times 10^{9}\ \text{N·m}^2/\text{C}^2$ to calculate the magnitude of the electric force between them. Write your answer in scientific notation. State whether the force is attractive or repulsive.

Coulomb's law says $F = k\dfrac{|q_1 q_2|}{r^2}$. Two charged balloons repel each other. Without calculating, state what happens to the magnitude of the force if the distance between the centers of the balloons is doubled and the charges stay the same.

A proton and an electron in a hydrogen atom are separated by $5.3 \times 10^{-11}\ \text{m}$. Each has a charge of magnitude $1.60 \times 10^{-19}\ \text{C}$. Use $k = 8.99 \times 10^{9}\ \text{N·m}^2/\text{C}^2$ to find the magnitude of the electric force between them. Give your answer in scientific notation.

Two point charges exert a force of $12\ \text{N}$ on each other when they are $0.10\ \text{m}$ apart. Without changing the charges, Emma moves them to a separation of $0.40\ \text{m}$. Find the new force magnitude. Then find the force if, from the original setup, she instead triples one charge and keeps the distance at $0.10\ \text{m}$.

In a lab, Malik measures the force between two small charged spheres at different separations and records the data below. Both charges stay fixed.

1. a) Show that the data are consistent with an inverse-square relationship.
2. b) Predict the force at $r = 0.025\ \text{m}$.

Two identical small spheres each carry a charge of $+4.0 \times 10^{-7}\ \text{C}$ and are held $0.15\ \text{m}$ apart. Use $k = 8.99 \times 10^{9}\ \text{N·m}^2/\text{C}^2$.

1. a) Calculate the force one sphere exerts on the other.
2. b) Each sphere has a mass of $2.0 \times 10^{-3}\ \text{kg}$. Find the magnitude of the initial acceleration of one sphere when it is released.

Three point charges lie on a straight line (the $x$-axis): $q_A = +2.0\ \mu\text{C}$ at $x = 0$, $q_B = -3.0\ \mu\text{C}$ at $x = 0.20\ \text{m}$, and $q_C = +4.0\ \mu\text{C}$ at $x = 0.50\ \text{m}$. Use $k = 8.99 \times 10^{9}\ \text{N·m}^2/\text{C}^2$ and $1\ \mu\text{C} = 10^{-6}\ \text{C}$.

1. a) Find the force exerted on $q_B$ by $q_A$ and the force exerted on $q_B$ by $q_C$, each with its direction.
2. b) Find the net force on $q_B$, giving magnitude and direction.
3. c) Explain why the net force on $q_B$ is not the same as the net force on $q_A$.

A charge $q_1 = +9.0\ \mu\text{C}$ is fixed at $x = 0$ and a charge $q_2 = +1.0\ \mu\text{C}$ is fixed at $x = 0.40\ \text{m}$. A small third charge $q_3$ is placed on the line between them.

1. a) Find the position $x$ where the net force on $q_3$ is zero. Show that your answer does not depend on the sign or size of $q_3$.
2. b) Suppose $q_2$ were changed to $-1.0\ \mu\text{C}$. Explain, using the directions of the forces, whether there is still a point between the charges where the net force on $q_3$ is zero.