24. Electric Force & Field; Gauss' Law

If the force between two charges is F when the distance is d, what will the force between the two charges be if they were moved to a distance of 2d?

In which direction will the −1 C charge move? If it has a mass of 10 g, what will its initial acceleration be?

What is the direction of the net force on the charge at the center of the square in the following figure?

Three point charges are arranged along the $x$-axis. Charge $q_1=+3.00$ $\mu$C is at the origin, and charge $q_2=-5.00$ $\mu$C is at $x=0.200$ m. Charge $q_2=-8.00$ $\mu$C. Where is $q_3$ located if the net force on $q_1$ is $7.00$ N in the $-x$-direction?

Three point charges are arranged on a line. Charge $q_3=+5.00$ nC and is at the origin. Charge $q_2=-3.00$ nC and is at $x=+4.00$ cm. Charge $q_1$ is at $x=+2.00$ cm. What is $q_1$ (magnitude and sign) if the net force on $q_3$ is zero?

Suppose you had two small boxes, each containing $1.0$ g of protons.

(a) If one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light (and very long!) string, what would be the tension in the string? Express your answer in newtons and in pounds. Do you need to take into account the gravitational forces of the earth and moon on the protons? Why?

(b) What gravitational force would each box of protons exert on the other box?

Two small plastic spheres are given positive electric charges. When they are $15.0$ cm apart, the repulsive force between them has magnitude $0.220$ N. What is the charge on each sphere if one sphere has four times the charge of the other?