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?

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 aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. What fraction of all the electrons in each sphere does this represent?

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?

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 the two charges are equal?

Two small aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude $1.00\times {10}^4$ N (roughly $1$ ton)? Assume that the spheres may be treated as point charges.

The nuclei of large atoms, such as uranium, with $92$ protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4\(\times\)10^{-15}$ m. What magnitude of electric field does it produce at the distance of the electrons, which is about $1.0\times {10}^{-10}$ m?