24. Electric Force & Field; Gauss' Law

As a rough rule, anything traveling faster than about 0.1c is called relativistic—that is, special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom (radius 0.53 x 10^-10 m) and state whether or not it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.)

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?

Compare the electric force holding the electron in orbit (r = 0.53 x 10^-10) around the proton nucleus of the hydrogen atom, with the gravitational force between the same electron and proton. Give the ratio of these two forces.

Which of the following best describes Coulomb’s Law for the electrostatic force between two point charges?

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

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?

According to Coulomb's Law, what happens to the magnitude of the electric force between two point charges if the distance between them doubles? $F=\frac{k{q}_1{q}_2}{r^2}$

According to Coulomb's Law, what is the magnitude of the electric force between two point charges $q_1$ and $q_2$ separated by a distance $r$ in vacuum?

Two small, identical conducting spheres A and B are a distance R apart; each carries the same charge Q. (a) What is the force sphere B exerts on sphere A? (b) An identical sphere with zero charge, sphere C, makes contact with sphere B and is then moved very far away. What is the net force now acting on sphere A? (c) Sphere C is brought back and now makes contact with sphere A and is then moved far away. What is the force now on sphere A?

According to Coulomb's Law, how does the magnitude of the electric force between two point charges change as the distance between them increases?

A massless spring is attached to a support at one end and has a 2.0 μC charge glued to the other end. A −4.0 μC charge is slowly brought near. The spring has stretched 1.2 cm when the charges are 2.6 cm apart. What is the spring constant of the spring?

According to Coulomb's Law, what is the magnitude of the electric force between two point charges $q_1$ and $q_2$ separated by a distance $r$ in vacuum?