Question

Two massive, positively charged particles are initially held a fixed distance apart. When they are moved farther apart, the magnitude of their mutual gravitational force changes by a factor of n. Which of the following indicates the factor by which the magnitude of their mutual electrostatic force changes?
a. 1/n2
b. 1/n
c. n
d. n2

Answer 1

c. n

The magnitude of the gravitational force is given by Newton's law of universal gravitation:

$F_g=-G\frac{m_1m_2}{d^2}$

Here G is the gravitational constant, $m_1, m_2$ are the masses of the particles and d is the distance between them.

The magnitude of the electrostatic force is given by Coulomb's law:

$F_e=k\frac{q_1q_2}{d^2}$

Here k is the Coulomb constant, $q_1, q_2$ are the chargues of the particles and d is the distance between them.

As can be seen, both forces are inversely proportional to the square of the distance. Thus, the factor is the same in both cases.