Question

1. You and a friend are spending the weekend making up missed lab experiments. You are on to second semester material and are studying the electrostatic interaction of two charges. You notice that two charges are exerting a certain force on one another. If the distance between two electric charges doubles, then the force they exert on each other changes by how much?A) 4 times as large
B) 2 times as large
C) ½ as large
D) ¼ as large

Answer 1

Answer:

D) ¼ as large

Explanation:

The magnitude of the electric force between two charges is

$F=k\frac{q_1 q_2}{r^2}$

where

k is the Coulomb's constant

q1 and q2 are the magnitudes of the two charges

r is the separation between them

From the formula we see that the magnitude of the force is inversely proportional to the square of the distance.

In this problem, the distance is doubled:

$r'=2r$

So the new force will be

$F'=k\frac{q_1 q_2}{(2r)^2}=\frac{1}{4}k\frac{q_1 q_2}{r^2}=\frac{1}{4}F$

So the force will decrease to 1/4 of its original value.