Two point charges are 4 cm apart.They are moved to a new separation of 2 cm.By what factor does the resulting mutual force between them change?

Question

Quizplus · Accepted Answer

The force between two point charges is given by Coulomb's law: F = k*q1*q2/r^2 
where k is the Coulomb constant, q1 and q2 are the magnitudes of the charges, and r is the separation between them.
When the charges are moved to a new separation of 2 cm (one-half of the original separation), the new force between them can be calculated using the same formula with r = 2 cm. 
If we substitute r = 2 cm and r = 4 cm, respectively, we get:
F2/F1 = (k*q1*q2/2^2) / (k*q1*q2/4^2) 
= (1/4)
Therefore, the mutual force between the two charges changes by a factor of 4/1, which is 4. So the correct answer is D.

Two Point Charges Are 4 Cm Apart