Question

two point electric charges possess an electric potential energy U when they are separated by a distance d. If this distance is increased to 4d, what will the potential energy now be?

Answer 1

Answer: The potential energy is one forth of the initial potential energy.

Explanation:

Given that,

Distance = d

Let us considered two point charges $q_{1}$ and $q_{2}$.

The potential energy is

$U =\dfrac{1}{4\pi \epsilon_{0}}\dfrac{q_{1}q_{2}}{d}$

Where, d = distance of charges

So, we can say that the potential energy is inversely proportional to the distance between the charges.

$U\propto \dfrac{1}{d}$

If this distance is increased to 4d.

Then, the potential energy is

$\dfrac{U}{4} \propto \dfrac{1}{4d}$

Hence, the potential energy is one forth of the initial potential energy.