Question

A moving charge positive approaches a negative charge. What happens to the potential energy of the system?
A. Remain constant
B. Decrease
C. Increase
D. may increases or decrease

Answer 1

Hint: Potential energy of a system of two charges in free space is just the potential energy of one charge due to the other. Note that positive and negative charge have a natural attractive force in between them. Therefore the amount of work required would be less.

Complete step-by-step answer:
We know the potential energy of a system is defined as the work done in assembling the system. That is the work done in bringing each charge from infinity and assembling one by one.
Let’s say we first brought the negative charge from infinity. This process required no work to be done because no charges were present and hence No forces were acting on the charge.
Now, with the negative charge in place, let us bring a positive charge from infinity to a distance $r$. Since the initially placed charge is exerting a force on the new charge, we need to do some work.
This work done in bringing the positive charge ${q_1}(say)$ near to a charge ${q_2}(say)$ is given by :
$W= \dfrac{1}{4\pi \epsilon} \dfrac{q_1 q_2}{r}$

So the potential energy of a two charge system is the sum of these two works.
$PE = 0+W= \dfrac{1}{4\pi \epsilon} \dfrac{q_1 q_2}{r}$.

For a system of one negative charge and one positive charge, ${q_1}$ is positive and ${q_2}$ is negative. Thus, the potential energy of the system is negative.
Now, as the charge ${q_1}$ approaches closer to ${q_2}$, the distance between them decreases. From eqn(1), we see that as $r$ decreases, the potential energy increases in magnitude. But a negative potential energy implies that The potential energy is decreasing as we approach the stationary charge.
So the correct answer would be option B.

Additional Information:
The negative sign in potential energy is always an indicator of attractive forces. This means that we need not do any work, but instead it would give us energy if taken slowly there. If we could take it there through an apparatus that could convert this released energy into useful forms, we would get energy.

Note: We should not forget to consider the negative sign in the equation for total energy that we obtained. Also, while calculating potential energy of systems containing more charges, each charge has to be placed one after the other.