Question

If an electron is brought toward another electron, the electric potential energy of the system

• A. becomes zero
• B. increases
• C. remains the same
• D. decreases.

Answer 1

Answer: (B)

increases

Answer 2

If two charges are of the same sign, they repel each other. Thus if two electrons are brought closer, some work is done against the force of repulsion. Therefore the electric potential energy of the system increases.

Mathematically, the potential due to one electron at the position of the other electron is $\frac{-K e}{r}$ and hence
the potential of the other $=-\frac{K e(-e)}{r}=\frac{K e^{2}}{r}$,
where $r$ is the distance between the two electrons. Now if $r$ decreases, $P . E$. increases.