Question

An electron having charge -e located at A in the presence of a point charge +q located at O is moved to the point B such that OAB forms an equilateral triangle. The work done in the process is equal to :

• A. $\frac{q}{AB}$
• B. $\frac{qe}{AB}$
• C. $-\frac{qe}{AB}$
• D. $\text{z}ero$

Answer 1

The correct option is D $\text{z}ero$

Since Electrostatic forces are conservative, work done in a process is equal to the change in energy of the system.

If, $s$ is the side of the equilateral triangle $OAB$,

Potential energy of the electron when it is at $A$ is $U=\frac{-qe}{4\pi {ϵ}_{0}s}$

Potential energy of the electron when it is at $B$ is $U_B=\frac{-qe}{4\pi {ϵ}_{0}s}=U_A$

Thus, Work done is $W=U_B-U_A=0$