Question

Consider the small electric dipole with magnitude of dipole moment $p$ which is placed far away from point $A$ as shown. The electric potential at the point $A$ is:

• A. $\frac{kp}{r^2}$
• B. $\frac{-kp}{r^2}$
• C. $\frac{kp}{r}$
• D. exactly zero

Answer 1

Answer: (B)

$\frac{-kp}{r^2}$

The magnitude of electric dipople moment is $p$.
At a point distance $r$ from point $A$. It this situation, the dipole moment tries to rotate the dipole as given in the above figure.
So, considering the position of $P$, the resultant potential at $A$ is
$V_A=\frac{kp\cos \pi }{r^2}$
$=-\frac{kp}{r^2}[\because \cos \pi =-1]$.