Question

Two equal and opposite charges $q$ with a separation $2a$ form an electric dipole of dipole moment $p=\left(2qa\right)$. The line joining the midpoint of dipole to a point $R$ at a distance $r$ from it makes an angle $\theta$ with the dipole axis. The electric potential at $R$ (when $r>>a$) will be

• A. $V=\frac{p\sin \theta }{4\pi {ϵ}_{0}r}$
• B. $V=\frac{p\cos \theta }{4\pi {ϵ}_0{r}^2}$
• C. $V=\frac{p\cos \theta }{4\pi {ϵ}_{0}r}$
• D. $V=\frac{p\sin \theta }{4\pi {ϵ}_0{r}^2}$

Answer 1

The correct option is B $V=\frac{p\cos \theta }{4\pi {ϵ}_0{r}^2}$

As dipole is a vector quantity, we can divide it into two perpendicular components.

• Along the direction of the point, where the potential to be calculated.
• Perpendicular to the direction.

Potential:
$V=[V_{p\cos \theta }{]}_{\text{axis}}+[V_{p\sin \theta }{]}_{\perp \text{bisector}}$

$V=\frac{Kp\cos \theta }{r^2}$

$V=\frac{p\cos \theta }{4\pi {ϵ}_0{r}^2}$
Hence, option $\left(A\right)$ is correct.