Question

The electric potential due to an extremely short dipole at a distance r from it is proportional to

• A. $\frac{1}{r}$
• B. $\frac{1}{r^2}$
• C. $\frac{1}{r^3}$
• D. $\frac{1}{r^4}$

Answer 1

Answer: (B)

Potential at point $P=\frac{KV}{r_1}-\frac{KV}{r_2}$
$V=KV\left(\frac{r_2-r_1}{r_1{r}_2}\right)$
we are taking extremely short dipole $r_1\cong r_2=r$
$r_2-r_1\cong d\cos \theta$
$V=\frac{KVd\cos \text{ theta }}{r^2}$
$V=\frac{KP\cos \text{ theta }}{r^2}P=Vd$,
where $P$ is the dipole moment.
$\therefore V\propto \frac{1}{r^2}$