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)

$\frac{1}{r^2}$

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 $r_1\underset{–}{\simeq }{r}_2=r$
$r_2-r_1\underset{–}{\simeq }dcos\theta$

$V=\frac{KVdcostheta}{r^2}$

$V=\frac{KPcostheta}{r^2}$ $P=Vd$, where P is the dipole moment.

$\therefore V\propto \frac{1}{r^2}$