Solveeit Logo
Login

Question

Question: The value of electric potential at any point due to any electric dipole is...

The value of electric potential at any point due to any electric dipole is

A

k.p→×r→r2k.\frac{\overset{\rightarrow}{p} \times \overset{\rightarrow}{r}}{r^{2}}

B

k.p→×r→r3k.\frac{\overset{\rightarrow}{p} \times \overset{\rightarrow}{r}}{r^{3}}

C

k.p→⋅r→r2k.\frac{\overset{\rightarrow}{p} \cdot \overset{\rightarrow}{r}}{r^{2}}

D

k.p→⋅r→r3k.\frac{\overset{\rightarrow}{p} \cdot \overset{\rightarrow}{r}}{r^{3}}

Answer

k.p→⋅r→r3k.\frac{\overset{\rightarrow}{p} \cdot \overset{\rightarrow}{r}}{r^{3}}

Explanation

Solution

Potential due to dipole in general position is given by

V=k.pcos⁡θr2V = \frac{k.p\cos\theta}{r^{2}} ⇒ V=k.pcos⁡θrr3=k.(p→.r→)r3V = \frac{k.p\cos\theta r}{r^{3}} = \frac{k.(\overrightarrow{p}.\overrightarrow{r})}{r^{3}}