Question

A dipole is placed at the origin such that its dipole moment is $p\hat{i}$. The electric field and potential at $(0,d,0)$ respectively are:

• A. $\frac{p}{4p{\epsilon }_0{d}^3}\hat{i},0$
• B. $\frac{-p}{4p{\epsilon }_0{d}^3}\hat{i},0$
• C. $\frac{2p}{4p{\epsilon }_0{d}^3}\hat{i},0$
• D. $\frac{-2p}{4p{\epsilon }_0{d}^3}\hat{i},0$

Answer 1

The correct option is B $\frac{-p}{4p{\epsilon }_0{d}^3}\hat{i},0$

Clearly it is the axial position
$\overrightarrow{E}=-\frac{k\overrightarrow{p}}{r^3}=\frac{1}{4\pi {\epsilon }_0}\frac{p}{r^3}\hat{i}$
put $r=d$
$\overrightarrow{E}=-\frac{p}{4\pi {\epsilon }_0{d}^3}\hat{i}\Rightarrow V=0$