Question

A point dipole $\vec{p}=-p_0\hat{x}$ is kept at the origin . The potential and electric field due to this dipole on the y-axis at a distance $d$ are , respectively :
(Take $V=0$ at infinity) :

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

Answer 1

Answer: (D)

$V=0E=\frac{K\vec{P}}{r^3}=-\frac{\vec{p}}{4\pi {\epsilon }_0{d}^3}$