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{\left|\vec{p}\right|}{4\pi\varepsilon_{0}d^{2}} , \frac{-\vec{p}}{4\pi\varepsilon_{0} d^{3}} $
• B. $0 , \frac{\vec{p}}{4\pi\varepsilon_{0} d^{3}} $
• C. $\frac{\left|\vec{p}\right|}{4\pi\varepsilon_{0}d^{2}} , \frac{\vec{p}}{4\pi\varepsilon_{0} d^{3}} $
• D. $0, \frac{-\vec{p}}{4\pi\varepsilon_{0} d^{3}} $

Answer 1

Answer: (D)

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