question_answer

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:                         [JEE Main Held on 12-4-2019 Morning]

(Take V = 0 at infinity):

A) \[\frac{|\vec{p}|}{4\pi {{\varepsilon }_{0}}{{d}^{2}}},\frac{-\vec{p}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}\]           

B) \[0,\frac{{\vec{p}}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}\]

C) \[\frac{|\vec{p}|}{4\pi {{\varepsilon }_{0}}{{d}^{3}}},\frac{{\vec{p}}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}\]           

D) \[0,\frac{-\vec{p}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}\]

Correct Answer: D

Solution :

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