A point dipole `vecp=-p_(0)xhatx` 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)

Options

A. `(|vec(P)|)/(4pi in_(0) d^(2))`
B. `0,(|vec(p)|)/( 4 pi in_(0) d^(3))`
C. `(|vec(p)|)/( 4 x in_(0) d^(2)),(vec(p))/(4 pi in_(0) d^(3))`
D. `0, (vec(p))/(4 pi in_(0) d^(3))`

Answer

B

Explanation

`vec(P)=-P_(0)hatx`
`V_(M)=(1)/(4piepsi_(0))((-q))/(sqrt(1^2+d^2))+(1)/(4piepsi_0)(q)/(sqrt(1^2+d^2))," "costheta=(1)/(sqrt(1^2+d^2))`
`V_(M)=0`
For short dipole at equatorial position `vec(E)_(M)=(-vecP)/(4piepsi_(0)d^(3))`