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Question

A point dipole p=p0^x kept at the origin. The potential and electric field due to this dipole on the yaxis at a distance d are, respectively :
(Take V=0 at infinity)

A
0,|p|4πε0d2
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B
0,p4πε0d3
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C
|p|4πε0d2,p4πε0d3
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D
0,p4πε0d3
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Solution

The correct option is B 0,p4πε0d3
The dipole lies along negative x axis and the given point is on y axis.

So, the given point lies on the equatorial line of a point dipole.

The electric potential due to a point dipole is given by,

V=14πε0pcosθd2

On the equatorial line, θ=180

V=0

We know that, the electric field due to a point dipole on the equatorial line is given by,

E=p4πε0 d3(^p)

Hence, option (B) is correct.

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