The ratio of electric fields on the axis and at equator of an electric dipole will be

Question

The ratio of electric fields on the axis and at equator of an electric dipole will be (A)  1:1  (B)  2:1  (C)  4:1  (D)  1:4

Tardigrade Admin · Accepted Answer

The electric field on the axis of a dipole of length small compared to point where electric field is to be determined is

E_{A} = \frac{1}{4 π ε _{0}} \cdot \frac{2 p}{r ^{3}}

... (i)
where

p

is electric dipole moment.
Intensity at a point on the equatorial line of a dipole is

E_{E} = \frac{1}{4 π ε _{0}} \cdot \frac{p}{r ^{3}} N / C

...(ii)
From Eqs. (i) and (ii),
we get

\frac{E _{A}}{E _{E}} = \frac{2 p}{r ^{3}} \times \frac{r ^{3}}{p} = \frac{2}{1}

Q. The ratio of electric fields on the axis and at equator of an electric dipole will be