Q. 53.5( 2 Votes )

An electric dipole is placed at the centre of a sphere. Mark the correct options:
A. The flux of the electric field through the sphere is zero.

B. The electric field is zero at every point of the sphere.

C. The electric field is not zero anywhere on the sphere.

D. The electric field is zero on a circle on the sphere.

Answer :

A dipole consists of an equal positive and negative charge separated by a distance. Hence, the net charge due to a dipole is 0. Since the sphere encloses the dipole, by Gauss’ law,


where


𝚽 = electric flux,


ds = area element,


q = charge enclosed,


E = electric field,


ϵ = electric permittivity of vacuum.


q(enclosed charge) = 0. Hence, flux = 0(option a).


At any point on the sphere, the electric field is given by


, where


p = dipole moment


r = distance of the point from the centre of the dipole


E = electric field


Ө = angle between the dipole and the line joining the dipole with that point


ϵ = electric permittivity of vacuum



Hence, the electric field anywhere on the sphere is not 0, since cos2Ө cannot be equal to -1(option c).

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