Q. 33.7( 3 Votes )

A charge Q is uniformly distributed on a thin spherical shell. What is the field at the centre of the shell? If a point charge is brought close to the shell, will the field at the centre change? Do your answer depend on whether the shell is conducting or nonconducting?

Answer :

If we consider a thin spherical shell, then all its charge is concentrated in the centre. According to Gauss’ law, the flux through a closed surface is time the charge enclosed.


flux through the closed surface, ,


where


𝜖0 is the electric permittivity of vacuum,


E = electric field,


ds = surface element,


q = charge enclosed.


Now in this case since all the charge is bound to the surface, the charge enclosed by the sphere (at the centre) is 0.


Hence,


and hence the electric field is also 0.


If a point charge is brought close to the shell, the charge enclosed the sphere will still be 0. Hence the field inside the sphere will still be 0.


The flux will remain 0 if the shell is conducting, since in a conductor, the charge always remains on the surface.


Thus, for a non-conducting shell, there might be some charge induced inside, due to which the electric field might change.


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