The charge resides on the surface of a conductor. Thus, a hollow charged conductor is equivalent to a charged spherical shell. Let’s consider a spherical Gaussian surface of radius (r < R). If E is the electric field inside the shell, then by symmetry electric field strength has the same magnitude Ei, on the Gaussian surface and is directed radially outward.
Electric flux through the Gaussian surface is given by,
Now, the Gaussian surface is inside the given charged shell, so charge enclosed by the
Gaussian surface is zero.
Therefore, using Gauss’s theorem, we have
Thus, the electric field at each point inside a charged thin spherical shell is zero.
The graph above shows the variation of electric field as a function of R.