Consider a conducting cylinder, whose place surfaces are connected to a battery. Now, if we assume electric field inside it is constant, and electric field just outside it is zero, then circulation of the electric field is non zero at the cylindrical surface. However, in steady state, the circulation must be zero (since curl of electric field is negative of time derivative of magnetic field). This implies that the electric field just inside the curved surface must be zero.
How to find the exact distribution of electric field in the cylinder?
