We all know from a course on electrostatics that the electric field inside a perfect conductor, placed inside a static electric field, is zero. Now imagine the same perfect conductor is connected to a DC voltage source by perfectly conducting wires. What is the electric field inside the conductor in such a situation?
Since $\vec{E}=\rho\vec{j}$, and resistivity $\rho=0$ for a perfect conductor, here too, the electric field inside seems to be zero. Also since $E=(V_A-V_B)/\ell$, and since there is no voltage drop between the points $A$ and $B$ in the absence of resistance, there is no electric field.
But isn't this odd? If the electric field inside is zero, what causes the electrons to move through the conductor and maintain a steady current?
