[Physics] Why the potential inside a solid conducting sphere is non zero while the electric field inside is zero

Question

I don't know why V is not zero inside the sphere. If we use the formula that V= $\int_{0}^{\infty}(kdq/r)$, how do we get that $V_{in}$ = kq/r?

Answer 1

The potential difference inside a conductor is always zero [I edited your question]. The potential inside a conductor is not always zero. The potential is same at all points inside a conductor. Now, you see why the potential difference is zero. To obtain the expression for potential, you can use the expression, $\int_{0}^{\infty}(kdq/r)$ in spherical polar coordinates. Express dq as $\rho$dV. Here dV is $r^2$sin($\theta$)drd$\theta$d$\phi$.

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