A conductor fills the region $x_3^3\leq Re\sqrt{R^2-x_1^2-x_2^2}$, bounded by surface $\Sigma$. If, asymptotically as $x_1^2+x_2^2\to\infty$, the surface density charge approaches to a certain...
A conducting cylinder of radius $R$ is placed where there's a constant electric field $E$, with direction orthogonal to the axis of the cylinder. Find potential outside the cylinder.