A conducting sphere is charged up such that the potential on…

A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere’s radius were half as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity?

In a certain region, the electric potential due to a charge…

In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 1.5x2y2 + 0.5yz3- z3x, where x, y, and z are measured in meters and V is in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0).