If the electric potential is given by \(\chi=cxy\), calculate the electric field. Discussion: $$ E_x=-\frac{\partial\chi}{\partial x}=-cy$$ $$ E_y=\frac{\partial \chi}{\partial y}=-cx$$ Hence electric field $$...

A metal sphere having a radius \(r_1\) charged to a potential \(\phi_1\) is enveloped by a thin-walled conducting spherical shell of radius \(r_2\). Determine the potential \(\phi_2\) acquired by the sphere after it has been connected for a short time to the shell by...