Question

Question 2. A spherical ball is charged uniformly with charge density, ρν except for a small spherical hole which is uncharged. The radius of the ball is R and the radius of the whole is Rh The hole center is displaced from the center of the sphere by d. Calculate the E-field inside the hole?

Answer 1

E^vector_2 E^Vector_p = E^Vector_1 - E^Vector_2 electric field at point p if there is no unit E^Vector electric field due to unit E^Vector_0: electric field inside the hole E^Vector = rho v/3 epsilon_0 r^Vector E^Vector_1 = rho v/3 epsilon_0 r^Vector_1, E^Vector_2 = rho v/3 epsilon_0 r^Vector_2 E^Vector_p = rho v/3 epsilon_0 [r^Vector_1 - r^Vector_2] d^Vector + r^Vector_2 = r^vector_1 = > r^Vector_1 - r^Vector_2 = d^vector = > E^Vector_p = rho_v (d^Vector) Electric field inside hole E_p = rho_v/3 epsilon_0 d