A hollow conducting sphere of radius R is given a charge such that its surface electric potential is V . What is the magnitude of the electric field intensity at the center of the sphere and at a distance of 3R from the center, respectively?

Step-by-step solution

The electric field inside a hollow conducting sphere is zero everywhere. Therefore, the electric field at the center ( r = 0 ) is zero. The electric potential at the surface of the sphere of radius R is given by V = 1 4 ₀ Q R , which gives the total charge Q = 4 ₀ V R . At a distance r = 3R from the center (which is outside the sphere), the electric field is given by E = 1 4 ₀ Q r² . Substituting r = 3R and the expression for Q , we get: E = 1 4 ₀ 4 ₀ V R (3R)² = V R 9R² = V 9R . Answer: 0 and V 9R