Two charged conducting spheres A and B are connected by a thin conducting wire. If the ratio of the electric field magnitudes at the surfaces of spheres A and B is 4 : 1 , what is the ratio of their radii ( R_A R_B ) ?

Step-by-step solution

When two conducting spheres are connected by a wire, charge flows until they reach the same electrostatic potential ( V_A = V_B ). The electric field magnitude at the surface of a conducting sphere is given by E = V R . Since the potential V is the same for both spheres, the electric field is inversely proportional to the radius ( E 1 R ). Therefore, E_A R_A = E_B R_B R_A R_B = E_B E_A . Given E_A E_B = 4 , we find R_A R_B = 1 4 . Answer: 1 : 4