JEE MainPhysicsElectrostatics
Two conducting spheres A and B are connected by a long conducting wire and a total charge is given to the system. After the system reaches electrostatic equilibrium, the electric field at the surface of sphere A is found to be 4 times the electric field at the surface of sphere B . The ratio of the volume of sphere A to the volume of sphere B is
Options
- A1:64
- B64:1
- C1:4
- D1:8
Correct answer
A. 1:64
Step-by-step solution
When two conducting spheres are connected by a wire, they reach the same potential, so V_A = V_B . The electric field at the surface of a conducting sphere is given by E = V R . Therefore, E_A R_A = E_B R_B R_A R_B = E_B E_A . Given that E_A = 4 E_B , we have R_A R_B = 1 4 . The ratio of their volumes is Volume _A Volume _B = ( R_A R_B )^3 = ( 1 4 )^3 = 1 64 . Answer: 1:64