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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

  1. A1:64
  2. B64:1
  3. C1:4
  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

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