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Two spherical conductors A and B of radii R and 2 R respectively, are separated by a large distance. If some charge is given to both the spheres and later they are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is

Options

  1. A1 : 4
  2. B4   :   1
  3. C1   :   2
  4. D2   :   1

Correct answer

D. 2   :   1

Step-by-step solution

When the spherical conductors are connected by a conducting wire, charge is redistributed and the spheres attain a common potential V . ∴ Intensity E A = 1 4 πε 0 Q A R A 2 or E A = 1 × C A V 4 πε 0 R A 2 = 4 πε 0 R A V 4 πε 0 R A 2 = V R A Similarly E B = V R B ∴ E A E B = R B R A = 2 1 .

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