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Two conducting spheres A and B of radius a and b respectively are at the same electric potential. The ratio of the surface charge densities of A and B is

Options

  1. Ab a
  2. Ba b
  3. Ca 2 b 2
  4. Db 2 a 2

Correct answer

A. b a

Step-by-step solution

Given electric potential of spheres are same i.e., V A = V B 1 4 π ε 0 Q 1 a = 1 4 π ε 0 . Q 2 b Q 1 Q 2 = a b A surface charge density σ = Q 4 π r 2 ⇒ σ 1 σ 2 = Q 1 Q 2 × b 2 a 2 = a b × b 2 a 2 = b a

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