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In the given diagram, there is a conducting sphere of radius r 1 which is surrounded by a dielectric of relative permittivity ε r . If conducting sphere is given charge q , then the surface density of polarization charges, on the outer surface of the dielectric layer, is

Options

  1. Aε r q 4 π r 2 2
  2. Bq 4 π ε r r 2 2
  3. C( ε r - 1 ) q 4 π r 2 2
  4. D( ε r - 1 ) q 4 π ε r r 2 2

Correct answer

D. ( ε r - 1 ) q 4 π ε r r 2 2

Step-by-step solution

Induced charge = q 1 - 1 ε r Surface density = q 1 - 1 ε r 4 π r 2 2 = q ε r - 1 4 π ε r r 2 2

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