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The quarter disc of radius R (see figure) has a uniform surface charge density σ . Find electric potential at a point O , O , Z .

Options

  1. Aσ 8 ϵ 0 1 - Z R 2 + Z 2
  2. Bσ 4 ϵ 0 R 2 + Z 2 + Z
  3. Cσ 8 ϵ 0 R 2 + Z 2 - Z
  4. Dσ 8 ϵ 0 1 + Z R 2 + Z 2

Correct answer

C. σ 8 ϵ 0 R 2 + Z 2 - Z

Step-by-step solution

V = ∫ 0 R k α π r d r α r 2 + z 2 = σ 8 ϵ 0 ∫ 0 R r d r r 2 + z 2 t 2 = r 2 + z 2 t d t = r d r V = σ 8 ϵ 0 ∫ z 2 2 + R 2 d t = σ 8 ϵ 0 R 2 + z 2 - z

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