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A circle of radius a has charge density given by λ = λ 0 cos 2 ⁡ θ on its circumference, where λ 0 is a positive constant and θ is the angular position of a point on the circle with respect to some reference line. The potential at the centre of the circle is

Options

  1. Aλ 0 4 ε 0
  2. Bzero
  3. Cλ 0 2 ε 0
  4. Dλ 0 ε 0

Correct answer

A. λ 0 4 ε 0

Step-by-step solution

d q = λ a d θ = λ 0 cos 2 ⁡ θ a   d θ q =   ∫ θ = 0 θ = 2 π λ 0 cos 2 ⁡ θ a   d θ = λ 0 π a   V = q 4 π ε 0 a = λ 0 4 ε 0

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