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Two infinitely long wires carry linear charge densities + λ and - λ respectively, as shown.The potential difference between points A (at a distance a from the first wire) and B (at a distance b from the second wire) is

Options

  1. Aλ 2 π ε 0 ln d - a d - b a b
  2. Bλ 2 π ε 0 ln ⁡ d 2 a b
  3. Cλ 4 π ε 0 ln ⁡ d - a d - b a b
  4. Dλ 2 π ε 0 ln ⁡ d - b b / d - a a

Correct answer

A. λ 2 π ε 0 ln d - a d - b a b

Step-by-step solution

The potential difference between A and B is V B - V A = - ∫ A B E → . d r → V B - V A = - λ 2 π ε 0 ∫ A B 1 r + 1 d - r d r V B - V A = - λ 2 π ε 0 ∫ a d - b d r r + ∫ a d - b d r d - r V A - V B = λ 2 π ε 0 ln d - b a - ln b d - a V A - V B = λ 2 π ε 0 ln d - a d - b a b

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