NTA Abhyas JEE Main2020PhysicsElectrostaticsPractice
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
- Aλ 2 π ε 0 ln d - a d - b a b
- Bλ 2 π ε 0 ln d 2 a b
- Cλ 4 π ε 0 ln d - a d - b a b
- 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