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JEE Advanced2015PhysicsElectrostaticsActual

An infinitely long uniform line charge distribution of charge per unit length λ lies parallel to the y -axis in the y - z plane at z = 3 2 α (see figure). If the magnitude of the flux of the electric field through the rectangular surface A B C D lying in the x - y plane with its centre at the origin is λ L n ε 0 ( ε 0 = permittivity of free space), then the value of n is

Correct answer

0

Step-by-step solution

d ϕ = λ 2 π ϵ 0 d 2 + x 2 . d d 2 + x 2 L d x ϕ = λ d L 2 π ϵ 0 ∫ - a 2 a 2 d x d 2 + x 2 = λ d L 2 π ϵ 0 1 d 2 tan - 1 ⁡ x d 0 a 2 = λ L π ϵ 0 tan - 1 ⁡ a 2 . a 3 2 = λ L π ϵ 0 π 6 ∴ n = 6

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