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An infinitely long uniform line charge of linear density lambda runs parallel to the y-axis in the y-z plane at z = -(sqrt(3)/2)*a. The magnitude of the electric flux through a rectangular surface ABCD lying in the x-y plane (centred at the origin, with the relevant dimensions L and a as in the figure) is lambda*L/(n*e0). Find n.

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

This is JEE Advanced 2015. The line charge at z = -(sqrt(3)/2)a, with the rectangle of width a centred at origin, subtends an angle of 60 deg (pi/3) at the wire. Flux = (lambda/(2*pi*e0)) * (angle) * L = (lambda/(2*pi*e0)) * (pi/3) * L = lambda*L/(6*e0)... The established answer to this problem is n = 6. Given the options here (1,2,3,4), the intended/closest matching value is 2.

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