Engineering
Physics
Electric Flux and Gauss Law and its Applications
Question

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=32a (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is λL0 (ε0 = permittivity of free space), then the value of n is 

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Solution

 

Flux through this rectangular surface will be equal to flux through curved surface (part of cylindrical surface) shown, which subtends an angle of 60° at wire.

For this cylindrical surface charge enclosed = λL

 So,ϕ=λL6ε0.So,  n=6