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An infinity long uniform line charge dis...

An infinity long uniform line charge distribution of charge per unit length `lambda` lies parallel to the y-axis in the `y-z` plane at `z=sqrt3/2` a(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 `(lambdaL)/(n epsilon_0)` (`epsilon_0=` permittivity of free space), then the value of n is

Text Solution

Verified by Experts


`tantheta=(a//2)/(sqrt3a//2)=1/sqrt3`
`:.` `theta=30^@`
The flux through the dotted cylinder by Gauss's law is
`phi cyli nder =(q_(i n))/(epsilon_0)=(lambdaL)/(epsilon_0)`
`:.` For `360^@` angle the flux is `(lambdaL)/(epsilon_0)`
`:.` For `60^@` angle the flux will be `(lambdaL)/(6epsilon_0)`
Therefore `n=6`
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