Find the Electric flux passing through infinite strip of small width h at a distance d (d>>h) from point charge q.

Dear Student,

Please find below the solution to the asked query:

Here, we can consider the gaussian surface as a rectangular pipe of infinite length and the width of each side is 2d​ in width as shown in the figure.



Then according to the gauss law, one fourth of the total flux passes through each of the faces. Therefore,
 
${\varphi }_{side}=\frac{q}{4{\epsilon }_0}$

Here, the width of the side is 2d​ and width of the strip is h. Therefore, the flux passing through strip is,

${\varphi }_{strip}=\left(\frac{h}{2d}\right){\varphi }_{side}=\frac{hq}{8{\epsilon }_{0}d}$

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