Q. A cylinder of length L and radius b has its axis coincident with the x-axis. The electric field in this region is $ \displaystyle \vec{E}= 200 \hat{i}$ . Find the flux through the left end of the cylinder.

(a) 0

(b) 200 πb²

(c) 100 πb²

(d) 200 πb²

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Ans: (d)

Sol: $ \displaystyle \phi = \vec{E}.\vec{S}$

Electric field is along X- axis & area Vector is along -ve X -axis

$ \displaystyle \phi = (200)\hat{i}.(\pi b^2)(-\hat{i}) $

$ \displaystyle \phi = – 200 .\pi b^2 $