# An electric field along x-axis is given by $\overrightarrow{E}= 100 \widehat{i}N/C$ for x > 0 and $\overrightarrow{E}= -100 \widehat{i}N/C$ for x <0. A right circular cylinder of length 20cm and radius 5cm lies parallel to the x-axis, with its centre at the origin and one face at x = + 10cm, the other face at x = -10cm. Calculate the net outward flux through the cylinder.

x=-10cm                                        x=10cm

From the figure, we can see that on each face the electric field E and small area elements S are parallel. Therefore, outward flux, $\phi = E\Delta S$

On the left side $\phi_{1}= E \Delta S$

$= 100 \widehat{i}\Delta S$

$= +100 \Delta S$, sincec$\Delta S = - \Delta S$

$= 0.785Nm^{2}C^{-1}$

On the side of the cylinder electric field is perpendicular to $\Delta S$ and hence $E.\Delta S=0$.

Therefore, outward flux on the side of the cylinder

$\phi = 0.785 + 0.785 + 0= 1.57N m^{2}C^{-1}$

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