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An electric field is uniform, and in the positive x direction for positive x, and uniform with the same magnitude but in the negative x direction for negative x. It is given that $E = 200 \hat i N/C$ for $x > 0$ and $E = –200 \hat i N/C$ for $x < 0$. A right circular cylinder of length $20\; cm$ and radius $5\; cm$ has its centre at the origin and its axis along the x-axis so that one face is at $x = +10 cm$ and the other is at $x = –10 cm$ (see the figure given below).What is the net outward flux through each flat face?

1 Answer

We can see from the figure that on the left face E and S are parallel. Therefore, the outward flux is
$\phi _L =E. \Delta S= -200 \hat i \Delta S$
$\qquad =+200 \Delta S$ since $\hat i . \Delta S =- \Delta S$
$\qquad= +200 \times \pi (0.05)^2 =+ 1.57 N m^2 C^{-1}$
On the right face, E and $\Delta S$ are parallel and therefore
$\phi _R= E. \Delta S =+ 1.57 Nm^2 C^{-1}$
Hence A is the correct answer.
answered Jun 2, 2014 by meena.p

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