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 gt 0` and `E=-200 hat(i) N//C` for `x lt 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
What is the net outward flux through each flat face?

Explanation

(a) we can see from the that on the left face E and `triangle S` are parallel therefore the outward flux is
(b) for any point on the side of the cylinder E is perpwendicular to `triangle S` and hence E `triangleS=0` therefore the flux out of the side of the cylinder is zero
(c ) net outward flux through the cylinder
`Phi =1.57 +1.57 +0=3.14 N m^(2) c^(-1)`

(d) the net charge within the cylinder can be found by using gauss.s law which gives
`q=epsilon_(0) Phi`
`=2.78 xx10^(-11) c`