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
`vec(E) = 200 hat(i) N//C for x gt 0 and vec(E) = -200 hat(i) N//C` for x gt 0. A right circular cylinder of length 20 cm and raidus 5cm has its center 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`.
(a) What is the net outward flux through the side of the cylinder ? (b) What is the net outward flux through the cyclinder ? (c) what is net charge inside the cylinder ?

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`