An electric field is uniform and in the positive xdirection for positivex and uniform with the same magnitude but in the negative x direction for negative x. It is given that `E= 200 hati N//C" for "x gt 0 and E=- 200 hati N//C" for "3 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 tace is at x = +10 em and the other is at x=10 cm
a. What is the net outward flux through cach flat face?
b. What is the flux through the side of the cylinder?
c. What is the net outward flux through the cylinder?

Explanation

From the figure, on the left face. E and `triangleS` are parallel. Therefore, the outward flux is `phi_(L)=E triangle S=-200 hati. triangleS=+ 200 triangleS," since"hati. Triangl S=-triangleS`
`=+200 xx pi (0.05)^(2) =+ 1.57 Nm^2 C^(-1)`
On the right face, E and `triangleS` are parallel and therefore.
` phi_(R)=E. triangleS=+1.57 Nm^(2) C^(-1)`
(b). For any point on the side of the cylinder, E is perpendicular to `triangleS 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 withing the cylinder can be formed by using Gauss. law which gives.
`q=epsi_(0) phi =3.14 xx 8.854 xx 10^(-12) C= 2.78 xx 10^(-11)C`