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

We can see from the figure that on the left face E and `Delta S` are parallel. Therefore, the outward flux is
`phi_(L)=E. Delta S=-200 hat(i). Delta S`
`=+200 Delta S`, since `hat(i).Delta S=-Delta S`
`=+200xx pi (0.05)^(2)=+1.57 Nm^(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)`.