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 flux through the side of the cylinder?

Explanation

(a) `phi_(1)= vec(F). vec(A)= vec(E)'.vec(A)'`
`= 1.57 Nm^(2) //C`
(b) `vec(E) ` is parallel to sides of cylinder so `phi` through sides `=0`
(c ) `phi_(1)= vec(F). vec(A)= vec(E)'.vec(A)'= 2EA`
`= 2 xx 200 xx pi ( 5 xx 10^(-2) )^(2) N m^(2) //C`
`= 3.14 Nm^(2) //C`
(d) `Q = phiepsilon_(0)`
` 3.14 Nm^(2) //C xx8.854 xx 10^(-12) C^(2) N ^(-1) m^(2)`
`= 2.78 xx 10^(-11) C`