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 hati N//C for x gt 0 and E = –200 hati 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 (Fig. 1.28). (a) What is the net outward flux through each flat face? (b) What is the flux through the side of the cylinder? (c) What is the net outward flux through the cylinder? (d) What is the net charge inside 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`