An electric field is e = 200 n/c i for x > 0 and e = -200 n/c i for x < 0. a cylinder of length 20 cm and radius 3 cm has its center at the origin and its axis along the x axis such that one end is at x = +10 cm and the other is at x = -10 cm. what is the net charge inside the cylinder?

The net charge inside the cylinder is

To solve this problem, we have to determine the electric flux

φc = EAcosθ

where θ is the angle between area vector and electric field.

θ = 90°, cos90° = 0

φc = EA * 0 = 0

The flux through the curved surface = 0

when x > 0

φ1 = EA cos0 = φ1 = EA *1 = EA

when x < 0

φ = E.A = EA*cos0

φ2 = EA

Net Flux of charge = φ(net) = φ(c) + φ1 + φ2 = 0 + EA + EA

φ(net) = 2EA

From Gauss Law

given that;

ε = 8.85*10^-12 c^2/Nm^2

A = πr^2

r = 0.09m

Substitute the value into φ(net)

From the calculations above, the net charge inside the cylinder is 1.778*10^-11C

learn more about electric flux here;

e/c, where e is its total energy