Question

Using Gaussis law find the electric feild near the middle of a very long plastic cylinder of raduis b at point where r<b. The plastic cylinder has a uniform charge density of p.

Answer 1

Let rho is the charge density.

imagine a gaussian cyllindrical surface with radius r and with length L.

Let E is the electric field at r distance from center.

total electric flux through the gaussian surface, integral E.ds = E*2*pi*r*L

charge enclosed by this gaussian surface, Qin = volume charge density*volume of the gaussian cyllinder

= rho*pi**r^2*L

From gauss law, integral E.ds = Qin/epsilon

E*2*pi*r*L = rho*pi*r^2*L/epsilon

E = rho*r/(2*epsilon) <<<<<<<--------------Answer