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**

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