A very long solid cylinder is made from a material in which the net charge density is constant. The electric field within the cylinder is proportional to: A) r 3 B) r 2 C) r D) constant E) 1/r

C) r

Explanation:

Let ρ be volume charge density of the solid charged cylinder. It is constant

To know the electric field inside the cylinder, we shall carve out a gaussian surface of cylindrical shape of radius r and length l of the size of length of cylinder.

The electric field will be axially symmetrical. Let it be E

Electric flux over curved surface of the cylinder

= 2πr l x E

Charge inside the Gaussian surface

q = πr² l x ρ

According to Gauss's theorem

2πr l x E = q / ε

= πr² l x ρ / ε

E = ρ r / 2ε

E is proportional to r. option C is correct.