Question

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

Answer 1

C) r

Step-by-step 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.