Avery 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.