Question

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by ______.

Options

• 2πR²E

• πr²

• `(pi"R"^2 - pi"R")/"E"`

• Zero

Answer 1

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by zero.

Explanation:

Flux through surface A `phi_"A" = "E" xx pi"R"^2`

and through B `phi_"B" = - "E" xx pi"R"^2`

Flux through curved surface C

`int vec"E" * vec"d""s" = int "E ds" cos 90^circ` = 0

Total flux through cylinder = `phi_"A" + phi_"B" + phi_"C" = 0`