Question

A long, thin straight wire with linear charge density λ runs down the center of a thin, hollow metal cylinder of radius R. The cylinder has a net linear charge density 2λ. Assume λ is positive. Part A Find expressions for the magnitude of the electric field strength inside the cylinder, r

Answer 1

`E=(\lambda)/(2\pi r\epsilon_0)`

Step-by-step explanation:

We are given that

Linear charge density of wire=
`\lambda`

Radius of hollow cylinder=R

Net linear charge density of cylinder=
`2\lambda`

We have to find the expression for the magnitude of the electric field strength inside the cylinder r<R

By Gauss theorem

`\oint E.dS=(q)/(\epsilon_0)`

`q=\lambda L`

`E(2\pi rL)=(L\lambda)/(\epsilon_0)`

Where surface area of cylinder=
`2\pi rL`

`E=(\lambda)/(2\pi r\epsilon_0)`