Question

An infinitely long straight wire has a uniform linear charge density of Derive the 4. equation for the electric field a distance R away from the wire using Gauss's Law for Electrostatics.

Answer 1

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

Step-by-step explanation:

Let the linear charge density of the charged wire is given as

`(q)/(L) = \lambda`

here we can use Gauss law to find the electric field at a distance r from wire

so here we will assume a Gaussian surface of cylinder shape around the wire

so we have

`\int E. dA = (q)/(\epsilon_0)`

here we have

`E \int dA = (\lambda L)/(\epsilon_0)`

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

so we have

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