Question

An infinitely long wire is charged uniformly with a charge density λ and placed in the air, the electric field at a distance r from the wire will be:

• A. $\frac1{4πε_0} \frac{λ}{r}$
• B. $\frac1{4πε_0} \frac{λ}{r^2}$
• C. $ \frac{λ}{2ε_0}$
• D. $ \frac{λ}{2\piε_0 r}$

Answer 1

The Correct Option is D

The correct answer is (D): $ \frac{λ}{2\piε_0 r}$

Consider an infinity long straight conductor of linear charge density 

Consider a cylindrical Gaussian surface of radius r and length l.
charge enclosed by the surface
\(q=λl\)

By Gauss law
$\phi  \vec{E}.ds = \frac{q}{ε_0} = \frac{λl}{ε_0} $

$ \vec{E}\phi ds= \frac{λl}{ε_0} $

$ \vec{E} \times 2\pi rl = \frac{λl}{ε_0} $ 

$ E =  \frac{λ}{2\pi rε_0}$