Question

Which of the following correctly gives the electric field at a distance R above an infinitely long line of charge with constant linear charge density λ?

Answer 1

Correct option is B) Consider a Gaussian surface (cylinder in this case) of radius r and length l. Then according to the Gauss's Law of electrostatics:∫E.dA=ϵ0​qenclosed​​From the symmetry of the surface, we can easily say that the electric field would only be along the radial direction. And the amount of charge enclosed by this cylinder is qenclosed​=λ×l and the surface area of the cylinder A=2πrl. So, E×2πrl=ϵ0​λl​ E=(2πϵ0​1​)rλ​

Step-by-step explanation: