Question

A long thin wire has a linear charge density of 2.05C per meter. Determine the magnitude of the electric field at a distance of 2.0m away from it. Except for any basic law derive any equation used. Need a lil help with the derivation, could someone plz give a hint. I was think a lil on the lines of used gauss' law.

Answer 1

Gauss' Law:\[\epsilon \int\limits_{ }^{ }EdAcos \theta=q\]Linear Charge Density:\[\lambda=dq/dx\] Therefore, \[\epsilon \int\limits_{ }^{ }EdAcos \theta=\int\limits_{ }^{ }\lambda dx\]Then, \[\epsilon E \int\limits_{ }^{ }dA=\int\limits_{ }^{ }\lambda dx\]And solve for E.