Two infinitely long parallel wires are separated by a distance r in free space. One wire carries a uniform linear charge density + and the other carries a uniform linear charge density - . What is the magnitude of the electrostatic force per unit length experienced by either of the wires?

Step-by-step solution

The electric field produced by the first wire (with charge density + ) at the location of the second wire (at distance r ) is given by: E = 2 ₀ r Let us consider a segment of length L of the second wire. The charge on this segment is q = L . The magnitude of the electrostatic force experienced by this segment due to the electric field of the first wire is: F = qE = ( L) ( 2 ₀ r ) Therefore, the magnitude of the force per unit length is: F L = ^2 2 ₀ r Answer: ^2 2 ₀ r