Two long wires are placed on a smooth horizontal table. The linear charge densities of these wires are `+- lambda C//m`. For unit length of the wires, calculate the work requrired to increase the separation between the wires from a to 3a.

Explanation

As is known electric field strength due to wire 1 at the site of wire 2 at a distance r from the wire is
`E = (lambda)/(2pi in_(0) r)`
`:.` Force on wire 2 of unit length is
`F = lambda E = lambda ((lambda)/(2pi in_(0) r)) = (lambda^(2))/(2pi in_(0) r)`
This force is attractive.
work done is against this force to increase the separation from a to 3a is
`W = int_(a)^(3a) F dr = int_(a)^(3a) (lambda^(2))/(2pi in_(0) r) dr`
`= (lambda^(2))/(2pi in_(0)) [log_(e) r]_(a)^(3a) = (lambda^(2))/(2pi in_(0)) log_(e)^(3)`