Linear charge densities of two parallel wires of infinite length is `lambda_(1)` and `lambda_(2)` . Distance between two wires is R. Force acting on any one wire per unit length is ......

Options

A. `k(lambda_(1)lambda_(2))/R`
B. `k(lambda_(1)lambda_(2))/R^(2)`
C. `(2klambda_(1)lambda_(2))/R`
D. `(2lambda_(1)lambda_(2))/R^(2)`

Answer

C

Explanation

Electric field produced at distance R from wire (1),

`E_(1) = (2klambda_(1))/R`
Charge on wire-2, of length I,
`q=lambda_(2)l`
`therefore` Force acting on wire-2 of length l,
`F = Eq = (2klambda_(1))/R xx lambda_(2)l`
`therefore` Force acting per unit length,
`F/l = (2klambda_(1)lambda_(2))/R`