Two infinitely long parallel wires having linear charge densities `lambda_(1)` and `lambda_(2)` respectively are placed at a distance of `R` metres. The force per unit length on either wire will be `(k= 1/(4piepsilon_(0)))`

Options

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

Answer

2

Explanation

Electric field due to `①` at `② , E = (lambda)/(2 pi in_(0) R)`
force on `dl` length `(dq = lambda_(2) dl)`
`dF = dqE = (lambda_(1) lambda_(2))/(2 pi in_(0) R) dl`
`(dF)/(dl) = (lambda_(1) lambda_(2))/(2 pi in_(0) R) = (1)/( 4pi in_(0)) .(2 lambda_(1) lambda_(2))/(R )`
`= k .(2 lambda_(1) lambda_(2))/(R )`