A conductor `AB` of length `10 cm` at a distance of `10cm` from an infinitely long parallel conductor carrying a current `10A` . What work must be done to move `AB` to a distance of `20cm` if it carries `5A` ?

Explanation

Force on a conductor at a distance X is `F = (mu_0i_1 i_2 l)/(2pi x)` work done to displace it through a small distance
`dx = dW = vecF.vecdx`
`dW = (mu_0i_1 i_2 l)/(2pi x) dx`
` W = int_(0.1)^(0.2) (mu_0 i_1 i_2 l)/(2pi x) dx `
`W = (mu_0 i_1 i_2 l)/(2pi) [log_e x]_(0.1)^(0.2)`
`W = (4pi xx 10^(-7) xx 10 xx 5 xx 10 xx 10^(-2) )/(2pi) log e^2`
`W = 0.693 xx 10^(-6) J`