A conductor AB of length 10 cm at a distance of 10 cm 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= (mu_0 i_1 i_2l)/(2 pi xx)`
Work done to displace it through a small distance `"dr" = "force" xx "direction"`
`rArr dw = (mu_0 i_1 i_2 l)/(2pir) dr`
`w = int_(0.1)^(0.2) = (mu_0 i_1 i_2 l)/(2pir) dr ,`
`w = (mu_0 i_1 i_2 l)/(2pi) ["log"_e xx]_(0.1)^(0.2)`
` w= (4 pi xx 10^(-7) xx 10 xx 5 xx 10 xx 10^(-2))/(2pi) "log"_e 2`
`w = 0.693 xx 10^(-6)J.`