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_(0)i_(1)i_(2)l)/(2pix)`
Work donw to displace it through a small distance
`dx=dW=vec(F).vec(dx)`
`dW=(mu_(0)i_(1)i_(2)l)/(2pix)dx`
`W=underset(0.1)overset(0.2)int (mu_(0)i_(1)i_(2)l)/(2pix)dx` ,brgt `W=(mu_(0)i_(1)i_(2)l)/(2pi)[log_(e)x]_(0.1)^(0.2)`
`W=(4pixx10^(-7)xx10xx5xx10xx10^(-2))/(2pi)loge^(2)`
`W=0.693xx10^(-6)J`