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 is
`F=(mu_(0)i_(1)i_(2)l)/(2pix)`
Wone done to displace it through a small distance
`dx=dW=vecF.vec(dx)` `dW=(mu_(0)i_(1)i_(2)l)/(2pix)dx`
`W=int_(0.1)^(0.2)(mu_(0)i_(1)i_(2)l)/(2pix)dx` `W=(mu_(0)i_(1)i_(2)l)/(2pi)[log_(e)x]_(0.1)^(0.2)`
`W=(3pixx10^(-7)xx10xx5xx10xx10^(-2))/(2pi)log_(e)2`
`W=0.693xx10^(-6)J`