A rod CD of length b carrying a current l, is placed in a magnetic field due to a thin log wire AB carrying currrent I as shown in fig. Then find the net force experienced by the wire

Explanation

Magnetic induction due to a straight wire at a position of small element in at a distance x from the conductor `dB=(mu_(0))/(2pi)(I_(1))/x`
force on the current element is `vecdF=dBI_(2)dxsin90^(@)`
`dF=(mu_(0))/(2pi)(I_(1)I_(2))/xdx`
Net force on conductor is `F=int_(a)^(a+b)(mu_(0))/(2pi)(I_(1)I_(2))/xdx`
`=(mu_(0))/(2pi)I_(1)I_(2)[logx]_(a)^(a+b)=(mu_(0))/(2pi)I_(1)I_(2)log(1+b/a)`