A rod `CD` of length `b` carrying a current `I_(2)` is placed in a magentic field due to a thin long wire `AB` carrying current `I_(1)` as shown in figure. Then find the net force experience by the wire

Explanation

Magnetic induction due to a straight wire at a positiion of small element `dx` at a distance `x` from the conductor `AB` is `(mu_(0))/(2pi)(I_(1))/(x)` . Force on the current element is `vec(dF)=dBI_(2)dx sin 90^(@),`
`(mu_(0))/(2pi)(I_(1)I_(2))/(x)dx`. Net force on conductor is `F=underset(a)overset(a+b)int(mu_(0))/(2pi)(I_(1)I_(2))/(x)dx`
`=(mu_(0))/(2pi)I_(1)I_(2)[logx]_(a)overset(a+b)=(mu_(0))/(2pi)I_(1)I_(2)log(1+(b)/(a))`