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 position 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_2dx sin 90^@, dF = (mu_0)/(2pi) (I_1 I_2)/(x) dx` . Net force on conductor is
`F = int_(a)^(a+b) (mu_0)/(2pi) (I_1 I_2)/(x) dx`
` =(mu_0)/(2pi) I_1 I_2 [log x]_(a)^(a+b) = (mu_0)/(2pi) I_1 I_2 log ( 1 + b/a)`