A conductor `AB` of length `l` carrying current `i` is placed perpendicular to a long straight conductor carrying a current `I` as shown. Force on `AB` will be

Explanation

Magnetic field at distance `x` from long wire
`B = (mu_(0)i_(0))/(2pi x), ox`
Force on length `dx` of wire `AB`
`dF = Bidx = (mu_(0)i_(0)i)/(2pi)(dx)/(x)`
`F_(AB) = (mu_(0)i_(0)i)/(2pi) int_(a)^(a + l) (dx)/(x) = (mu_(0)i_(0)i)/(2pi)|log_(e) x|_(a)^(a + l)`
`= (mu_(0)i_(0)i)/(2pi)[log_(e)(a + l) - log_(e)(a)]`
`= (mu_(0)i_(0)i)/(2pi) log_(e) (1 + (l)/(a))`, upward
Point of application of force acting on `AB`
`x' = (int_(0)^(L) xdF)/(int_(0)^(L) dF) = ((mu_(0)i_(0)i)/(2pi) int_(a)^(a + l)dx)/((mu_(0)i_(0)i)/(2pi)1n(1 + (l)/(a))) = (l)/(1n(1 + (l)/(a)))`
`x'` is distance from lonf wire.