A triangular loop `(ABC)` having current `i_(2)` and an infinite wire having current `i_(1)` are placed in the same plane.Find the magnetic force of interaction between the infinite wire and the loop `ABC`.

Answer

`(mu_(0)i_(1)i_(2)tantheta)/(2pi)[ln(d+l)/d-l/(d+l)]` towards left

Explanation

Force of interaction will act an `AB` and `AC` only
`F_(AB)=underset(0)overset(l//cos theta)int(mu_(0)i_(1)i_(2)sin theta)/(2pi(d+x cos theta))dx`
`(mu_(0)i_(1)i_(2)tan theta)/(2pi)ln (d+l)/d` towards left
`F_(AC)= (mu_(0)i_(1)i_(2)tan theta)/(2pi)ln l/(d+l)` towards right
`F_("net")=F_(AB)-F_(AC)`
`F_("net")=(mu_(0)i_(1)i_(2)tan theta)/(2pi)[ln (d+l)/d-l/(d+l)]` towards left