Calculate the force on a current carrying wire in a uniform magnetic field as shown in Fig. 1.59.

Explanation

The net force from `A` to `B` is `dvecF=I(dvecLxxvecB)`
`int_A^BdvecF=int_A^PI[dvecL_1xxvecB]+int_P^QI[dvecL_2xxvecB]+int_Q^RI[dvecL_3xxvecB]+int_R^TI[dvecL_4xxvecB]+int_T^BI[dvecL_5xxvecB]`
The entire path can be broken down into element vectors joined to each other in sequence. We known, from polygon law of addition of vectors, that vector joining the tail of the first vector to the
head of the last vector is the resultant.
`vecF=I(vecLxxvecB)`
where `|vecL_1|=a+sqrt(c^2-b^2+2r+d`
`F_("net") =IB(a+sqrt(c^2-b^2)+2r+d)` and its direction is upward on plane of paper.