An infinite wire , placed along z axis has current I1 in positive z direction . A conducting rod placed parallel to y axis has current I2 in positive y direction. The ends of rod subtens +30 and -60(degrees) at the origin with positive x direction.The rod is distance a from the origin . Find net force on the rod.

hi ,

first the magnetic field at any point by i1 willbe =  µ/2pi *i1 / r

force on any current element  =  i2 * (  dl X B)

let i2 is placed at a distance apart from origin

    by vector anaysis force on  upper part of I2 will be in +z direction whereas  on lower part it willbe in -z direction

   let any current element dl  substed  Ø at the origin with positive x direction   then 

l/a = tan  Ø 

emplies  dl = a sec^2 Ø  dØ

&  r = a secc

putting in (1)..

      dF =  i2 * (  a sec^2 Ø  dØ  *  µ/2pi *i1 / a sec Ø  )  sin  Ø 

        = µ/2pi *  I1*I2 *  tan Ø   dØ 

total force on upper part ,

                              F1 = §[ µ/2pi *  I1*I2 *  tan Ø   dØ  ]₀³⁰

_{^{on lower part    F2 =}} §[ µ/2pi *  I1*I2 *  tan Ø   dØ  ]₀⁶⁰

total force on wire = F1 -F2

                               =  - §[ µ/2pi *  I1*I2 *  tan Ø   dØ  ] ₀³⁰

                                      ⁼ µ/2pi *  I1*I2 *ln sec Ø  ] ₀³⁰

                                                    =µ/2pi *  I1*I2 *ln 2/3 ^{1/2    _{in the -z direction}}