Magnetic field force between two perpendicular wires

[ssarpal]

Homework Statement

Two wires, 1 and 2, are carrying currents I1 and I2. They are perpendicular to each other and separated by distance d.

What is the force exerted on a segment of wire 2 of length L from the point where they would have intersected if they were on the same plane.

Relevant Equations

https://openstax.org/books/university-physics-volume-2/pages/12-2-magnetic-field-due-to-a-thin-straight-wire

What is the magnetic field at a point P, located a distance R from the wire?
Using Biot-Savart law, equation 12.8 gives the magnetic field.


https://openstax.org/books/university-physics-volume-2/pages/11-4-magnetic-force-on-a-current-carrying-conductor

Using Equation 11.12 to calculate the force.

There are a couple of problems with the same setup. On plugging in the values and solving for the integral, I am not getting the expected values of the force. Is there something wrong in the solution attached?

 

[kuruman]

I see nothing wrong in what you have done so far. Can you show what you got when you integrated?

Also, you show that segment $L$ is symmetrically disposed about the bottom wire. Could it be that "segment of wire 2 of length L from the point where they would have intersected if they were on the same plane" starts at that point and ends a distance $L$ away? Is there a figure that goes with this problem?