Magnetic field force between two perpendicular wires

AI Thread Summary
The discussion centers on the calculation of the magnetic field force between two perpendicular wires, where one participant is struggling to obtain expected force values after integrating. Another participant suggests reviewing the integration process and clarifying the starting and ending points of the wire segment in question. There is a mention of the symmetry of the wire segment relative to the bottom wire, which may affect the calculations. Additionally, the need for a figure to visualize the problem is highlighted. The conversation emphasizes the importance of accurate integration and clear definitions in solving physics problems.
ssarpal
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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?
 

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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?
 
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