Magnetic field force between two perpendicular wires

In summary, the conversation discusses problems with the setup and solving for the integral to get the expected values of the force. The speaker also suggests that a segment of wire may start at a certain point and end a distance away. They also mention the possibility of a figure accompanying the problem.
  • #1
ssarpal
7
1
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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  • #2
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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Related to Magnetic field force between two perpendicular wires

What is the magnetic field force between two perpendicular wires?

The magnetic field force between two perpendicular wires is the interaction force that arises due to the magnetic fields generated by the currents flowing through the wires. When two wires are perpendicular, the magnetic field created by one wire can exert a force on the other wire, and vice versa, according to the principles of electromagnetism.

How do you calculate the magnetic field force between two perpendicular wires?

To calculate the magnetic field force between two perpendicular wires, you need to use the Biot-Savart law or Ampère's law to determine the magnetic field created by one wire at the location of the other wire. Then, using the Lorentz force law, you can calculate the force exerted on the second wire by the magnetic field of the first wire. The force depends on the current, the distance between the wires, and the orientation of the wires.

Does the distance between the two perpendicular wires affect the magnetic field force?

Yes, the distance between the two perpendicular wires significantly affects the magnetic field force. The magnetic field strength decreases with increasing distance from the wire, following an inverse relationship. As a result, the force between the wires will also decrease as the distance between them increases.

What role does the current in the wires play in the magnetic field force between them?

The current in the wires plays a crucial role in the magnetic field force between them. The magnetic field generated by a wire is directly proportional to the current flowing through it. Therefore, the greater the current in the wires, the stronger the magnetic field and, consequently, the greater the force between the wires.

Can the magnetic field force between two perpendicular wires be attractive or repulsive?

The magnetic field force between two perpendicular wires is neither purely attractive nor repulsive in the traditional sense. Instead, the force depends on the relative direction of the currents and the resulting magnetic fields. The force can be complex due to the perpendicular arrangement, often resulting in a combination of attractive and repulsive components, depending on the specific configuration and positions of the wires.

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