Magnetic force b/w wires of unequal length

In summary, the force between two parallel wires of non-equal length can be calculated using the Biot-Savart integral with finite limits. However, this method is only accurate if the longer wire is significantly longer than the shorter wire. Integrating the field of the longer wire over the shorter wire can also provide the desired result.
  • #1
diagopod
98
3
Is there a formula for the force between two parallel wires of non-equal length? Would one just use the length of the shorter of the two wires?
 
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  • #2
That would only work if the longer wire were very much longer.
You can get the field of the longer, but finite, wire by the usual Biot-Savart integral with finite limits. Then integrate this field over the shorter wire.
 
  • #3
clem said:
That would only work if the longer wire were very much longer.
You can get the field of the longer, but finite, wire by the usual Biot-Savart integral with finite limits. Then integrate this field over the shorter wire.

Thanks, that does makes sense.
 

1. What is the magnetic force between wires of unequal length?

The magnetic force between wires of unequal length is determined by the strength of the current in each wire and the distance between them. The longer wire will experience a greater force due to the larger surface area for the magnetic field to act upon.

2. How does the magnetic force change if one wire is longer than the other?

If one wire is longer than the other, the magnetic force will be stronger on the longer wire. This is because the magnetic field produced by the shorter wire will be spread over a larger area, resulting in a weaker force.

3. Can the magnetic force be calculated for wires of unequal length?

Yes, the magnetic force between wires of unequal length can be calculated using the formula F = (μ0 * I1 * I2 * L) / (2 * π * d), where μ0 is the permeability of free space, I1 and I2 are the currents in each wire, L is the length of the longer wire, and d is the distance between the wires.

4. How does the distance between the wires affect the magnetic force?

The distance between the wires has an inverse relationship with the magnetic force. As the distance between the wires increases, the magnetic force decreases. This is because the magnetic field weakens as it spreads out over a larger area.

5. Can the magnetic force between wires of unequal length be amplified?

Yes, the magnetic force between wires of unequal length can be amplified by increasing the strength of the current in the wires or by decreasing the distance between them. Additionally, using magnetic materials such as iron or cobalt between the wires can also increase the magnetic force.

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