Net magnetic force on circuit segment due to 2 parallel wires

In summary, the net magnetic force on a circuit segment due to two parallel wires is determined by the interaction of the magnetic fields generated by each wire. When currents flow through the wires, they create magnetic fields that exert forces on each other. The direction and magnitude of the net force depend on the direction of the currents and the distance between the wires. If the currents are in the same direction, the wires attract each other, while if they are in opposite directions, they repel each other. The total force on a segment of wire can be calculated using the Biot-Savart law and Ampère's force law.
  • #1
risakapal
6
1
Homework Statement
Two long, parallel wires are separated by a distance d and carry current I flowing in opposite directions, as shown in the figure. A circuit segment of length L is parallel to the long wires and carries a current of I' flowing in the direction shown. The circuit segment is at distance R from the wires. The +z direction is to the right, the +x direction is up, and the +y direction is out of the screen. Approximate the net magnetic force F acting on the circuit segment in terms of the given quantities and physical constants, assuming that R >> d. Express the force using ijk unit vector notation.
Relevant Equations
F∝ l x B
Do not approximate the distance between each wire and the wire segment as 𝑅. Rather, make approximations when comparing higher orders of 𝑅 and 𝑑. For example, assume that 𝑅^2 + 𝑑^2 ≈ 𝑅^2, and so forth.
Screenshot 2024-03-14 at 11.19.28 PM.png
Screenshot 2024-03-14 at 11.21.46 PM.png

This answer is incorrect when I try submitting it.
 
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  • #2
Hi,
A bit hard to read on my phone, but: what is the ijk notation (:wink:) and which way is the force ?
 
  • #3
BvU said:
Hi,
A bit hard to read on my phone, but: what is the ijk notation (:wink:) and which way is the force ?
Thank you for your response. Would the force on the circuit be to the left since the wire with the current in the same direction is closer? I thought it might be in the negative z-direction.
 
  • #4
Hmm, i am lost a bit -- think you're right...
 
  • #5
  • #6
risakapal said:
This answer is incorrect when I try submitting it.
Your answer looks right to me, but…
What would your answer be if all the wires were length L? Would you expect the result to be the same for both scenarios?
I am not at all sure… just asking.
 
Last edited:
  • #7
The answer worked! It seems I did not need a subscript for the constant. Thank you very much for your help!
 
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Likes BvU

FAQ: Net magnetic force on circuit segment due to 2 parallel wires

What is the net magnetic force on a circuit segment due to two parallel wires carrying currents in the same direction?

The net magnetic force on a circuit segment due to two parallel wires carrying currents in the same direction is attractive. This is because the magnetic fields generated by the currents in each wire interact in such a way that they pull the wires towards each other.

How does the distance between two parallel wires affect the net magnetic force on a circuit segment?

The net magnetic force between two parallel wires is inversely proportional to the distance between them. As the distance between the wires increases, the magnetic force decreases. Mathematically, the force per unit length \( F/L \) is given by \( F/L = \frac{\mu_0 I_1 I_2}{2\pi d} \), where \( \mu_0 \) is the permeability of free space, \( I_1 \) and \( I_2 \) are the currents in the wires, and \( d \) is the distance between the wires.

What happens to the net magnetic force if the currents in the two parallel wires are in opposite directions?

If the currents in the two parallel wires are in opposite directions, the net magnetic force between the wires is repulsive. The magnetic fields generated by the currents interact in such a way that they push the wires away from each other.

How can you calculate the net magnetic force on a specific segment of a circuit due to two parallel wires?

The net magnetic force on a specific segment of a circuit due to two parallel wires can be calculated using the formula \( F = I L B \), where \( I \) is the current in the segment, \( L \) is the length of the segment, and \( B \) is the magnetic field at the location of the segment due to the other wire. The magnetic field \( B \) produced by a long straight wire at a distance \( d \) is given by \( B = \frac{\mu_0 I}{2\pi d} \).

Does the orientation of the circuit segment relative to the parallel wires affect the net magnetic force?

Yes, the orientation of the circuit segment relative to the parallel wires affects the net magnetic force. The force is maximized when the segment is perpendicular to the magnetic field lines generated by the parallel wires. If the segment is parallel to the wires, the force will be zero because the magnetic field lines are parallel to the current direction in the segment, resulting in no force.

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