Magnetic force on a wire due to a loop

The magnetic force on the wire carrying I2 is indeed 0 because of the direction of the magnetic field lines and the fact that I2's own magnetic field does not intersect with it. This is supported by the Biot-Savart law and Ampere's law. The section of the wire shown is the only one that needs to be considered in calculations. Your intuition is correct.
  • #1
Ngineer
64
1
Homework Statement
Calculate the net magnetic force on I2 due to I1
Relevant Equations
Fmag = I * ([a] x [B1])
where:
[a] is a vector representing the length and direction of the wire carrying I2.
[B1] is the magnetic field vector due to I1 (Please see figure.)
242335


I just need to confirm my intuition that the magnetic force on the wire carrying I2 is 0.
Basis for my intuition:

* Right above the center of the loop carrying I1, the magnetic field lines are in exactly the same direction as the piece of wire carrying I2, so [a] x [B1] = 0.
242336
(photo from HyperPhysics)

* I2's own magnetic field is curling around it (Biot-Savart law and Ampere's law), and never goes through it, meaning an external field that actually goes through the wire will have no effect on it.

Note: only the shown section of the wire carrying current I2 is to be considered in calculations.

Is my intuition correct?
Thank you
 
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  • #2
Your reasoning correctly supports your intuition.
 

Related to Magnetic force on a wire due to a loop

1. What is magnetic force on a wire due to a loop?

The magnetic force on a wire due to a loop is the force exerted on a wire by a magnetic field generated by a current-carrying loop.

2. How is the magnetic force on a wire due to a loop calculated?

The magnetic force on a wire due to a loop can be calculated using the formula F = I * L * B * sin(theta), where F is the force, I is the current, L is the length of the wire, B is the magnetic field strength, and theta is the angle between the wire and the magnetic field.

3. What factors affect the magnetic force on a wire due to a loop?

The magnetic force on a wire due to a loop is affected by the strength of the current, the length of the wire, the strength of the magnetic field, and the angle between the wire and the magnetic field.

4. How does the direction of the current affect the magnetic force on a wire due to a loop?

The direction of the current affects the direction of the magnetic force on a wire due to a loop. If the current is parallel to the magnetic field, there will be no force exerted on the wire. If the current is perpendicular to the magnetic field, the force will be at its maximum.

5. What is the relationship between the magnetic force on a wire due to a loop and the distance from the loop?

The magnetic force on a wire due to a loop is inversely proportional to the distance from the loop. As the distance increases, the force decreases. This is known as the inverse square law.

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