Net magnetic force on a loop parallel to a wire

In summary, for a long, straight wire carrying a current of 15.8 A and a square loop with sides of 1.17 m and a distance of 1.42 m carrying a current of 2.66 A in the same direction as the wire, the magnitude of the net force acting on the loop is equal to 6.93*10^-6 N. However, using the right hand rule, it can be determined that the force vectors on the perpendicular sides of the loop cancel each other out, leaving only the parallel parts to be considered. This results in a net force of 0 N acting on the loop.
  • #1
Cheezay
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Homework Statement



A long, straight wire carries a current of I1 = 15.8 A. Next to the wire is a square loop with sides L = 1.17 m in length. d = 1.42 m, as shown in the figure below.

The loop carries a current of I2 = 2.66 A in a direction parallel to the wire. Calculate the magnitude of the net force acting on the loop.


Homework Equations



The equation i have used is Force = I2*L*[(μ0*I1)/(2*pi*d)]

The Attempt at a Solution



Because i am looking for force of the loop, here are my numbers plugged in:

Force = 2.66*1.17*[(μ0*15.8A)/(2*3.14*1.42m)]
= 6.93*10^-6N, answer is incorrect


I am stumped.. any help would be greatly appreciated, thanks!
 
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  • #2
Remember that the straight wire's magnetic field decreases when distance increases. What happens to the force in the parts of the loop that are perpendicular to the wire? Which way are the force vectors pointing?
 
Last edited:
  • #3
The left perpendicular side of the loop has a force vector pointing up, towards the straight wire, and the right side has a force vector pointing down. Am i using the right equation, or is there more i need to add to it?
 
  • #4
Cheezay said:
The left perpendicular side of the loop has a force vector pointing up, towards the straight wire, and the right side has a force vector pointing down.

No. Use the right hand rule. Thumb points where current points, index points towards the magnetic field and middle shows the direction of force. You're right, thought, they point in different directions an are equal in magnitude so they cancel each other out. All you have to worry is the parallel parts.

Am i using the right equation, or is there more i need to add to it?

That's the right equation. You just need to remember that distance affects the magnitude of the wire's magnetic field.
 

1. What is the net magnetic force on a loop parallel to a wire?

The net magnetic force on a loop parallel to a wire is the sum of all the individual magnetic forces acting on each segment of the loop. It is also known as the magnetic moment of the loop and is calculated by multiplying the current in the wire by the area of the loop.

2. How does the direction of the current in the wire affect the net magnetic force on the loop?

The direction of the current in the wire determines the direction of the magnetic field created by the wire. This magnetic field will interact with the magnetic field of the loop, resulting in a net magnetic force that is either attractive or repulsive depending on the direction of the current.

3. Can the distance between the wire and the loop affect the net magnetic force?

Yes, the distance between the wire and the loop can affect the net magnetic force. According to the inverse square law, the magnetic force is inversely proportional to the square of the distance between two objects. This means that as the distance between the wire and the loop increases, the net magnetic force will decrease.

4. What is the difference between a loop parallel to a wire and a loop perpendicular to a wire?

A loop parallel to a wire will experience a net magnetic force due to the interaction of the magnetic fields, whereas a loop perpendicular to a wire will not experience any net magnetic force. This is because the magnetic fields are in the same direction for a parallel loop, but in opposite directions for a perpendicular loop, resulting in a cancelation of forces.

5. How can the net magnetic force on a loop parallel to a wire be increased?

The net magnetic force on a loop parallel to a wire can be increased by increasing the current in the wire, increasing the area of the loop, or decreasing the distance between the wire and the loop. Additionally, using materials with higher magnetic permeability can also increase the net magnetic force.

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