Determining the magnetic torque on a loop

In summary, the conversation discussed the calculation of torque on a current loop in a uniform magnetic field, with the angle between the sides of the loop and the field being important in determining the trigonometric function to use in the equation. The angle θ represents the angle between the magnetic field and the normal to the plane of the loop, which can be visualized as a line perpendicular to the plane of the loop. The equivalent expression for torque is IABcos(θ).
  • #1
warfreak131
188
0

Homework Statement



A current [tex]I[/tex] flows in a plane rectangular current loop with height a and horizontal sides b. The loop is placed into a uniform magnetic field [tex]\vec{B}[/tex] in such a way that the sides of length a are perpendicular to [tex]\vec{B}[/tex] (Part A 1 figure), and there is an angle [tex]\theta[/tex] between the sides of length [tex]b[/tex] and [tex]\vec{B}[/tex] (Part A 2 figure).

Calculate [tex]\tau[/tex], the magnitude of the torque about the vertical axis of the current loop due to the interaction of the current through the loop with the magnetic field.
Express the magnitude of the torque in terms of the given variables. You will need a trigonomeric function [e.g., [tex]\sin(\theta)[/tex] or [tex]\cos(\theta)[/tex]]. Use [tex]B[/tex] for the magnitude of the magnetic field.

Figure A 1
17718_a.jpg


Figure A 2
17718_b.jpg


Homework Equations



[tex]\tau=IAB\sin(\theta)[/tex] (Assuming only 1 loop of wire)

The Attempt at a Solution



I know that the area is [tex]a{\cdot}b[/tex], the current is [tex]I[/tex], the field is [tex]B[/tex], and the angle is [tex]\theta[/tex]. I put my answer in as

[tex]\tau=I(a{\cdot}b)B\sin(\theta)[/tex]

the feedback on my answer said to check my trigonometry, so I changed my answer to be the cosine instead of the sine and it was correct. Why is this? What is theta supposed to be the angle in between?
 
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  • #2
In the expression

[tex]
\tau=IAB\sin(\theta)
[/tex]

angle θ is the angle between the magnetic field and the normal to the plane of the loop.
 
  • #3
kuruman said:
In the expression

[tex]
\tau=IAB\sin(\theta)
[/tex]

angle θ is the angle between the magnetic field and the normal to the plane of the loop.

so would the normal be a line perpendicular to the plane assuming its a top down view, like in figure 2?
 
  • #4
Yes, it would be down and to the right in figure 2 as required by the right hand rule for the current shown. In short, it is the direction of the magnetic dipole moment associated with the current loop.
 
  • #5
oh i see, so the equivalent answer would be IABsin(90-theta)) which is teh same as IABcos(theta)?
 
  • #6
Precisely.
 

1. What is magnetic torque?

Magnetic torque is the tendency of a magnetic field to rotate a magnetic object. It is a measure of the strength of the force that causes rotation.

2. How is the magnetic torque on a loop determined?

The magnetic torque on a loop can be determined by multiplying the strength of the magnetic field by the area of the loop and the sine of the angle between the direction of the magnetic field and the normal to the plane of the loop.

3. What factors affect the magnetic torque on a loop?

The strength of the magnetic field, the area of the loop, and the angle between the direction of the magnetic field and the normal to the plane of the loop all affect the magnetic torque on a loop. Additionally, the material and shape of the loop can also impact the torque.

4. How can the magnetic torque on a loop be increased?

The magnetic torque on a loop can be increased by increasing the strength of the magnetic field or by increasing the area of the loop. Additionally, using a material with a higher magnetic susceptibility can also increase the torque.

5. What are some real-world applications of determining the magnetic torque on a loop?

Determining the magnetic torque on a loop is important in various fields such as electrical engineering, physics, and materials science. It is used in designing and testing electric motors, generators, and transformers. It is also used in magnetic resonance imaging (MRI) technology in medicine.

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