Radius of coil in magnetic field

In summary, the problem involves two coils with the same number of circular turns and carrying the same current, rotating in different magnetic fields. Both coils experience the same maximum torque. The question is asking for the radius of the second coil, which can be found by setting the torque equations for both coils equal to each other and solving for the area of the second coil. However, this approach did not yield the correct answer. Alternative methods, such as using the magnetic dipole moment equation or considering the relationship between the area and the magnetic field, may be needed to solve the problem.
  • #1
larkinfan11
9
0

Homework Statement



Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field in a setup similar to the square coil in the figure below. Coil 1 has a radius of 4.2 cm and rotates in a 0.19 T field. Coil 2 rotates in a 0.42 T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2?

http://www.webassign.net/CJ/21-21.gif



Homework Equations



Torque= NIABsin(phi)

The Attempt at a Solution



I thought that since each coil experienced the same maximum torque and received the same current that I could set their respective NIABsin(phi) equations equal to each other, cancel out current, and solve for the area of the second coil, but the answer that I got was incorrect (8.899 cm). So I know that there has to be another way to solve this question, but I'm at a loss as to how to approach it. Can anyone offer any guidance or insight on what I'm doing wrong?
 
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  • #2
I don't understand how you got your answer; show exactly what you did.
 
  • #3
Help needed

I am stuck on the same problem. I tryed B=muI/2pir. I used the one where we have all the infromation except for the I. I then used this I and put into a new equation to slove for r. I just thought it was smiple subistion. Because for you you don't have the I and for the other you need to find the r. NO clue after that.
 
  • #4
[tex]\vec \tau = \vec \mu \times \vec B[/tex] where [tex]\vec \mu = N i \vec A[/tex] is the magnetic dipole moment. So you are given that [tex]\vec \tau[/tex] are the same and i guess current too. so it is just a matter of finding area then radius... you should expect the area, ie. radius for loop 2 be smaller since field is stronger there...
 
  • #5
i figured it out
 
  • #6
Ok I'm also trying to figure this one out and having trouble. I'm assuming I somehow need to use the area of the given radius' coil and the magnitude its magnetic field to find the area of the ungiven radius' coil?

I'm just confused as to how.
 

What is the radius of a coil in a magnetic field?

The radius of a coil in a magnetic field refers to the distance from the center of the coil to the outer edge. It is an important factor in determining the strength and direction of the magnetic field produced by the coil.

How does the radius of a coil affect the strength of the magnetic field?

The larger the radius of the coil, the stronger the magnetic field will be. This is because a larger radius allows for more loops of wire and therefore, more current flowing through the coil. More current results in a stronger magnetic field.

What is the equation for calculating the magnetic field produced by a coil?

The equation is B = μ0 * n * I, where B is the magnetic field strength, μ0 is the permeability of free space, n is the number of turns in the coil, and I is the current flowing through the coil.

Does the orientation of the coil affect the radius in a magnetic field?

Yes, the orientation of the coil can affect the radius in a magnetic field. For example, if the coil is oriented perpendicular to the magnetic field, the radius will be the distance from the center of the coil to the outer edge. However, if the coil is oriented parallel to the magnetic field, the radius will be the distance from the center of the coil to the center of the magnetic field.

How does changing the radius of the coil affect the direction of the magnetic field?

Changing the radius of the coil does not directly affect the direction of the magnetic field. However, it can indirectly affect the direction by changing the strength of the magnetic field. A larger radius will result in a stronger magnetic field that can potentially change the direction of the field lines.

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