Radius of coil in magnetic field

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Two coils with the same number of turns and current are rotating in different magnetic fields, experiencing the same maximum torque. The first coil has a radius of 4.2 cm in a 0.19 T field, while the second coil operates in a stronger 0.42 T field. Participants in the discussion are attempting to equate the torque equations for both coils to find the radius of the second coil, but are struggling with their calculations. They recognize that the area and radius of the second coil should be smaller due to the stronger magnetic field. The discussion highlights the need for a clearer approach to solving for the radius using the relationship between torque, magnetic field strength, and coil area.
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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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I don't understand how you got your answer; show exactly what you did.
 
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.
 
\vec \tau = \vec \mu \times \vec B where \vec \mu = N i \vec A is the magnetic dipole moment. So you are given that \vec \tau 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...
 
i figured it out
 
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.
 

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