What is the Maximum Torque on a Flat Coil in a Magnetic Field?

[purduegirl]

Homework Statement

A narrow flat coil wound on a square frame has 160 turns and sides of 34.0 cm. It carries a current of 5.30 A and is positioned in a 0.260- T magnetic field. What is the maximum torque that can be exerted by the field on the coil?

Homework Equations

Torque = (Number of turns)(Area)(Magnetic Field)(sin of the angle)

The Attempt at a Solution

I calculated the torque using the above information and assuming that the angle was 90 because it was a square. I think my reasoning with the 90 degrees angle is incorrect. For my answer I got, 480.9 J.

 

[alphysicist]

Hi purduegirl,

Homework Statement

A narrow flat coil wound on a square frame has 160 turns and sides of 34.0 cm. It carries a current of 5.30 A and is positioned in a 0.260- T magnetic field. What is the maximum torque that can be exerted by the field on the coil?

Homework Equations

Torque = (Number of turns)(Area)(Magnetic Field)(sin of the angle)

The Attempt at a Solution

I calculated the torque using the above information and assuming that the angle was 90 because it was a square. I think my reasoning with the 90 degrees angle is incorrect. For my answer I got, 480.9 J.

I don't think your equation is quite right. What should it be?

Also, the reasoning in the statement "the angle was 90 because it was a square" is not right. There is something in the problem that tells you what angle to use. Do you see what it is?

 

[purduegirl]

That is the equation my prof. gave us in class. I looked it up in the book and found that torque is equal to NIABsin theta. In the book, it says the angle is between the magnetic field and a line perpendicular to the current loop. I'm not exactly sure what that means however.

 

[alphysicist]

That is the equation my prof. gave us in class. I looked it up in the book and found that torque is equal to NIABsin theta.

This formula from the book is correct; the one from your professor is missing the current for some reason.

In the book, it says the angle is between the magnetic field and a line perpendicular to the current loop. I'm not exactly sure what that means however.

It is important to figure out what that means (you'll have to determine that angle in quite a few problems); however, in this problem they want to know what the maximum torque magnitude would be. From looking at the formula, the reasoning you want to follow is what angle makes the torque become as large as possible?

 

[purduegirl]

I would be 90 or 270 degrees. I think it would be either of those because the torque would be in the plane of the coil.

 

[alphysicist]

I would be 90 or 270 degrees. I think it would be either of those because the torque would be in the plane of the coil.

Yes, that's the right angle; and since they just want magnitudes 90 degrees is fine. (Because that's when the magnetic field is in the plane of the coil.)

 

[purduegirl]

Thank you so much!

 

[alphysicist]

Sure, glad to help!