What Factors Affect the Torque on a Circular Current Loop?

[Bubofthedead]

Homework Statement

Note getting the right answer.

Question:
a). What is the magnitude of the torque on the circular current loop in the figure?
b). What is the loop's equilibrium position.

Homework Equations

Torque = [(I*A)*B*(sin(theta))]

L= 2.0cm
a= 2.0mm
Iwire = 2.0A
Iloop = 0.20A

The Attempt at a Solution

First, I tried to find theta using tan^-1(x/y).
Second, I tried to find B, using B= [(1.257E-6T*(m/A)*(I)] /(2*pi*r).
Finally, I tried Torque = [(I*A)*B*(sin(theta))].

 

[Doc Al]

First, I tried to find theta using tan^-1(x/y).

Not sure what you did here. Theta is the angle between the field from the wire and the magnetic moment of the loop (which is perpendicular to the loop).

Second, I tried to find B, using B= [(1.257E-6T*(m/A)*(I)] /(2*pi*r).
Finally, I tried Torque = [(I*A)*B*(sin(theta))].

Looks OK.

 

[Bubofthedead]

So my angle is 90deg, and I didn't need to solve for it?

 

[merryjman]

What did you use for r? It's not L, you have to use the pythagorean theorem with L and a as your legs.

 

[Bubofthedead]

For r, I did the square root of [(L)^2+(a/2)^2].

 

[merryjman]

OK good, you've got that. Maybe:

1) Did you account for both torques, one for each wire in the loop?
2) Did you use the correct area for the loop?
3) Are the directions correct? I think the force on the bottom piece would be up and to the left, and the force on the top would be up and to the right..

If not that I can't see what else might be wrong.

 

[Bubofthedead]

1). Aren't both torques the same, so I would double it?
2). Isn't the area A= [(pi)*(R)^2]?
3). I don't think direction is important, because it just wants the magnitude of torque.

Let me know I made any bad assumptions on these 3.

**Also, can someone confirm that the angle in my calculation for Torque = [(I*A)*B*(sin(theta))] is 90deg because of the figure being perpendicular.

Thanks so far

 

[Bubofthedead]

Still could use a reply, to my last post (especially about the 90deg).

Thanks

 

[Doc Al]

For r, I did the square root of [(L)^2+(a/2)^2].

I wouldn't bother with that, since the distance from wire to loop segment varies along the loop. Instead I would make the approximation that the loop is small enough that the field from the wire can be considered uniform across the loop. Use the field at a distance L from the wire.

1) Did you account for both torques, one for each wire in the loop?
2) Did you use the correct area for the loop?
3) Are the directions correct? I think the force on the bottom piece would be up and to the left, and the force on the top would be up and to the right..

The loop is circular, not rectangular.

**Also, can someone confirm that the angle in my calculation for Torque = [(I*A)*B*(sin(theta))] is 90deg because of the figure being perpendicular.

Yes. In the orientation shown in the diagram, the angle between the loop magnetic moment (perpendicular to the loop) and the magnetic field is 90 degrees.