What Factors Affect the Torque on a Circular Current Loop?

In summary, the question is asking for the magnitude of torque on a circular current loop in a uniform magnetic field. The homework equations used are Torque = [(I*A)*B*(sin(theta))], B = [(1.257E-6T*(m/A)*(I)] /(2*pi*r), and A = [(pi)*(R)^2]. The loop is approximated as small enough for the field to be uniform across it, and the angle between the loop's magnetic moment and the field is 90 degrees.
  • #1
Bubofthedead
16
0

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))].
 

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  • #2
Bubofthedead said:
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.
 
  • #3
So my angle is 90deg, and I didn't need to solve for it?
 
  • #4
What did you use for r? It's not L, you have to use the pythagorean theorem with L and a as your legs.
 
  • #5
For r, I did the square root of [(L)^2+(a/2)^2].
 
  • #6
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.
 
  • #7
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
 
  • #8
Still could use a reply, to my last post (especially about the 90deg).

Thanks
 
  • #9
Bubofthedead said:
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.

merryjman said:
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.

Bubofthedead said:
**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.
 

What is torque on circular current?

Torque on circular current refers to the rotational force experienced by a circular current loop when placed in a magnetic field. It is the product of the current, the magnetic field, and the area of the loop.

How is torque on circular current calculated?

The torque on circular current can be calculated using the formula τ = IABsinθ, where τ is the torque, I is the current, B is the magnetic field, A is the area of the loop, and θ is the angle between the magnetic field and the plane of the loop.

What factors affect the torque on circular current?

The torque on circular current is affected by the strength of the magnetic field, the current in the loop, the size and shape of the loop, and the angle between the loop and the magnetic field.

Can the direction of torque on circular current be changed?

Yes, the direction of torque on circular current can be changed by altering the direction of either the current or the magnetic field. This can be achieved by either changing the orientation of the loop or the direction of the current flowing through it.

What is the significance of torque on circular current?

Torque on circular current is important in many practical applications, such as electric motors and generators. It is also used in scientific experiments to study the behavior of magnetic fields and electric currents.

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