Torque on circular current loop

In summary: Keep in mind that the magnetic moment of a loop is defined as IA, where I is the current and A is the area enclosed by the loop. Also, be careful with your units and make sure they are consistent throughout your calculations. In summary, the speaker is attempting to solve a question involving a long wire and a dipole. They calculate the B-field and μ0, but are confused as to why their answer is incorrect. They receive help by being reminded of the proper symbol for magnetic moment and the need for consistent units in calculations.
  • #1
skyesthelimit
5
0
Homework Statement
What is the magnitude of the torque on the circular current loop?
Relevant Equations
Torque =IAxB=IABsin(theta)
r=3cm
So I'm having a little trouble getting to the solution to this question so here's my attempt at a solution and I'm not seeing the issue with it

1. I calculated the B-field due to the long wire (approximating the distance from the dipole to be equivalent to that in the centre since r>d)
B= μ0*I/(2πr) = 1.3367E-5

2. Calculated μ0 =IA =0.2*(πr^2) =0.2*[π*(1E-3)^2] = 6.28312E-6

3. Calculated torque using IAB = 1.7E-11 (since theta =90 degrees)

However, that's not the right answer and I'm a little lost as to why. Could someone point me in the right direction please? Thanks!
 

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  • #2
skyesthelimit said:
1. I calculated the B-field due to the long wire (approximating the distance from the dipole to be equivalent to that in the centre since r>d)
B= μ0*I/(2πr) = 1.3367E-5
OK. You should include the units along with your numerical value.

2. Calculated μ0 =IA =0.2*(πr^2) =0.2*[π*(1E-3)^2] = 6.28312E-6
I don't get E-6 here.

3. Calculated torque using IAB = 1.7E-11 (since theta =90 degrees)
I don't see how you can get this answer from your values of B and IA.
 
  • #3
TSny said:
OK. You should include the units along with your numerical value.
okay so B=1.3367E-5 T
TSny said:
I don't get E-6 here.
sorry this is my bad. I got μ0=6.28312E-7 instead.
TSny said:
I don't see how you can get this answer from your values of B and IA.
I got this value using IAB=2*1.3367E-5*6.28312E-7=1.7E-11
Should I have used I=0.2A instead?
 
  • #4
skyesthelimit said:
okay so B=1.3367E-5 T
Yes

sorry this is my bad. I got μ0=6.28312E-7 instead.
This is the value of IA. (Units?) I would not use the symbol μ0 for this. μ0 is reserved for the permeability of free space constant. IA is the magnetic moment of the loop and would be denoted by μ, not μ0.

I got this value using IAB=2*1.3367E-5*6.28312E-7=1.7E-11
Why did you include a factor of 2? Note that IAB = (IA)(B). You have already calculated IA and B.
 
  • #5
TSny said:
Yes

This is the value of IA. (Units?) I would not use the symbol μ0 for this. μ0 is reserved for the permeability of free space constant. IA is the magnetic moment of the loop and would be denoted by μ, not μ0.

Why did you include a factor of 2? Note that IAB = (IA)(B). You have already calculated IA and B.
oh! I see it now. I got a little confused after calculating the μ (which you rightly pointed out that I used the wrong symbol) ! Thanks so much for the help!
 
  • #6
Ok. Good work.
 

What is torque on a circular current loop?

Torque on a circular current loop refers to the rotational force experienced by a loop of current-carrying wire when placed in a magnetic field. It is a result of the interaction between the magnetic field and the magnetic moment of the loop.

How is torque on a circular current loop calculated?

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

What factors affect the torque on a circular current loop?

The torque on a circular current loop is affected by the strength of the magnetic field, the current in the loop, the area of the loop, and the angle between the magnetic field and the plane of the loop. Additionally, the shape of the loop and the material it is made of can also affect the torque.

What is the direction of torque on a circular current loop?

The direction of torque on a circular current loop is determined by the right-hand rule. If the fingers of the right hand curl in the direction of the current, and the thumb points in the direction of the magnetic field, then the palm of the hand will point in the direction of the torque.

What are the practical applications of torque on a circular current loop?

Torque on a circular current loop has many practical applications, such as in electric motors, generators, and electromagnets. It is also used in devices such as galvanometers and compasses to detect and measure magnetic fields.

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