Torque on circular current loop

AI Thread Summary
The discussion focuses on calculating torque in a circular current loop, where the user initially miscalculated the magnetic moment and torque due to incorrect values and symbol usage. The magnetic field B was calculated as 1.3367E-5 T, but the user mistakenly used the wrong value for the magnetic moment, denoted as μ instead of μ0. Clarifications were provided regarding the need to avoid using μ0 for the magnetic moment and to ensure proper unit inclusion in calculations. The user also realized they incorrectly included a factor of 2 in their torque calculation. Ultimately, the user acknowledged the mistakes and expressed gratitude for the guidance received.
skyesthelimit
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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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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.
 
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?
 
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.
 
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!
 
Ok. Good work.
 
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