Torque on circular current loop

[skyesthelimit]

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!

 

[TSny]

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.

 

[skyesthelimit]

OK. You should include the units along with your numerical value.

okay so B=1.3367E-5 T

I don't get E-6 here.

sorry this is my bad. I got μ0=6.28312E-7 instead.

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?

 

[TSny]

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.

 

[skyesthelimit]

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!

 

[TSny]

Ok. Good work.