Help finding the spring constant in a magnetic field

[enforcer53]

Homework Statement

Consider a wire loop in a 1.88 T magnetic field (coming out of the board at a 55.0° angle). The loop is 0.300 m tall and 0.400 m wide, carrying a 2.90 A current traveling in a clockwise direction. The loop feels a torque that causes the spring to compress. If the spring is compressed by 4.30 mm, what is the spring constant?


The attempt at a solution
This is what i tried. I don't feel I am getting the right answer.

Torque is T = IABsinθ
(2.90 A)(0.120 m^2)(1.88 T)sin(55.0) =0.536

I know that Torque is also = Frsinθ
I then rearranged the formula to get F = Torque/rsinθ (0.536)/(0.15)(sin55) = 4.36 = F

I plug my Force value into the F=kx formula. In order to find k, I did (4.36)/(0.0043) which gave me k = 1013.9

This does not seem correct to me. Where did I go wrong?

 

[NascentOxygen]

Hi enforcer53,

I think we'd need to see the diagram.

 

[enforcer53]

Here are the diagrams

 

[NascentOxygen]

Okay. Where did you get this equation from:

Torque is T = IABsinθ

If you resolve B into a component normal to the plane of the loop and a component within the plane of the loop, you will, I think, see that as far as the current-carrying-loop is concerned, only one side contributes a force which the spring can oppose.

 

[enforcer53]

I got the IABsinθ equation from class. I gave this problem another try.

I set it up so Kx = ILBsinθ. I rearranged to get K = ILBsinθ/x... Plug and chug (2.90)(0.400)(1.88)(sin55)/(0.0043) = 415.4

Am I getting closer?

 

[NascentOxygen]

How did you decide what value to use for L?

 

[enforcer53]

The dimensions of the loop are 0.400 and 0.300. So I used the length of 0.400

 

[NascentOxygen]

The dimensions of the loop are 0.400 and 0.300. So I used the length of 0.400

Why did you decide on 0.400?

 

[TerraForce469]

The dimensions of the loop are 0.400 and 0.300. So I used the length of 0.400

Ah, but what is the length of the side of the current in which we are concerned with in opposing the spring?