What is the Force on a Current Loop in a Magnetic Field?

[james11223]

Homework Statement

Here is the problem and the picture that goes along with it. I am really stuck because our teacher never explained a problem like this to us before. Any help is appreciated! THank you so much

http://a2.sphotos.ak.fbcdn.net/hphotos-ak-ash4/229022_113377112081455_100002275016913_125327_6984938_n.jpg

Homework Equations

 

[praharmitra]

What is the force b/w to parallel wires carrying currents?

The first equation in http://en.wikipedia.org/wiki/Ampère's_force_law

 

[james11223]

Here are the equations that I was given

http://a2.sphotos.ak.fbcdn.net/hphotos-ak-snc6/223417_113388105413689_100002275016913_125390_5418139_n.jpg

 

[praharmitra]

Ok, in your formulas, use

$$F = BI l \sin\theta$$

$$B_{wire}=\frac{\mu_0I}{2\pi r}$$
to find out the force per unit length b/w two infinite parallel wires carrying currents $$I_1, I_2$$. Can you do that?

 

[james11223]

THank you so much!

 

[james11223]

Sorry I just realized... irdg what you meant
@praharmitra...

sorry can you explain a little bit more

 

[praharmitra]

Ok, what I want you to do is find the force per unit length b/w a pair of infinite wires separated at a distance r. Here's what you do.

You have one wire carrying current $I_1$. What magnetic field does it produce at a distance r from itself?

Now the second wire carrying current $I_2$, is in the presence of the magnetic field you calculated above. Therefore, what is the force per unit length on this wire?

That is your answer for the force b/w two wires.

 

[james11223]

Would you do it like this:??

F_net = F_near - F_far = (µ_oI₁I₂)(ℓ_near)/(2πd_near) - (µ_oI₁I₂)(ℓ_far)/(2πd_far) = (µ_oI₁I₂ℓ)/(2π) * (1/d_near - 1/d_far) = [(4π x 10^-7T·m/A) (2A)(3A)(6m)]/(2π) * [1/1 - 1/3] = 4.74 x 10^-5N away from the wire


doest that make sense? llol

Thank you so much for all the help guys!

 

[praharmitra]

yes, that is correct yes.