1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Current Loop in a nonuniform magnetic field

  1. Mar 15, 2013 #1
    1. The problem statement, all variables and given/known data

    A nonuniform magnetic field exerts a net force on a current loop of radius R. The figure shows a magnetic field that is diverging from the end of a bar magnet. The magnetic field B at the position of the current loop makes an angle θ with respect to the vertical, as the same magnitude at each point on the current loop. (I know that I need to solve in terms of R, I, B, and θ
    2013-03-15 19.24.19.jpg
    2. Relevant equations

    F=IlxB

    F=IlBsinθ

    τ=μxB

    τ=μBsinθ

    3. The attempt at a solution

    I fought the urge to use the force equation after substitution 2∏r for l. Instead I examined the force on one small segment and planned to integrate. The length would be in terms of arc length Δs. The I would be a constant. It seems that the problem indicates that the magnetic field B is constant (surely that is an assumption because the distance from the magnet was not indicated, right?) I also thought that the angle should be the only thing changing (I doubt this is a double integral problem). The subscript i indicates that this is for some segment i.

    So

    Fi=IΔsBsinθi

    The first thing that jumps out at me is that we don't have the necessary Δθ, but we do have Δs. Δs=ΔθR, but this is for a different θ, right? So, here is where I got lost and thought that something was wrong.

    Next I tried relating it with torque.

    τ=μBsinθ=FR
    τ=IABsinθi
    τ=I((2∏R^2)/(θ)/2∏B))sinθi=FR

    But here again we have a different θ value, correct?

    I would very much appreciate some help. Thank you!
     
  2. jcsd
  3. Mar 15, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    What are you supposed to solve for?
     
  4. Mar 16, 2013 #3
    Net force
     
  5. Mar 16, 2013 #4

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Use the differential form of your F equation above, which is
    d F = I d l x B for the force on an element d l of the loop.

    Then integrate around the loop - an easy integration since the force is constant everywhere around the loop.
     
  6. Mar 16, 2013 #5
    I know that the answer is to be 2πRIBsinθ, but I don't see how or why.

    dF=IdlxB is the same as saying dF=IΔsxB or dF=IBsinθΔs integrating yields

    F=IBssinθ or F=2πRsinθ.

    But doesn't the value of theta change for each segment?

    Oh wait! No, it doesn't. It should remain constant as the ring has rotational symmetry. Am I correct in my reasoning here?
     
  7. Mar 16, 2013 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

    It is important to note that in the formula F = I B Δs sinθ, θ is not the same θ as given in the diagram. Remember, in the formula, sinθ is coming from a cross product of Δs and B.
     
  8. Mar 16, 2013 #7

    rude man

    User Avatar
    Homework Helper
    Gold Member

    That is correct! And take note of what tsny says about theta. Keep track of angles when you take your cross-product!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Current Loop in a nonuniform magnetic field
Loading...