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Eq. for displacement of current-carrying wire due to magnet

  1. Mar 23, 2015 #1

    1. The problem statement, all variables and given/known data

    a3vab1i.png
    This is for a physics lab I am working on. A flowing current causes the wire to deflect towards the right a certain amount that varies depending on the current strength.

    I need to derive the equation d=(L/mg)F
    where
    -- L is the distance between contact 1 and 2 both of which lie in the same vertical line.
    -- mg is the weight attached at the end of the wire.
    -- F is the strength of the magnetic field.
    -- d is the horizontal displacement of the wire at the magnet

    The magnets are located in the center of the setup and the vertical distance from contact 1 to the magnet can be approximated to be L/2

    For the full lab, see http://skipper.physics.sunysb.edu/~physlab/phy134Lab5Magnetic_Force_v4.pdf

    2. Relevant equations
    Derive: d = (L/mg)F
    F = 2*F_W *sin(theta)
    theta = d/L/2 = 2d/L
    See below for the derivations of the second two equations.

    3. The attempt at a solution
    MOMDYs7.png
    Here is a free-body diagram of the wire at the point where a magnetic field moves it to the right. Equation (1) is for theta, the angle that F_W makes with the vertical.
    fTqxDOs.png
    I got the equation for theta as follows. Tan(theta) = Opposite/Adjacent. Taking theta to be the angle of the wire to the horizontal, opposite is equation to d and adjacent is taken to be L/2 so this will be the triangle formed by the top half of the wire and the magnet. Thus tan(theta)=d/L/2=2d/L

    So I've gotten close but the 4 shouldn't be there. I know I have an error somewhere and likely, the 2s of the equations before should have canceled each other once I combined them.
     

    Attached Files:

  2. jcsd
  3. Mar 23, 2015 #2
    I also got the same eqn as yours. Check the questiin again
     
  4. Apr 6, 2015 #3
    Bump.
     
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