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Homework Help: Net magnetic force on a loop parallel to a wire

  1. Mar 4, 2009 #1
    1. The problem statement, all variables and given/known data

    A long, straight wire carries a current of I1 = 15.8 A. Next to the wire is a square loop with sides L = 1.17 m in length. d = 1.42 m, as shown in the figure below.

    The loop carries a current of I2 = 2.66 A in a direction parallel to the wire. Calculate the magnitude of the net force acting on the loop.

    2. Relevant equations

    The equation i have used is Force = I2*L*[(μ0*I1)/(2*pi*d)]

    3. The attempt at a solution

    Because i am looking for force of the loop, here are my numbers plugged in:

    Force = 2.66*1.17*[(μ0*15.8A)/(2*3.14*1.42m)]
    = 6.93*10^-6N, answer is incorrect

    I am stumped.. any help would be greatly appreciated, thanks!!
  2. jcsd
  3. Mar 4, 2009 #2
    Remember that the straight wire's magnetic field decreases when distance increases. What happens to the force in the parts of the loop that are perpendicular to the wire? Which way are the force vectors pointing?
    Last edited: Mar 4, 2009
  4. Mar 9, 2009 #3
    The left perpendicular side of the loop has a force vector pointing up, towards the straight wire, and the right side has a force vector pointing down. Am i using the right equation, or is there more i need to add to it?
  5. Mar 9, 2009 #4
    No. Use the right hand rule. Thumb points where current points, index points towards the magnetic field and middle shows the direction of force. You're right, thought, they point in different directions an are equal in magnitude so they cancel each other out. All you have to worry is the parallel parts.

    That's the right equation. You just need to remember that distance affects the magnitude of the wire's magnetic field.
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