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Electromagnetism with Lentz's Law

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A rectangular loop of wire resistance R and dimensions h and w moves with a constant speed v toward and through a region containing a uniform magnetic field of strength B directed into the plane of the page. The region has a width of 2w as shown above. (I think our teacher told us this was a free response question from a Physics C exam, although I don't know what year it's from. Also I didn't include part a because I knew how to solve it.)

    (b) On the axes below, plot the following as functions of position x of the right edge of the loop shown above.

    i) The induced current I in the loop
    ii) The applied force F required to keep the loop moving at a constant speed.

    Let the counterclockwise current be positive, clockwise current be negative, forces to the right be positive, and forces to the left be negative. The graphs should begin with the loop in the position shown (x = 0) and continue until the right edge of the loop is a distance 2w to the right of the region containing the field (x = 5w). Sorry I don't have a picture of the graph, I would link a website that has a pdf of the question, but I'm pretty sure that's not allowed.

    2. Relevant equations

    The question only asks for relative values of current and force versus time, so it's mostly right-hand rule, but I = V/R = E/R = Blv/R and Fp = Fb = BIlsinθ, and Eavg = ΔBAcosθ/Δt

    3. The attempt at a solution

    First of all, for both graphs the current and force will be zero from 0w to w and from 4w to 5w because the loop is outside of the field.
    For current: From w to 2w, the current is counterclockwise and constant because there's a constant increase in flux (Lentz's law, field points into page). From 2w to 3w, the current is zero again because there's no change in magnetic flux (the entire loop is inside the magnetic field). From 3w to 4w, the current is clockwise and constant (Lentz's Law, field points into the page but magnetic flux is decreasing).
    For applied force: From w to 2w it's constant to the right (right-hand rule, field points into the page, current in the right side of the loop travels upward, magnetic force pushes left). From 2w to 3w, there's no applied force because F=BIL and I=0 from 2w to 3w. From 3w to 4w, the force is constant to the right (right-hand rule, field points into the page, current travels upward because the left side of the loop is in the magnetic field).

    I've discussed with some classmates and this is the best we could figure it out, but I'm still not sure if what I've written is correct or if the current increases from w to 2w and then remains constant and counterclockwise from 2w to 3w because the current is caused by an average induced emf over the given time interval. Anyways if you made it through the whole post, thanks and I appreciate your help.
     
    Last edited: Mar 11, 2012
  2. jcsd
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