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Faraday's Law

  1. May 9, 2010 #1
    1. The problem statement, all variables and given/known data
    A square of side 2cm, in the first quadrant of the x-y plane, with a corner at the origin, is in a magnetic field pointing out of the page of magnitude 4t2y.

    Calculate the emf around the square at t = 2.5s and give its direction.

    2. Relevant equations

    [tex] \epsilon = - \frac{d}{dt} \Phi [/tex]

    3. The attempt at a solution

    Do I do it like this?

    [tex] \epsilon = -\frac{d}{dt} \int ^2 _0 \int ^2 _0 4t^2 y \ dx \ dy [/tex]

    If so, then great. If not, what do I do?
  2. jcsd
  3. May 9, 2010 #2
    Yeah, that seems correct as you are just using the definition of flux:
    [tex]\phi = \int \vec{B} \cdot \vec{dA} [/tex]

    And subbing that into your above expression for the emf.

    It looks correct but I'm not certain as I'm only a mere first year so you should probably get someone else to confirm.
  4. May 9, 2010 #3
    It looks correct, but I would double check the units of distance, magnetic field and voltage. What system of units are you using for Maxwell's equations? I normally use SI units with meters, Telsa and Volts, so I would have set my upper limits at 0.02 rather than 2. However, if you are using CGS units it may be correct - just double check it.
  5. May 9, 2010 #4
    Yeah, I screwed up the units in the OP; had them right in my paper calculation.
  6. May 9, 2010 #5
    OK, good! I guess you're using SI units. I think with cgs (or, more accurately Gaussian) units there might be a speed of light factor involved.
    Last edited: May 9, 2010
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