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Homework Help: Direction of Induced EMF (Faradays Law) Confusion

  1. Dec 8, 2011 #1
    1. The problem statement, all variables and given/known data

    See figure attached.

    2. Relevant equations



    3. The attempt at a solution

    If we attempt to solve part a) in this question we encounter several confusions.

    If we assume i(t) to be a positive current, the magnetic flux will flow through the core in a counter clockwise direction.

    How are we supposed to deduce the direction of the induced voltage,

    [tex]e_{ind}[/tex]

    ?

    If you tell me whether or not i(t) is increasing or decreasing or remaning constant I can then tell you how eind relates to v.

    Are we just supposed to assume it is either increasing or decreasing? If so, the relation to v to eind will have a sign difference in each case.

    Assume i(t) is increasing,

    [tex]e_{ind} = -v = -\frac{d\psi}{dt}[/tex]

    Assume i(t) is decreasing,

    [tex]e_{ind} = v = -\frac{d\psi}{dt}[/tex]

    As you can, depending on which case I assume, my expression of v will change by a negative sign.

    This will affect the answer in part b).

    How do we know which one to choose?
     

    Attached Files:

  2. jcsd
  3. Dec 8, 2011 #2
    Looking at the picture, I take the up arrow to indicate positive current, an increasing current causes the polarity as indicated in the coil N2? So for part b increasing current leads to positive voltage? Any others?
     
  4. Dec 9, 2011 #3
    Thus,

    [tex]e_{ind} = v = -\frac{d\psi}{dt} = -\frac{250\mu_{0}N_{1}N_{2}d^{2}}{a}\frac{di(t)}{dt}[/tex]

    Why does my expression for v turn out to be negative while theirs is positive?

    I was told that the expression for eind is always,

    [tex]e_{ind} = -\frac{d\psi}{dt}[/tex]

    I agree that the positive induced current, if i(t) is increasing, will flow from the positive terminal of v to the negative terminal of v.
     
    Last edited: Dec 9, 2011
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