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Homework Help: Physics Faraday's Law and Induced Electric Fields

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data
    A wire loop with area 8.00 cm2 is placed inside a 20.0 cm long solenoid with 5.00×10^4 turns that carries a current of 1.10 A. The loop is concentric with the solenoid. If the length of the solenoid is stretched so that its length increases at a rate of 8.000e-2 m/s, with the number of turns remaining constant, what is the initial induced potential difference in the wire loop?

    2. Relevant equations
    Magnetic Field for Solenoid B = μ*I*n (n is number of loops per unit length)
    E= ΦB/dt
    Area circle = ∏r^2

    3. The attempt at a solution

    I know that the area of the circle is 0.0008m^2 and that is not changing
    The angle is 90°
    For E= ΦB/dt there are three things that can change to cause the change in B.
    1- change in area so you have (dA)/dt * B* cosθ
    2 - change in flux so you have A*(dB/dt)*cosθ
    3 - change in the angle A*B*-sinθ

    Since the question is asking about the flux through the wire loop and the change is occurring in the length of the solenoid - I do not think Area (A) is changing. I also don't think that the angle is changing. Since, the length of the solenoid is changing I think that magnetic field is what is changing as a function of time.
    The formula for magnetic field is B = μ*I*n (n is number of loops per unit length). This is where I start getting messed up (at least I think this is where my troubles start)...

    Another thought I had was to find B initial - which I found to be (0.346T) and then multiple it by 1/8.0*10^-2m/s so get dB/dt.

    Any advice is appreciated!!

  2. jcsd
  3. Apr 1, 2012 #2


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    hi tnbstudent! :smile:

    (try using the X2 and X2 buttons just above the Reply box :wink:)

    your difficulty is in finding dB/dt, when the question only gives you dL/dt (L is the length)

    so write B as a function of L, and use the chain rule dB/dt = dB/dL dL/dt :wink:

    (btw, are you ok now on your other solenoid question?)
  4. Apr 1, 2012 #3
    This definitely gets the dL/dt in the equation which I was missing.
    When I write B in terms of L I get:
    B=μ*I*t/l (where t is the number of turns)
    dB/dL = μ*I*t*(-1/l^2)
    Is the length in this the original (.20m) or (.20m*8.0m/s *10^-2)

    Our book gives answers for most questions but changes one variable. This one uses dL/dt as 3.0m/s and the answer is 4.15 *10^-4V.
    When I use the information you gave me above (thanks for that - I would not have remembered to use the change rule) and I use l as .20meters I get an answer that is off by one decimal point.

    Any suggestions for something I should take another look at?

    (yes, i was able to get my other solenoid question - it was very easy... simply plug in the numbers but I used the wrong angle)
  5. Apr 1, 2012 #4


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    i don't think so :confused:

    (btw, it's the chain rule, and it's called that because eg dx/dt = dx/dy dy/dz dz/dw dw/dt, in a chain! :wink:)
  6. Apr 1, 2012 #5
    Thanks for your help. I think the book is just off by one decimal place. I did the equation using the chain rule and I got 1.11e-4 which was wrong... so I tested e-3 and it was correct.
    Either way - I'm glad I understand how to do it.

    Thanks again
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