1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)...
    dB/dt=(4*∏X10^-7)*(1.1A)*[(5.0*10^4turns)/(.20m*8.0*10^-2m/s)

    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!!

    Thanks
     
  2. jcsd
  3. Apr 1, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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
    Thanks
    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Physics Faraday's Law and Induced Electric Fields
Loading...