1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: EMF in a loop; non-constant magnetic field

  1. Apr 6, 2013 #1
    1. The problem statement, all variables and given/known data

    Refer to Figure attached.

    The current in the long straight wire is

    i = (4.5A/s2)t2-(10A/s)t

    Find the EMF in the square loop at t=3.0s.

    2. Relevant equations

    [itex]\xi = -\frac{d \Phi}{dt}[/itex]

    And Biot-Savart law for straight wires of infinite length:

    [itex]B = \frac{\mu_0 i}{2 \pi R}[/itex]

    3. The attempt at a solution

    Solution: 600 nV

    I cannot recreate this result.

    I consider two loops, one below the wire in the picture and one above.
    I calculate their EMFS separately as:

    [itex]\xi = -\frac{A \mu_0}{2 \pi R} \frac{di}{dt}[/itex]

    and find the difference between them.
    This doesn't reveal 600 nV.

    I try integrating with respect to R, and get mathematical gibberish (ln[0]).

    I must be missing something fundamental in my setup - any suggestions?

    Attached Files:

    Last edited: Apr 6, 2013
  2. jcsd
  3. Apr 6, 2013 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Think about the flux through the shaded areas in the figure.
    [EDIT: This can help avoid dealing with r = 0. But I don't get 600 nV either. You will need to integrate.]
    [Edit 2: OK, it does come out 600 nV.]

    Attached Files:

    Last edited: Apr 6, 2013
  4. Apr 6, 2013 #3
    The change in flux for those areas cancel.

    So, I consider the third region.

    4cm away from the source.
    8cm long, 16cm wide (not shown in figure)

    [itex]\xi = \frac{\mu_0 * 8cm * 16 cm * 17A/s}{2 \pi} \int^{12cm}_{4cm} \frac{1}{R}[/itex] = 47 nV.

    If I don't integrate, and instead just find the difference, I get closer, but it doesn't make sense to do that. ( = 725 nV)
  5. Apr 6, 2013 #4

    You were right, it does come out to 600 nV.
    Infinitesimal lengths :).

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted