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!

Induced Current Question

  1. Apr 22, 2017 #1
    1. The problem statement, all variables and given/known data
    A 5.0-cm-diameter coil has 20 turns and a resistance of 0.50Ω. A magnetic field perpendicular to the coil is B=0.020t+0.010t^2, where B is in tesla and t is in seconds.

    Find an expression for the induced current I(t) as a function of time.

    2. Relevant equations


    3. The attempt at a solution


    [tex] \varepsilon = \frac{d\phi}{dt} [/tex]
    [tex] \varepsilon dt = d\phi [/tex]
    [tex] \int\varepsilon dt = \int d\phi [/tex]
    [tex] \phi = (0.020t + .010t^2) * \pi r^2 [/tex]
    [tex] \varepsilon \int dt = \int d\phi [/tex]
    [tex] \varepsilon t = \pi r^2 [ (1/2) (0.020t^2) + (1/3)(.010t^3)] [/tex]
    [tex] \varepsilon = \frac {I}{R} [/tex]
    [tex] I = \frac{\pi r^2 [ (1/2) (0.020t^2) + (1/3)(.010t^3)]}{tR} [/tex]
     
  2. jcsd
  3. Apr 22, 2017 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    OK, except you haven't taken into account that you have 20 turns in the coil.

    Don't do this.

    Use your expression ## \phi = (0.020t + .010t^2) * \pi r^2 ## in ## \varepsilon = \frac{d\phi}{dt} ## along with the correction for the 20 turns.
     
  4. Apr 22, 2017 #3
    So [tex] I = \frac{20\pi r^2 [ (1/2) (0.020t^2) + (1/3)(.010t^3)]}{R} [/tex]

    So like this?
     
  5. Apr 22, 2017 #4

    TSny

    User Avatar
    Homework Helper
    Gold Member

    No. The numerator in your expression for ##I## does not equal ##\varepsilon##.

    If ## \phi = (0.020t + .010t^2) * \pi r^2 ##, then what is ##\frac{d\phi}{dt} ##?
     
  6. Apr 23, 2017 #5
    Oh ok I get it now. The answer should be [tex] \frac {20\pi r^2(0.020+.020t)}{R}[/tex]
     
  7. Apr 23, 2017 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

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

Have something to add?
Draft saved Draft deleted