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 electric field in a solenoid

  1. Dec 13, 2012 #1
    1. The problem statement, all variables and given/known data

    A long solenoid with 1000 turns per meter and radius 2cm carries an oscillating current given by [itex](5A)\sin(100\pi t)[/itex]. What is the electric field induced at radius r=1cm from the axis of the solenoid? What is the direction of this electric field when the current is increasing counterclockwise in the coil?


    2. Relevant equations

    [tex]\oint\vec{E}\cdot d\vec{l}=-\frac{d\Phi_B}{dt}[/tex]
    [tex]\Phi_B=\oint\vec{B}\vec{dA}[/tex]and I have this on my formula sheet so I will start at this point (magnetic field inside a solenoid with n turns per unit length and current I[tex]B=\mu_0nI[/tex]


    3. The attempt at a solution

    So I think in this situation I can say [tex]\Phi_B=BA=(\mu_0nI)(\pi r^2)[/tex]So[tex]\frac{d\Phi_B}{dt}=\pi\mu_0nr^2\frac{dI}{dt}[/tex]
    Also
    [tex]\oint\vec{E}\cdot d\vec{l}=2E\pi r[/tex]
    So I got (ignoring the negative, just considering the magnitude)
    [tex]E=\frac{\pi\mu_0nr^2}{2\pi r}\frac{dI}{dt}= \frac{1}{2} \mu_0nr\frac{dI}{dt}=\frac{1}{2}\mu_0nr\omega I_{max}\cos(\omega t)[/tex]where [itex]\omega=100\pi[/itex] and [itex]I_{max}=5A[/itex]

    This makes sense to me but is not getting me the correct answer! Also I only reasoned that the electric field would be clockwise, but not really sure on that part. Does anyone see where I am going wrong?
     
  2. jcsd
  3. Dec 13, 2012 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Your work looks good to me. Did you convert r to SI units?
     
  4. Dec 13, 2012 #3
    ah sorry. this was the correct answer! the solution I was looking at messed up. what a waste of time typing that out! thank you for looking at this for me!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Induced electric field in a solenoid
  1. Induced Electric Field (Replies: 7)

Loading...