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Homework Help: Faraday's Law and a solenoid

  1. Nov 24, 2009 #1
    1. The problem statement, all variables and given/known data
    A long solenoid with 1000 turns per meter and a radius 2.00 cm carries an oscillating current given by I = (5.00A) sin (100 pi t). What is the electric field induced at a radius r = 1.00 cm.from the axis of the solenoid? What is the direction of the electric field when the current is increasing counterclockwise in the coil?

    2. Relevant equations
    Eq. 1: [tex]\epsilon=\frac{-d\phi}{dt}[/tex]

    Eq. 2: [tex]\phi=BA[/tex]

    Eq. 3: [tex]B=\mu_0 n \frac{-dI}{dt}[/tex]

    Eq. 4: [tex]E=\frac{\epsilon}{2 \pi r}[/tex]

    3. The attempt at a solution

    I think that you just sub Eq.3 into Eq.2 and then Eq.2 into Eq.3 and then into Eq 4 and take the derivative of I:

    [tex]E = \frac{R^{2} \mu_0 n}{2 r} 500 \pi sin (100\pit)[/tex]

    My confusion is where to put the r=1cm and R=2cm.

    Also, how do you know which direction the E field is going?

    Thanks for your help. =)
    Last edited: Nov 24, 2009
  2. jcsd
  3. Nov 24, 2009 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper


    Agreed. Question for you: what is A here? More specifically, what size loop are you using to get Φ?

    Eq. 3 is wrong. Look it up again, what is the B-field inside a solenoid?

    Agreed. Question for you: what is r here? More specifically, what size circle are you using to relate ε and E?

    What happened to Eq. 1? I think you better show what steps you took to get this equation.

    See my comments after Eq's 2 and 4.

    Lenz's Law is useful here.
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