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Homework Help: Magnetic Field and Electric field outside a long solenoid

  1. Feb 5, 2006 #1

    The question goes like this:

    A long solenoid has n turns per unit length and carries a current given by I=I₀sinωt. The solenoid has a circular cross section of radius R. Find the induced electric field at a radios r from the axis of the solenoid for (a) r<R (b) r>R

    Well, i got the first part as E=μR²N²ωI₀cos(ωt)/(2Rl). Does this looks like it?

    For the second bit, i found it as zero. But i am not really sure. And if it is zero, What should i say?
  2. jcsd
  3. Feb 7, 2006 #2
    Hello there,

    You'll have to excuse me because I'm not using the greek symbols.

    (a) r<R,

    int(E.dl)=-d(B.Area)/dt (definition of induced emf) take loop around

    E.2*pi*r = -pi*(r^2)*mu*n*I*omega*cos(omega*t)

    E= -(mu*n*I*omega*r*cos(omega*t))/2

    is the induced field inside solenoid. Your answer is close but use r instead of R (since we are inside).

    (b) r>R, outside

    You are confusing with the case when magnetic field is zero outside long solenoid due to cancellations between field due to currents in successive & opposite loops.

    In this case, (r>R...remember loop is longer)

    E*2*pi*r = -pi*(R^2)*mu*n*I*omega*cos(omega*t)

    (remember flux is over an area defined by pi*(R^2))

    E = -(mu*n*I*omega*(R^2)*cos(omega*t))/ (2*r)

    is the induced electric field outside.

    Hope that helps,
    Last edited: Feb 7, 2006
  4. Feb 7, 2006 #3


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    Staff: Mentor

    Are you sure they are asking about Electric fields? That doesn't make much sense. More often, you will be asked to solve for the magnetic field as a function of radius for the solenoid....
  5. Feb 11, 2006 #4
    Yea, i m asked to find electric field. And i just found out this is one of the question found from the textbook. And yes, thats the correct answers! but i am still not sure why it is not zero. isnt that when theres no magnetic field, theres no electric field as well?
  6. Feb 11, 2006 #5

    Physics Monkey

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    Science Advisor
    Homework Helper


    To understand why there is an electric field outside the solenoid, just think about Faraday's Law. If you draw a loop around the solenoid, the magnetic flux through the loop is changing as a function of time, right? Even though there is no magnetic field outside the solenoid there is still a changing magnetic flux (from the field inside the solenoid). What does this tell you about the electric field?
  7. Feb 12, 2006 #6
    Yea, thats amaze me. Why can there be magnetic flux but no magnetic field. So lif theres magnetic field, the magnetic flux is constant?
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