1. Not finding help here? Sign up for a free 30min 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!

Magnetic field of a hollow cylinder

  1. Dec 1, 2013 #1
    1. The problem statement, all variables and given/known data
    Find an expression for the magnetic field of a hollow finite solenoid carrying uniform current with n turns (there is no top or bottom surfaces and the turns a very closely winded) at a point arbitrary P both inside and outside. Lets just say windings around a hollow pvc pipe.


    2. Relevant equations
    I can use either biot savarts law and/or magnetic vector potential for surface currents. I'll use griffiths notation 3rd edition equations 5.39 and 5.64 respectively.


    3. The attempt at a solution
    I'll attempt this in cylinderical coordinates. Since the current is uniform. I'll use the

    [itex]\vec{A}\left(\vec{r}\right)=\frac{1}{4\pi}\int\frac{\vec{K\left(r'\right)}}{\tau}da'[/itex]

    Current density [itex]\vec{K}[/itex] is in the [itex]\hat{\phi}[/itex]

    so [itex]\vec{K}=\frac{nI}{z'}\hat{\phi}[/itex] ? Since current is uniform.
    [itex]\tau=\left|r-r'\right|[/itex]

    [itex]r=s\hat{s}+s\phi\hat{\phi}+z\hat{z}[/itex]
    [itex]r'=s\hat{s}?[/itex]

    [itex]da'=sd\phi'dz'[/itex]

    Where the limits of phi' is 0->2*pi and z' is 0 -> L (length of cylinder)
     
  2. jcsd
  3. Dec 1, 2013 #2
    Do you have an image of the particular set-up? Or could you reference to one in Griffiths?
     
  4. Dec 1, 2013 #3
    Hi Sandy, I just attached an image file its just turns of wire wrapped around a pvc. I looked up a few things I think I have to use elliptic integrals... My first aim is to write an expression for the current density and the position and source vectors r and r'.
     

    Attached Files:

  5. Dec 1, 2013 #4
    Are you neglecting fringing? If you use Biot-Savart, have you considered analyzing a single loop, and then applying superposition to n loops?
     
  6. Dec 1, 2013 #5
    I've thought about that since Jackson's has a solution to a single loop of wire. But I'm going to be inserting a ferromagntic material inside at some stage so I might need to take fringing fields into account?
     
  7. Dec 4, 2013 #6
    Well, I am not really in a position to help you with the fringing effects as I only have experience at the undergraduate level thus far.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Magnetic field of a hollow cylinder
Loading...