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!

Stumped on E&M problem

  1. Dec 10, 2007 #1
    1. The problem statement, all variables and given/known data
    infinitely long conducting cylinder (hollow, so outter radius = b and inner radius = a) which is grounded is in a constant E-field (E=Eo in direction of cylinders' axis) has a dielectric substand "painted" on it, with dielectric constant c and thickness D. Find the electric field everywhere!

    2. Relevant equations
    Well, for dielectrics the usual BC's are:
    E[parallel](inside) = E[parallel](outside)
    D[perpendicular](inside) - D[perpendicular](outside) = sigma <-- charge density

    Also, the general solution for potential in cylindrical coords is:
    V = Ao + Bo*ln(r) + [tex]\sum(An*r^n +Bn*r^(^-^n^))*(Cn*cos(n*phi)+Dn*sin(n*phi)[/tex]

    BC for infinite cylinder:
    dV/dz = 0
    V = -Eo*r*cos(phi) + constant, as r-->infinity (due to constant E-field.)

    3. The attempt at a solution
    I'm having some serious trouble with this problem. One thing I do know, however, is that all of the Dn*sin(n*phi) terms contribute nothing by symmetry and so we can kiss the Dn's goodbye. I think the BC's I stated above are correct, but I'm having problems using them. Other questions I have are: i) how does the dielectric effect V, and, ii)despite being grounded, wouldn't the external field effect the cylinder hence making it act like a dipole?

    Finally, can we assume the E-field inside is zero since it is a conductor? Or does the dielectric and external E-field change this? The E-field in the region a<r<b should be zero too, shouldn't it?

    Any help would be great!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Stumped on E&M problem
  1. Problem is. (Replies: 0)

  2. Lagrangian problem (Replies: 0)

  3. MCQ problem (Replies: 0)

  4. Griffiths 2.26 E&M (Replies: 0)

Loading...