(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the potential outside of a long grounded conducting cylindrical rod of radius

R placed perpendicular to a uniform electric field E0.

2. Relevant equations

V(s,[tex]\phi[/tex]) = [tex]a_{0}[/tex]+[tex]b_0{}[/tex]ln(s) + [tex]\sum[/tex]([tex]A_n{}[/tex]cos(n[tex]\phi[/tex])+[tex]B_n{}[/tex]sin(n[tex]\phi[/tex]))*([tex]C_n{}[/tex][tex]s^n{}[/tex]+[tex]D_n{}[/tex][tex]s^{-n}[/tex])

The sum being from n=1 to infinity

The problem is independent of Z (on which the axis of rod lies)

3. The attempt at a solution

I know how to solve these types of problems, but I need the boundary conditions first so that I can begin solving for the coefficients. I know that the inner boundary condition is V(R,[tex]\phi[/tex])=0 (since it is grounded), but I'm stuck on other boundary conditions. I also know that the potential on the entire inside is zero. But I don't think the boundary condition V(0,[tex]\phi[/tex]) is relevant in this case since we are talking about the outside potential.

I also know we can't set potential at infinity equal to zero since it was defined as a "long rod".

I'm also a little confused on what effect the E field has on the boundary conditions. I know that the charge will rearrange on the cylinder so that it creates an opposing E field on the inside to cancel out the external E field.

Any hints on what other boundary conditions there are would be much appreciated!

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# Homework Help: Boundary Conditions for infinite grounded cylinder (Laplace Equation)

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