Jackson Problem 3.12/3.18 -- Electric potential near two plates

[PP27]

Homework Statement

I need to solve a problem like Jackson 3.18. I need to find potential due to the same configuration but the position of two plates is opposite i.e. Plate at Z=0 contains disc with potential V and plate at Z=0 is grounded.

Homework Equations

The Attempt at a Solution

I think solution of problem 3.12 gives half of the solution as the value of potential in terms of bessel solution. But, i can't figure out what additional things must be done to complete this problem in addition to problem 3.12.

 

[TSny]

Hello, and welcome to PF!

You need to reconsider the function Z(z). The boundary condition for this function changes when going from prob. 3.12 to prob. 3.18.

 

[euphoricrhino]

This is a straightforward application of the result of problem 3.17, once you have the Green function, then simple application of equation 1.44 gives you the potential in the volume.