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*From*: Carl Mungan <mungan@usna.edu>*Date*: Tue, 2 Apr 2013 19:24:47 -0400

I am planning to put the following problem on a test tomorrow and I'm

somewhat surprised by the answer. So let me ask the list for insight:

A square waveguide extends from -infinity to infinity in the z direction.

It has two grounded plates at y=-0.5 and at y=0.5. The plate at x=-0.5 has

potential -sin(pi*y). The plate at x=0.5 has potential +sin(pi*y). What is

the surface charge density on the plate at y=-0.5?

(Actually the first part of the problem asks one to find the potential

everywhere inside the waveguide. I give them the hint to just write down

the appropriate form to match the boundary conditions. For those a bit

rusty on this kind of problem, this means a sinh in the x direction and a

sine in the y direction, with each coordinate multiplied by pi. You can now

find the overall scaling constant by fitting to the boundaries.)

Please see what you get for the preceding question and send me any comments

so I can revise the problem if necessary before the test! Thanks, Carl

--

Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)

Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363

mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/

**Follow-Ups**:**Re: [Phys-L] Laplace equation problem***From:*Carl Mungan <mungan@usna.edu>

**Re: [Phys-L] Laplace equation problem***From:*John Denker <jsd@av8n.com>

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