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Re: [Phys-L] charged paralle plates



In sketch form (I'm assuming we all know how to apply Gauss' law to infinitesimal sheets of charge and all of the reasonable approximations for "large" sheets):

Let x be the charge on the left side of the left plate. Because the field inside the left plate is zero, Gauss' law requires the total charge on the three remaining sides ALSO to be x. Thus

x = (2C - x) + (-3C) => x = -.5C

Gauss' law can now easily be used to find that

1. to the left of the plates E = (0.5 C/m^2)/epsilon0 to the left

2. in between the plates E = (2.5C/m^2)/epsilon0 to the right

3. to the right of the plates E = (0.5 C/m^2)/epsilon0 to the left

John Mallinckrodt
Cal Poly Pomona

On Jan 22, 2014, at 1:06 PM, Carl Mungan wrote:

A colleague and I were discussing this problem I made up:

Suppose there are two large parallel metal plates. To avoid the
problem of infinities, let us say each plate is 1 mm thick, each
plate is square of length 1 m on a side, and the two plates are
separated by 1 mm. A net charge of +2 C is put on the left plate and
charge -3 C on the right plate. Neglecting the fringing, what are the
electric fields to the left of the two plates, in the gap between the
two plates, and to the right of the two plates? Spell out all
physical assumptions used in your solution and not just the correct
numerical answers.

My solution is at:

http://usna.edu/Users/physics/mungan/_files/documents/Scholarship/ChargedParallelMetalPlates.pdf

After trying it yourself, I'd like to know what you think of my
solution. (But try it yourself first, so you're not biased by my
approach!) -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/
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