# Gauss' Law - Planar Symmetry HELP!

## Homework Statement

A square plate of edge length 9.0 cm and negligible thickness has a total charge of 6.3 x 10-6 C.

(a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.50 mm) by assuming that the charge is spread uniformly over the two faces of the plate.

(b) Estimate E at a distance of 62 m (large relative to the plate size) by assuming that the plate is a point charge.

## Homework Equations

E = magnitude of electric field
Omega = Surface Charge Density
e = 8.85 x 10^-12 C^2/Nm^2
pi = pi (ie 3.14...)
q = Charge

E = (Omega)/(2e)

and then I used E = [ 1/(4pie) ] [ q/r^2 ]

## The Attempt at a Solution

Well, I first used the second equation there with q = 6.3 x 10^-6 C
and r = .5 mm = .0005 m to find the magnitude of the electric field.

And then I plugged what I got there into E = (Omega)/(2e) to find Omega.

That was wrong :(. What am I doing wrong? Is there another equation?

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mjsd
Homework Helper
mmm... (a) is just the case of finding E field for an infiinitely large plate for the distance to plate is small compare to plate size... so r does not comes in at all...besides you had E = (Omega)/(2e), nowhere is there a "r" in here!

(b) as suggested by the hint, treat it as a point charge

"just off the center of the plate (at, say, a distance of 0.50 mm)"

So wouldn't the .50mm be the radius? Or am I just still not getting it?

mjsd
Homework Helper
IF you consider that the plate is effectively an infinite plate, THEN you use E=(Omega)/2e as suggested by you... and there is no "r" in this equation!