# Gauss' Law problem! Help please infinite sheet with charge density?

1. Feb 21, 2013

### nchin

Gauss' Law problem! Help please!!! infinite sheet with charge density?

In the figure below, a small circular hole of radius R = 1.80 cm has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density σ = 4.50 pC/m2. A z-axis, with its origin at the hole's center, is perpendicular to the surface. In unit-vector notation, what is the electric field at point P at z = 2.56 cm?

Figure
http://www.chegg.com/homework-help/...infinite-flat-nonconducting-surface--q1088630

Teachers Solution:
"The correct electric field can be gotten by adding the infinite charged plane with uniform
density σ to the disk with radius R and opposite charge density -σ."

I understand how to solve the problem but I don't understand why the charge density of the disk is negative? So why is it -σ??? HELP!

2. Feb 21, 2013

### ehild

Re: Gauss' Law problem! Help please!!! infinite sheet with charge dens

The hole can be imagined as a circle with zero charge density. But you can make zero charge density by putting a circle with opposite charge onto the plate, making the charge of unit area equal to σ+(-σ)=0

ehild

3. Feb 21, 2013

### nchin

Re: Gauss' Law problem! Help please!!! infinite sheet with charge dens

so if the surface has a uniform charge density, then the net charge on the surface is zero?

4. Feb 21, 2013

### ehild

Re: Gauss' Law problem! Help please!!! infinite sheet with charge dens

If the added surface has uniform charge density -σ, the net charge density on the circular area is zero.

ehild

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• ###### planehole.JPG
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Last edited: Feb 21, 2013
5. Feb 22, 2013

### nchin

Re: Gauss' Law problem! Help please!!! infinite sheet with charge dens

got it, thanks!

6. Feb 22, 2013

### ehild

Re: Gauss' Law problem! Help please!!! infinite sheet with charge dens

You are welcome

ehild