Gauss' Law and an infinite sheet

[catie1981]

Homework Statement

a small circular hole of radius R = 2.03 cm has been cut in the middle of an infinite, flat, nonconducting surface that has a uniform charge density σ = 4.61 pC/m^2. A z axis, with its origin at the hole's center, is perpendicular to the surface. What is the magnitude (in N/C) of the electric field at point P at z = 3.05 cm? (Hint: See Eq. 22-26 and use superposition.)

There is supposed to be a figure, but it really doesn't lend much to this. It is a flat sheet laid on the horizon, with the z axis going through a hole in the middle of the sheet. Point P is on the z axis, and R is just shown as the radius of the hole in the sheet. Which, is pretty much what was said in the problem...

Homework Equations

the equation mentioned above is
E = (σ / 2ε) *( 1- z/ (√z^2 + R^2))

but how I'm supposed to use that and superposition, I am not sure.

The Attempt at a Solution

I want to just plug in the given values, but I don't think that it right, because the question mentions superposition, but what am I adding together?! There was an additional hint about using a disc of equal magnitude and such, but oppostire direction. Wouldn't I then need a different equation? Help! (and Thanks)

 

[dynamicsolo]

There is a favorite trick for dealing with "holes" in charge distributions. You use the superposition of the field for an infinite sheet of uniform surface charge density σ , together with the field for a disk the size of the "hole", having uniform surface charge density -σ .

 

[catie1981]

oooo, so for the sheet I would use sigma/2*epsilon and the disc would have a -sigma value...then I add those numbers and viola! I have the solution. Thanks!

 

[dynamicsolo]

oooo, so for the sheet I would use sigma/2*epsilon

Yes, for its electric field, since this is a non-conducting sheet.

and the disc would have a -sigma value...

Yes, in the equation you were given for the field along the axis for a uniformly charged disk at a distance z from the plane of the disk.

then I add those numbers and viola!

That should do it.