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

[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/questions-and-answers/figure-small-circular-hole-radius-r-180-cm-cut-middle-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!

 

[ehild]

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

 

[nchin]

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

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

 

[ehild]

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

ehild

 

[nchin]

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

ehild

got it, thanks!

 

[ehild]

You are welcome

ehild