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

In summary, the conversation is about a Gauss' Law problem involving an infinite sheet with a charge density of 4.50 pC/m2 and a small circular hole with a radius of 1.80 cm. The problem asks for the electric field at a point P located 2.56 cm above the hole. The solution involves adding the charge density of the infinite sheet and the opposite charge density of the disk to find the net charge density, which is equal to zero.
  • #1
nchin
172
0
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!
 
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  • #2


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


ehild said:
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?
 
  • #4


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

ehild
 

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  • #5


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

ehild

got it, thanks!
 
  • #6


You are welcome:smile:

ehild
 

1. What is Gauss' Law and how does it relate to a problem with an infinite sheet of charge density?

Gauss' Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the enclosed electric charge. In the case of an infinite sheet with a uniform charge density, the electric field is constant and perpendicular to the sheet, making it a useful tool for solving problems involving this setup.

2. How do I determine the electric field at a point outside of the infinite sheet with charge density?

To determine the electric field at a point outside of the sheet, you can use Gauss' Law and choose a Gaussian surface that encloses the point of interest. The electric flux through this surface will be equal to the enclosed charge, and by rearranging Gauss' Law, you can solve for the electric field at the point.

3. Is the electric field inside the infinite sheet with charge density equal to zero?

Yes, the electric field inside an infinite sheet with a uniform charge density is equal to zero. This is because the electric field lines are parallel to the sheet and cancel out, resulting in a net electric field of zero inside the sheet.

4. Can Gauss' Law be used to solve problems with a non-uniform charge density on an infinite sheet?

Yes, Gauss' Law can still be used to solve problems with a non-uniform charge density on an infinite sheet. In this case, the electric field will vary across the sheet, but the overall concept of using a Gaussian surface and equating the electric flux to the enclosed charge still applies.

5. How is the electric field affected if the infinite sheet has a finite size instead of being truly infinite?

If the infinite sheet has a finite size, the electric field will not be constant and perpendicular to the sheet. Instead, it will decrease as you move further away from the sheet. However, Gauss' Law can still be used to solve for the electric field at a point outside of the sheet by choosing an appropriate Gaussian surface that encloses the point of interest.

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