Charge density on the surface of a conductor

In summary, you tried to solve the problem by setting a condition that the electric field inside the conductor has to be zero, but in this way you have two unknowns (σ1 and σ2). However, you found another equation involving the net charge of the conductor that works correctly.
  • #1
marcos7615
1
1
Homework Statement
There is a flat conductor, charge Q, very large surface area S and thickness
“a“ parallel to a surface charge distribution of density σ = 2Q/S
and separated a distance "d" from it, as shown in the figure. It is requested:

- The charge density σ1 on the outer surface of the conductor
of the load distribution.
Relevant Equations
σ = 2Q/S
1653165597565.png


I have tried to solve the problem by setting as a condition that the electric field inside the conductor has to be 0, but in this way I have two unknowns (σ1 and σ2):
1653166686126.png
 
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  • #2
marcos7615 said:
I have tried to solve the problem by setting as a condition that the electric field inside the conductor has to be 0, but in this way I have two unknowns (σ1 and σ2):
1653168712217.png

Check the signs of the terms on the left side.

Also, you should be able to come up with another relationship between ##\sigma_1## and ##\sigma_2## using the fact that the total charge on the conductor is given to be ##Q##.
 
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  • #3
Will it look like the picture below?
A12.jpg
 
  • #4
alan123hk said:
Will it look like the picture below?
I don't understand this picture. Volume charge density ##\rho## is not relevant to this problem.

You made a good start in your first post where you got a relation between the surface charge densities based on the fact that ##E## must equal zero inside the conductor. However, there is a sign error in your relation
1653484077758.png


Once you make the correction, this relation gives you one equation for the two unknowns ##\sigma_1## and ##\sigma_2##. The total charge ##Q## of the conductor and the the charge density ##\sigma## of the plane are considered as known.

Try finding another equation involving ##\sigma_1## and ##\sigma_2## based on the idea that the net charge of the conductor is ##Q##.
 
  • #5
Sorry I was in a hurry so the description in my previous post was wrong. By the way, I'm not the OP of this thread, I'm just interested in this question.

This is my answer after much deliberation. I believe this time should not go wrong.

A13.jpg
 
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  • #6
alan123hk said:
By the way, I'm not the OP of this thread, I'm just interested in this question.
Yes, I mistakenly assumed you were the OP. It has been several days without any response from the OP.

Your solution is correct.
 
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1. What is charge density on the surface of a conductor?

Charge density on the surface of a conductor refers to the amount of electric charge present per unit area on the surface of a conductor. It is typically measured in units of coulombs per square meter (C/m²).

2. How is charge density related to electric potential?

Charge density and electric potential are inversely related. As charge density increases, the electric potential decreases, and vice versa. This relationship is known as Gauss's law.

3. What factors affect the charge density on the surface of a conductor?

The charge density on the surface of a conductor is affected by the amount of charge present, the size and shape of the conductor, and the material properties of the conductor such as its conductivity and permittivity.

4. Can charge density on the surface of a conductor be changed?

Yes, the charge density on the surface of a conductor can be changed by adding or removing electric charge, or by changing the size or shape of the conductor. It can also be affected by external electric fields.

5. Why is charge density important in understanding conductors?

Charge density is important in understanding conductors because it helps explain how electric charges behave on the surface of a conductor. It also plays a crucial role in determining the electric field and potential on the surface, which ultimately affects the flow of current through the conductor.

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