Capacitors: How to determine the charge density at each surface?

In summary, there are two metal plates with charge densities of 3 C/m^2 and -3C/m^2 respectively. The charge density on surfaces 1 and 4 are zero, while the charge density on surfaces 2 and 3 are 3C/m^2 and -3C/m^2. There is a question about the possibility of the charge density on the surfaces being 1 C/m^2, 2 C/m^2, -2 C/m^2, and -1 C/m^2. However, this does not violate Gauss law as the E field inside the conductor needs to be zero. The final question is about the charge density on surfaces 1, 2, 3,
  • #1
AlonsoMcLaren
90
2
Suppose we have two metal plates, one with a charge density of 3 C/m^2, the other -3C/m^2

We are told that the charge density on surfaces 1 and 4 are zero and the charge density on surface 2 is 3C/m^2, on surface 3 is -3C/m^2

Any reason for that? Is it possible that the charge density on surface 1 is 1 C/m^2, on surface 2 is 2 C/m^2, on surface 3 is -2 C/m^2, on surface 4 is -1 C/m^2? I don't see it violating Gauss law..
 

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  • #2
The E field inside the conductor needs to be zero, do you see any problems.
 
  • #3
cragar said:
The E field inside the conductor needs to be zero, do you see any problems.

So what is the charge density on the surfaces 1, 2, 3, 4 if the upper plate has a total charge density of 3C/m^2 and the lower plate has charge density of 0?
 

FAQ: Capacitors: How to determine the charge density at each surface?

What is a capacitor and how does it work?

A capacitor is an electronic component that is used to store electrical charge. It consists of two conductive plates separated by a dielectric material. When a voltage is applied to the capacitor, one plate becomes positively charged and the other becomes negatively charged. This creates an electric field between the plates, which stores the electrical energy.

What is charge density and why is it important in capacitors?

Charge density is the measure of electric charge per unit area on the surface of a capacitor plate. It is important in capacitors because it determines the amount of electrical charge that can be stored in the capacitor and the strength of the electric field between the plates.

How do you calculate the charge density at each surface of a capacitor?

The charge density at each surface of a capacitor can be calculated by dividing the amount of charge on each plate by the surface area of the plate. This can be represented by the equation: ρ = Q/A, where ρ is the charge density, Q is the charge on the plate, and A is the surface area of the plate.

What factors affect the charge density in a capacitor?

The charge density in a capacitor is affected by the voltage applied to the capacitor, the distance between the plates, and the type of dielectric material used. A higher voltage or a smaller distance between plates will result in a higher charge density, while a higher dielectric constant of the material will also increase the charge density.

How does the charge density affect the capacitance of a capacitor?

The charge density is directly proportional to the capacitance of a capacitor. This means that a higher charge density will result in a higher capacitance, and vice versa. This relationship is represented by the equation: C = Q/V, where C is the capacitance, Q is the charge on the capacitor, and V is the voltage applied to the capacitor.

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