# Charge density, electric fields

• glid02
In summary, to find the charge density of each face of a square plate of copper in a uniform electric field, you can use Gauss's law with a Gaussian cylinder to calculate the charge contained within the cylinder for each surface. From this, you can find the charge density and use it along with the dimensions of the plate to calculate the total charge on each face. The idea of a Gaussian pillbox can also be used to simplify the calculation.
glid02
Here's the question:
A square plate of copper with 50.6 cm sides has no net charge and is placed in a region of uniform electric field of 80.9 kN/C directed perpendicularly to the plate.

a. Calculate the charge density of each face of the plate.

b. Calculate the total charge on each face.

I know I can find the total charge with density*area, and I know that density = Q/A, I just don't know how to convert the field into a charge, and I'm not even sure if that's what I'm supposed to do. Any help would be great.

Thanks a lot

Have you encountered the idea of a Gaussian pillbox?

That exact term hasn't been used but I have learned about Gaussian surfaces. The only example in my book that even somewhat deals with this question finds the electric field of a charged plane with a known density with a Gaussian cylinder.

glid02 said:
That exact term hasn't been used but I have learned about Gaussian surfaces. The only example in my book that even somewhat deals with this question finds the electric field of a charged plane with a known density with a Gaussian cylinder.
This is a very similar problem to the plane of charge. If you use a Gaussian cylinder with cylinder walls perpendicular to a surface of the plate, one end inside the metal, and the other end outside the metal in the constant electric field the surface integral of the field is very easy to compute. The field inside the metal is zero. The field outside is parallel to the walls of the cylinder so they do not contribute. The only contribution is from the one circular end where the field is perpendicular to the surface and constant.

If you apply Gauss's law for cylinders cutting each side of the plate seperately you can find the charge contained within the Gaussian cylinder for each surface. From this you can find the charge density of each plate. Using the charge density and the dimensions of the plate you can find the total charge on each face.

## 1. What is charge density?

Charge density is a measure of the amount of electric charge per unit volume or area. It can be calculated by dividing the total charge by the volume or area in which it is distributed.

## 2. How is charge density related to electric fields?

Charge density influences the strength of electric fields. The higher the charge density, the stronger the electric field will be. Electric fields are also used to calculate charge density by dividing the electric field strength by the permittivity of the material.

## 3. What is the unit of charge density?

The SI unit of charge density is coulombs per cubic meter (C/m3) for volume charge density and coulombs per square meter (C/m2) for surface charge density.

## 4. How does charge density affect the behavior of particles in an electric field?

In an electric field, particles with higher charge density will experience a stronger force and therefore will be more likely to move in the direction of the field. This can lead to the particles being accelerated or decelerated, depending on the direction of the electric field.

## 5. Can charge density be negative?

Yes, charge density can be negative. This occurs when there is an excess of negative charge compared to positive charge in a given volume or area. However, the overall charge of a system must still be balanced, meaning the total charge must be equal to zero.

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