# Surface charge density of Styrofoam

• Gear300
In summary, we are trying to determine the charge per unit area on a large horizontal sheet of plastic that has a uniform charge density on its surface. The sheet is supporting a 10.0g piece of styrofoam with a net charge of -.700 x 10^-6 C. To do this, we use the equation E=sigma/2e0, where E is the electric field, sigma is the surface charge density, and e0 is the permittivity of free space. We can find the electric field by equating it to the gravitational force acting on the styrofoam. Dividing this by the charge of the styrofoam gives us the electric field. Rearranging the equation, we
Gear300
A 10.0g piece of styrofoam carries a net charge of -.700 x 10^-6 C and floats above the center of a large horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet?

I've been trying to think a way to model this with a Gaussian surface (without using integrals)...but doesn't seem to work.

Hint: What electric field must the sheet of charge produce to support the styrofoam?

You can certainly use Gauss's law to find the field from a uniform sheet of charge, if you don't happen to know it.

The electric force should balance out the force of gravity. Dividing that by the charge of the styrofoam ball should give the electric field. But I keep bumping into the distance squared quantity. How would I eliminate it?

Gear300 said:
The electric force should balance out the force of gravity. Dividing that by the charge of the styrofoam ball should give the electric field.
Good.
But I keep bumping into the distance squared quantity. How would I eliminate it?
Where does the distance squared come from? (That appears in the force between two point charges, but that's not relevant here.)

What's the electric field from an infinite sheet of charge with some given surface charge density?

The electric field should be E = o/2e, in which o is the surface charge density and e is the permittivity of free space. Then that would also imply that o = E*2e. The Electric field is equal to the electric force divided by the charge of the styrofoam ball...oh. I see. I got it now. Thanks for the help.

So I understand that the electric F equals the gravitational force. Then I divide that by the charge given in the problem to get the electric field. Now, to get the charge per unit area we use the equation E=sigma/2e0. We know the electric field so we rearrange the equation to solve for sigma because that is the charge/unit area factor we are looking for.

So now I'm stuck with this equation:

sigma = E * 2e0

I know the electric field and 2e0 but when I multiply these 2 together I get a wrong answer and a wrong SIGN as well. What am I doing wrong?

Doc Z said:
I know the electric field and 2e0 but when I multiply these 2 together I get a wrong answer and a wrong SIGN as well. What am I doing wrong?
Everything you've said makes sense. To see what you've done wrong, show step by step exactly what you did.

FYI: Don't use equations to figure out the sign--use the rule that opposite charges repel.

## What is surface charge density?

Surface charge density is a measure of the amount of charge per unit area on the surface of a material. It is typically measured in units of coulombs per square meter (C/m^2).

## How is surface charge density of Styrofoam determined?

The surface charge density of Styrofoam can be determined by measuring the amount of charge present on a known area of the material. This can be done using a device called a surface charge density meter.

## What factors affect the surface charge density of Styrofoam?

The surface charge density of Styrofoam can be affected by various factors such as the material's composition, temperature, and humidity. It can also be influenced by the presence of other charged objects nearby.

## Why is the surface charge density of Styrofoam important?

The surface charge density of Styrofoam is important because it can affect the material's interactions with other charged objects. It can also impact the material's behavior and properties, such as its ability to repel or attract other materials.

## Can the surface charge density of Styrofoam be altered?

Yes, the surface charge density of Styrofoam can be altered by various means such as rubbing the material with a different material, exposing it to different temperatures or humidity levels, or applying an external electric field. These methods can change the amount and distribution of charge on the surface of the Styrofoam.

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