- #1

Gear300

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

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- Thread starter Gear300
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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

- #1

Gear300

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- 9

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

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- #2

Doc Al

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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.

- #3

Gear300

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- #4

Doc Al

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Good.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.

Where does the distance squared come from? (That appears in the force between two point charges, but that's not relevant here.)But I keep bumping into the distance squared quantity. How would I eliminate it?

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

- #5

Gear300

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- #6

Doc Z

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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?

- #7

Doc Al

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Everything you've said makes sense. To see what you've done wrong, show step by stepDoc 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?

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

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).

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.

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.

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.

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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