Surface charge density of Styrofoam

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Homework Help Overview

The discussion revolves around determining the surface charge density of a plastic sheet that supports a charged piece of styrofoam. The problem involves concepts from electrostatics, particularly the relationship between electric fields and forces acting on charged objects.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of Gauss's law and the balance between electric and gravitational forces to find the electric field. Questions arise about eliminating distance squared terms and understanding the implications of charge density on the electric field.

Discussion Status

Some participants have provided hints and guidance regarding the use of equations related to electric fields and charge density. There is an ongoing exploration of the relationship between the electric field and the charge per unit area, with some participants expressing confusion about signs and calculations.

Contextual Notes

Participants are working under the constraints of a homework problem, which may limit the information available and the methods they can use. There is a focus on understanding the principles rather than deriving a final answer.

Gear300
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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.
 
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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.
 
Doc Al - PLEASE help me.

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.
 

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