# Charge Density of Styrofoam

A 8.2 g piece of Styrofoam carries a net charge of -0.700 µC 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?

Ive solved some other related questions with charge densities, but I can't figure out where to start on this one.
None of Gauss's Laws seem to have anything to do with mass and the area is underminable using basic algebra.

8.2g carrying -0.0000007 C
so the charge per unit area will be with units C / m^2

the flux should be equal to the charge divided by Eo

any help about solving this would be appreciated

Gyroscope
brunie, you can apply Gauss's Law to find the electric field created by the large horizontal sheet of plastic, and if this sheet infinite, the electric field calculated is uniform.
You also know that the piece of styrofoam is in equilibrium, so what is the net force on it. I have already talked too much. :)

brunie, you can apply Gauss's Law to find the electric field created by the large horizontal sheet of plastic, and if this sheet infinite, the electric field calculated is uniform.
You also know that the piece of styrofoam is in equilibrium, so what is the net force on it. I have already talked too much. :)

i dont understand how the electric field can be calculated if the area is infinite, also where would the mass be taken into account?

Doc Al
Mentor
There are two things to understand:
(1) The field from a uniform (and infinite) plane of charge (which will be a function of the charge density). You can use Gauss's law to derive it. Hint: Start by drawing a Gaussian box around a section of the plane of charge.
(2) What field strength is required to support the piece of styrofoam? Hint: What force must the field exert on the charge styrofoam?

There are two things to understand:
(1) The field from a uniform (and infinite) plane of charge (which will be a function of the charge density). You can use Gauss's law to derive it. Hint: Start by drawing a Gaussian box around a section of the plane of charge.
(2) What field strength is required to support the piece of styrofoam? Hint: What force must the field exert on the charge styrofoam?

im not very good at deriving the equations, most of the stuff weve been doing on gauss's law has been pretty basic
could u walk me thu a few steps

should the field strength have to balance the gravitational force?

Doc Al
Mentor
im not very good at deriving the equations, most of the stuff weve been doing on gauss's law has been pretty basic
You'll find this pretty basic as well. I'd be surprised if it wasn't in your book. Anyway, see here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html#c1"

should the field strength have to balance the gravitational force?
To be suspended, the net force on the styrofoam must be zero: The upward electric force must balance the downward force of gravity.

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ok so

mg = ∂ / 2 Eo
(8.2/1000)*9.8 = ∂ / 2 (8.85 x 10^-12)

then do i solve for ∂ ?
y doesnt the given net charge come into account?

can n e 1 help?

Doc Al
Mentor
Careful. The electric field from a sheet of charge is:

$$E = \sigma / 2 \epsilon_0$$

What force does that field exert on the styrofoam? (That's where the charge comes in.)

ok, im just having trouble seeing the big picture
we have a electric field, a electric force and gravitational force

the net force should be zero since it is suspended

but i just dont understnad how to balance or equate these forces/fields

Doc Al
Mentor
First things first. What force does an electric field exert on a charge? (Hint: Look up the definition of electric field.)

ok
so should the expression be F / q = ∂ / 2Eo
where F = mg ?

Doc Al
Mentor
Now you're cooking. great, thanks 4 ur help