# Calculating Charge Density of Styrofoam and Plastic Sheet

• brunie
In summary, 8.2 grams of Styrofoam with a net charge of -0.700 µC is suspended above a large horizontal sheet of plastic with a uniform charge density on its surface. To find the charge per unit area on the plastic sheet, Gauss's Law can be applied to calculate the electric field created by the sheet, and the net force on the styrofoam must be zero for it to be in equilibrium. By equating the electric force and gravitational force on the styrofoam, the expression F/q = ∂/2Eo can be used to solve for the charge per unit area on the plastic sheet.
brunie
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

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. :)

Gyroscope said:
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 don't understand how the electric field can be calculated if the area is infinite, also where would the mass be taken into account?

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?

Doc Al said:
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 we've 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?

brunie said:
im not very good at deriving the equations, most of the stuff we've 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.

Last edited by a moderator:
ok so

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

then do i solve for ∂ ?
y doesn't the given net charge come into account?

can n e 1 help?

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, I am 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 don't understnad how to balance or equate these forces/fields

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 ?

Now you're cooking.

great, thanks 4 ur help

## 1. What is the charge density of Styrofoam?

The charge density of Styrofoam refers to the amount of electric charge per unit volume of the material. It is typically measured in coulombs per cubic meter (C/m^3).

## 2. How is the charge density of Styrofoam determined?

The charge density of Styrofoam can be determined through experiments that involve measuring the amount of charge on a given amount of the material. This can be done using a device called an electrometer, which can detect and measure electric charge.

## 3. Does the charge density of Styrofoam change under different conditions?

Yes, the charge density of Styrofoam can change under different conditions. Factors such as temperature, humidity, and exposure to certain substances can affect the charge density of the material.

## 4. What is the significance of the charge density of Styrofoam?

The charge density of Styrofoam is important in understanding the material's behavior in electric fields. It can also be used to determine the material's dielectric properties, which are important for applications such as insulation and capacitors.

## 5. Can the charge density of Styrofoam be manipulated?

Yes, the charge density of Styrofoam can be manipulated through various methods such as applying an external electric field or changing the material's composition. This can be useful in controlling the material's properties for specific applications.

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