Gauss's Law to Symmetric Charge Distribution

In summary, the problem involves a 10.0 gram piece of styrofoam with a net charge of -0.700\muC floating above a charged plastic sheet with a uniform charge density. The first step is to set the electric force on the styrofoam equal to the gravitational force acting on it, and then use this to solve for the electric field. The next step is to use this electric field to find the surface charge density on the plastic sheet using Gauss's Law. The final answer can be found by rearranging the equation sigma=2E(epsilon0).
  • #1
magda3227
19
0
A 10.0 gram piece of styrofoam carries a net charge of -0.700[tex]\mu[/tex]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?


Homework Equations


[tex]\Phi[/tex] = E[tex]\int[/tex]dA = [tex]\frac{q}{\epsilon}[/tex]


The Attempt at a Solution



I wasn't even sure how to start this problem. The fact that mass is given threw me off and I can't see how it would be used in the problem. I thought that possibly it could be used to find the electric force between the two objects since it must overcome the downward gravitational pull on the styrofoam (right?). From there, I used the equation that states F=qE to get that the magnitude of the electric field of the styrofoam is -1.4E5. Still, I have no idea how to find the charge per unit area of the plastic sheet and don't think my approach is anywhere near correct. Can someone please help me?
 
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  • #2
I think you're on the right track. Think about what kind of electric field a flat, charged surface creates.
 
  • #3
Since the styrofoam floats above the sheet of charge, its technically at rest there (with 0 velocity). In that case you could set the electric force its feeling equal to the gravitational force. Solve for the electric force and use that to solve for the electric field at that point. Use the electric field to find the surface charge density by applying Gauss's Law.
 
  • #4
Thank you for all your help. I believe I have solved the problem. It wasn't as difficult as I had made it seem. The most tedious step was probably noticing that the electric force on the styrofoam is equal to the gravitational force on it. In addition to this, the electric force on the plastic sheet is also equal to the electric force on the styrofoam due to Newton's Third Law. After that, the surface charge density is simple to calculate. Thanks again for the help.
 
  • #5
This is how far I got...

E=mg
E=.735

sigma = E * 2e0

because sigma is charge/area. What am I doing wrong?
 
  • #6
I did this problem so long ago, I'm not sure if I remember everything correctly.

However, I did notice you say E=mg. Actually, since F=mg and F=qE, your equation would actually be qE=mg. You have the charge of the object, therefore, you can solve for the electric field. I'm not sure how you got 0.735.

0.01 kg * 9.8 m/s2 = E
-0.0000007 C

You are obviously right that E= sigma/2(epsilon0).

So rearranging the equation, sigma is simply = 2E(epsilon0).

I'm not sure if that helps, but you have the right idea.
 
  • #7
Thank you very much, I really appreciate it.
 

What is Gauss's Law to Symmetric Charge Distribution?

Gauss's Law to Symmetric Charge Distribution is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It is used to calculate the electric field for a symmetric charge distribution, such as a point charge, line of charge, or plane of charge.

How is Gauss's Law to Symmetric Charge Distribution mathematically represented?

Gauss's Law to Symmetric Charge Distribution is represented by the equation ∮E⃗ · dA⃗ = Q/ε0, where ∮E⃗ · dA⃗ represents the electric flux through a closed surface, Q is the total charge enclosed by that surface, and ε0 is the permittivity of free space.

What are the assumptions made when using Gauss's Law to Symmetric Charge Distribution?

When using Gauss's Law to Symmetric Charge Distribution, it is assumed that the charge distribution is symmetric, the electric field is constant over the surface, and the surface is closed and encloses the charge completely.

What are some examples of symmetric charge distributions?

Some examples of symmetric charge distributions include a point charge, which has spherical symmetry, a line of charge, which has cylindrical symmetry, and a plane of charge, which has planar symmetry.

What is the significance of Gauss's Law to Symmetric Charge Distribution in physics?

Gauss's Law to Symmetric Charge Distribution is a fundamental law in electromagnetism and plays a crucial role in understanding the behavior of electric charges and electric fields. It allows us to relate the electric field to the charge distribution, and can be used to calculate the electric field for a wide range of symmetric charge distributions.

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