Gauss law and nonconducting spherical shells

In summary, there are two nonconducting spherical shells with fixed locations and different surface charge densities. Using Gauss' law, the net electric field at a specific point can be determined by calculating the individual electric fields of each shell in unit vector notation and applying the superposition principle.
  • #1
nogoodaatphys
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Homework Statement


there are two nonconducting spherical shells fixed in place. shell 1 has uniform surface charge density 6.0 uC/m^2 on its outer surface and radius 3.0cm. shell 2 has uniform surface charge density 4.0 uC/m^2 on its outer surface and radius 2.0cm. the shell centers are separated by l=10cm. in unit vector notation, what is the net electric field at x=2.0cm.
There is a picture that shows shell 1 with it's center at the origin, and shell 2 centered at (10,0) (because l=10)

Homework Equations


gauss' law, but not sure exactly what form.


The Attempt at a Solution


Well I'm unsure what to do, but I solved for the electric field created by both shells.
Shell 1=6*10^7
Shell 2= 9*10^7 (ignoring the units for the moment)

ok so I have that, but I have no idea how to determine the net field at any given point. can anyone help me get started? Thanks.
 
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  • #2
Well, the first step would be to put your two individual electric fields into unit vector notation (they are vector fields after all!), after that...what does the superposition principle tell you?
 

1. What is Gauss Law?

Gauss Law is a fundamental law in electromagnetism that describes the relationship between the electric flux through a closed surface and the charge enclosed within that surface. It is named after the German mathematician and physicist Carl Friedrich Gauss.

2. How is Gauss Law applied to nonconducting spherical shells?

In the case of nonconducting spherical shells, Gauss Law states that the electric field outside the shell is the same as that of a point charge located at the center of the shell. This means that the electric field inside the shell is zero, as the charges on the surface cancel each other out.

3. What is the significance of using a spherical shell in Gauss Law?

A spherical shell is often used in Gauss Law because of its symmetry. This allows for easier calculation of the electric flux through the surface and simplifies the application of the law.

4. How does the electric field change as the distance from the center of the shell increases?

According to Gauss Law, the electric field outside a nonconducting spherical shell is inversely proportional to the square of the distance from the center of the shell. This means that as the distance increases, the electric field decreases.

5. Can Gauss Law be applied to other shapes besides spheres?

Yes, Gauss Law can be applied to any closed surface as long as it encloses a charge. However, the calculation of the electric field may be more complex for other shapes compared to the simplicity of a spherical surface.

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