Gauss' Law: Net Electric Field of Two Spheres

In summary, two nonconducting spheres with surface charge densities of +6.0mC/m2 and +4.0 mC/m2, placed at x=0cm and x=10cm respectively, have a net electric field of -3.10x10^3 N/C at x=2.0 cm due to the outside charge of the spheres. The field inside a uniformly charged sphere is zero, but the field outside is equivalent to a point-charge at the center of the sphere.
  • #1
UWGGEOL
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Homework Statement


Two nonconducting spheres, of r1=3.0cm and r2=2.0cm, are placed of an x-axis. They have surface charge densities of +6.0mC/m2 and +4.0 mC/m2, respectively, on their outside surfaces. The center of sphere r1 is on the origin and the center of sphere r2 is 10 cm away. What is the net electric field at x=2.0 cm?



Homework Equations


E=kq/r2
Area=4pir2

The Attempt at a Solution


I noticed that x=2.0cm falls inside sphere r1 and that the Electric Field inside a sphere due to an outside charge equals 0. I think this is the answer but want to be sure.
 
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  • #2
I do not think so! because they are non conducting spheres... so we can not ignore the effect of the second sphere, I guess! i will look it up more though...
 
  • #3
The field inside a uniformly charged sphere is zero (the field of THIS sphere vanishes), but the field outside a uniformly charged sphere is the same as if all the charge was at its center (we can treat it like a point-charge on most regards)... You should get your answer easily!
 
  • #4
Yeah I tried that before you told me and it was pretty easy and good to know the way i thought was right. I got -3.10x10^3 N/C because of the direction of the field
 

1. What is Gauss' Law?

Gauss' Law is a fundamental law in electromagnetism that relates the electric fields produced by electric charges to the distribution of those charges. It states that the net electric flux through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space.

2. How does Gauss' Law apply to the net electric field of two spheres?

In the case of two spheres, Gauss' Law can be used to determine the net electric field at any point in space between the two spheres. The law states that the net electric field at that point is equal to the sum of the electric fields created by each individual sphere at that point.

3. What is the equation for calculating the net electric field of two spheres using Gauss' Law?

The equation for calculating the net electric field of two spheres using Gauss' Law is E = Q/(4πε0r2), where E is the net electric field, Q is the total charge enclosed by the surface, ε0 is the permittivity of free space, and r is the distance from the center of the spheres to the point in space where the field is being calculated.

4. Can Gauss' Law be used to calculate the net electric field of more than two spheres?

Yes, Gauss' Law can be extended to calculate the net electric field of any number of spheres. In this case, the equation becomes E = Σ(Q/(4πε0r2)), where Σ represents the sum of all the charges enclosed by the surface.

5. What are the assumptions made when using Gauss' Law for calculating the net electric field of two spheres?

The main assumptions made when using Gauss' Law for this calculation are that the spheres are perfectly symmetrical and that the charge distribution is also symmetrical. Additionally, the calculation assumes that the spheres are isolated in space and that the electric field between them is uniform.

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