Superposition of Spherical Charge Distributions

In summary, the conversation discusses using the superposition principle and Gauss's law to find the electric field inside a cavity created by two superimposed spheres with opposite charge densities. The main issue is accounting for the fact that the spheres are not concentric and determining whether to use the electric field inside or outside the spheres. The solution involves finding the fields inside each sphere and using vector form to calculate the individual fields.
  • #1
physicsphan89
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Homework Statement


http://photos-e.ak.fbcdn.net/hphotos-ak-snc1/hs031.snc1/2658_1060058793594_1589658877_146788_3259033_n.jpg


Homework Equations



e4ef2c130bca53d8ee3cb5e0056af2b1.png


The Attempt at a Solution



So I know that I should use the superposition principle, and treat it as 2 superimposed spheres of opposite charge densities. I can use Gauss's law to find the electric field of each. However I am having a little trouble figuring out how to take into account the fact that the spheres are not concentric. I also don't know whether to use the electric field inside or outside the spheres.
 
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  • #2
physicsphan89 said:

Homework Statement


http://photos-e.ak.fbcdn.net/hphotos-ak-snc1/hs031.snc1/2658_1060058793594_1589658877_146788_3259033_n.jpg


Homework Equations



e4ef2c130bca53d8ee3cb5e0056af2b1.png


The Attempt at a Solution



So I know that I should use the superposition principle, and treat it as 2 superimposed spheres of opposite charge densities. I can use Gauss's law to find the electric field of each. However I am having a little trouble figuring out how to take into account the fact that the spheres are not concentric. I also don't know whether to use the electric field inside or outside the spheres.

Well, you are interested in finding the electric field inside the cavity, that region lies within both the large sphere and the small sphere, so you want to use the fields inside each sphere.

What do you get for the individual fields fields, in vector form, inside the spheres?
 
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1. What is superposition of spherical charge distributions?

Superposition of spherical charge distributions is a concept in physics that describes the combined effect of multiple spherical charge distributions on a point in space. It is based on the principle that the electric field produced by each individual charge distribution can be calculated independently and then summed together to determine the total electric field at that point.

2. How is superposition of spherical charge distributions used in experiments?

In experiments, superposition of spherical charge distributions is used to predict the behavior of electrically charged particles in a given system. By calculating the electric field at different points in space, scientists can determine the forces and movements of charged particles and make predictions about their behavior.

3. What is the mathematical equation for superposition of spherical charge distributions?

The mathematical equation for superposition of spherical charge distributions is given by the following formula:
E = k * (q1/r1^2 + q2/r2^2 + q3/r3^2 + ...),
where E is the total electric field, k is the Coulomb constant, q is the charge of each spherical distribution, and r is the distance between the point in space and the center of each charge distribution.

4. How does the distance between charge distributions affect superposition?

The distance between charge distributions plays a significant role in superposition. The farther apart the distributions are, the weaker their combined effect on a point in space will be. This is because the electric field decreases with distance according to the inverse square law, meaning that the closer the charge distribution is to the point, the stronger its effect will be.

5. Can superposition of spherical charge distributions be applied to non-spherical charge distributions?

Yes, the concept of superposition can be applied to any type of charge distribution, not just spherical ones. However, the calculations become more complex as the shape of the charge distribution becomes more irregular, making it more difficult to accurately predict the electric field at a given point in space.

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