Charge Distribution on Concentric Spheres: Exploring Gauss's Law

In summary, the problem involves two concentric conducting spheres, one hollow and one solid, with initial charges of -6Q and +1Q on the outer and inner surfaces, respectively. In part (a), the question is asking for the amount of charge on each surface. In part (b), a wire is connected between the two spheres and electrostatic equilibrium is established, resulting in a charge of 0 on the inner surface of the inner sphere. In part (c), the outer sphere is connected to ground and then disconnected, resulting in a total charge of -6Q on the outer surface and a charge of 0 on the inner surface of the outer sphere.
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Homework Statement


Consider two concentric conducting spheres. The outer sphere is hollow and initially has a charge Q1 = -6Q deposited on it. The inner sphere is solid and has a charge Q2 = +1Q on it.

(a) How much charge is on the outer surface?
How much charge is on the inner surface?

(b) Suppose a wire is connected between the inner and outer spheres. Electrostatic equilibrium is established.
How much charge is on the outer surface of the outside sphere?
How much is on the inner surface?

(c) Suppose we return to the original conditions in (a), with +1Q on the inner sphere and -6Q on the outer. We now connect the outer sphere to ground with a wire and then disconnect it. How much total charge will be on the outer sphere?
How much charge will be on the inner surface of the outer sphere?
How much will be on the outer surface of this sphere?


Homework Equations



∫EdA = Qinside/ɛo

The Attempt at a Solution



Gauss's Law is very confusing, and I'm not quite sure I understand any of it. Any help appreciated. I know in part B that the inner shell has charge of 0.
 
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But I don't understand how to find the charges on the inner and outer surfaces. For part C, I'm not sure where to start.
 

Related to Charge Distribution on Concentric Spheres: Exploring Gauss's Law

1. What is Gauss's Law and how is it related to charges on spheres?

Gauss's Law is a fundamental law of electromagnetism that describes the relationship between electric charges and electric fields. It states that the electric flux through a closed surface is equal to the net charge enclosed by that surface divided by the permittivity of free space (ε0). This law is directly applicable to charges on spheres because it allows us to calculate the electric field at any point outside or inside a charged sphere.

2. How do you calculate the electric field due to a charged sphere using Gauss's Law?

To calculate the electric field due to a charged sphere, we can use Gauss's Law along with the fact that the electric field is spherically symmetric. This means that the electric field at any point on the surface of the sphere will have the same magnitude and direction. We can then use a Gaussian surface in the shape of a sphere that encloses the charged sphere and apply Gauss's Law to calculate the electric field at any point outside or inside the charged sphere.

3. Can Gauss's Law be used to calculate the electric field inside a charged sphere?

Yes, Gauss's Law can be used to calculate the electric field inside a charged sphere. This is possible because the electric field inside a charged sphere is also spherically symmetric, meaning that the electric field at any point inside the sphere will have the same magnitude and direction. By choosing a Gaussian surface inside the charged sphere and applying Gauss's Law, we can calculate the electric field at any point inside the sphere.

4. How does the charge distribution on a sphere affect the electric field?

The charge distribution on a sphere directly affects the electric field. If the charge is uniformly distributed on the surface of the sphere, the electric field will be constant at all points outside the sphere. If the charge is not uniformly distributed, the electric field will be stronger in areas where there is a higher concentration of charge and weaker in areas with a lower concentration of charge. This is because the electric field is directly proportional to the charge enclosed by the Gaussian surface.

5. Can Gauss's Law be used to calculate the total charge on a sphere?

No, Gauss's Law cannot be used to directly calculate the total charge on a sphere. It can only be used to calculate the electric field at a point due to a given charge distribution. To find the total charge on a sphere, other methods such as Coulomb's Law or integration must be used.

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