Gauss' Law Hollow Sphere with Charged Ball

In summary, the problem involves a uniformly charged ball of radius a and charge -Q at the center of a hollow metal shell with inner radius b and outer radius c, which has a net charge of +2Q. The electric field strength at different distances (r) from the center is determined, with the following results: for r < a, the net flux only depends on the charge inside the small ball; for a < r < b, the electric field is 0 due to the lack of net
  • #1
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Homework Statement


A uniformly charged ball of radius a and charge -Q is at the center of a hollow metal shell with inner raduis b and outer radius c. \The hollow sphere has net charge +2Q.

Determine the Electric Field Strength at r when r is,

r < a
a < r < b
b< r < c
r > c


Homework Equations


I'm struggling with the flux concepts in this case.


The Attempt at a Solution


I guess the main concepts I need clarification on is:
in the hollow sphere, there is flux pointing out from the metal spherical surface, but is there flux pointing into the hollow sphere? (in that case would there be a net flux into the small ball?)
Inside the actual shell of a charged metal sphere ( or inside a charged slab/puck/etc.), what is the flux, is it 0?



Here's my analysis for the problem

So when r < a , the net flux at r only depends on the charge inside the small ball.

When a < r < b, ok so this is where I'm struggling, please tell me if my analysis is wrong,
r is the hollow part, since all the charge gathers on the surface, r has no net charge, so it has no net flux, so its E field is 0?

when b < r < c, this is IN the shell of the charged outer sphere, now I know how to deal with the flux at the surfaces of conductors, so would this be the same thing?

when r > c, this is at a point outside the large sphere, so the flux is related to the net charge of the sphere and the ball
 
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  • #2
first of all, flux depends on total charge enclosed. So total charge of hollow sphere + ball = Q. So net flux is outwards.

for r<a, use uniformity of charge on ball, by finding charge density.
 

1. What is Gauss' Law Hollow Sphere with Charged Ball?

Gauss' Law Hollow Sphere with Charged Ball is a physics principle that relates the electric flux through a closed surface to the charge enclosed within that surface. It states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space.

2. How does Gauss' Law Hollow Sphere with Charged Ball apply to a hollow sphere with a charged ball inside?

In this scenario, the electric flux through the closed surface of the hollow sphere is equal to the charge of the ball divided by the permittivity of free space. This is because the electric field inside the hollow sphere is zero, and therefore the electric flux is only determined by the charge enclosed by the surface.

3. What is the significance of Gauss' Law Hollow Sphere with Charged Ball in physics?

Gauss' Law Hollow Sphere with Charged Ball is an important principle in electromagnetism, as it allows us to calculate the electric field at any point outside a charged hollow sphere with a ball inside. It also helps us understand the relationship between electric flux and charge, and how it is affected by the geometry of the system.

4. How is Gauss' Law Hollow Sphere with Charged Ball related to Coulomb's Law?

Gauss' Law Hollow Sphere with Charged Ball is a generalization of Coulomb's Law, which states that the electric field due to a point charge is inversely proportional to the square of the distance from the charge. In the case of a hollow sphere with a charged ball inside, Gauss' Law takes into account the distribution of charge within the system and allows us to calculate the electric field at any point outside the sphere.

5. What are some real-world applications of Gauss' Law Hollow Sphere with Charged Ball?

Gauss' Law Hollow Sphere with Charged Ball has many practical applications, such as in the design of capacitors and other electrical circuits. It also helps us understand the behavior of charged particles in electric fields, which is important in fields such as particle accelerators and plasma physics. Additionally, it plays a crucial role in the study of electrostatics and the behavior of electric fields in various materials.

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