Charge on a cavity wall and Gauss' law

So the charge on the cavity wall is equal to the negative of the particle charge within and the charge on the outer surface is 0In summary, the isolated conductor has a net charge of +14.0 × 10- 6 C and a cavity with a particle of charge q = +4.30 × 10-6 C. The solution for part (a) is that the charge on the cavity wall is the negative of the particle charge within, while for part (b) the charge on the outer surface is 0.
  • #1
Jrlinton
134
1

Homework Statement


An isolated conductor has a net charge of +14.0 × 10- 6 C and a cavity with a particle of charge q = +4.30 × 10-6 C. What is the charge (a) on the cavity wall and (b) on the outer surface?

Homework Equations

The Attempt at a Solution


So I understand that B is just adding the charge of the particle and conductor together
=1.8E-5C
I am lost on the solution to part A. I thought that the charge on or within the cavity wall of a gaussian shell was zero but that doesn't seem to be the answer they are looking for
 
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  • #2
Jrlinton said:
I am lost on the solution to part A. I thought that the charge on or within the cavity wall of a gaussian shell was zero but that doesn't seem to be the answer they are looking for
Imagine a Gaussian surface within the conducting material that encloses the cavity. What's the total charge?
 
  • #3
the net charge is zero so the charge on the wall is the negative of the particle charge within
 
  • #4
Jrlinton said:
the net charge is zero so the charge on the wall is the negative of the particle charge within
Exactly.
 

FAQ: Charge on a cavity wall and Gauss' law

Question 1: What is the charge on a cavity wall?

The charge on a cavity wall is the net amount of electric charge present on the surface of a cavity within a conductor.

Question 2: How is the charge on a cavity wall related to Gauss' law?

Gauss' law states that the net electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of free space. This means that the charge on a cavity wall can be calculated using Gauss' law by integrating the electric field over the surface of the cavity.

Question 3: Can the charge on a cavity wall be zero?

Yes, the charge on a cavity wall can be zero if there is no net charge within the cavity or if the electric field within the cavity is zero.

Question 4: How does the shape and size of a cavity affect the charge on its walls?

The shape and size of a cavity can affect the charge on its walls by changing the distribution of charge within the cavity. This, in turn, affects the electric field and the net charge on the walls.

Question 5: What is the significance of understanding the charge on a cavity wall and Gauss' law?

Understanding the charge on a cavity wall and Gauss' law is crucial in many fields of physics and engineering, including electromagnetism and circuit design. It allows us to accurately calculate electric fields and predict the behavior of electric charges in complex systems.

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