Electrostatics - conductors.

[cosmic_tears]

I'll try my best to describe the question, though Enligsh is not my mother-tounge. Hope I'm clear enough!

the problem:
There's a thick spherical shell made of insulated material (like a thick ring), with an inner radius a and outer radius b. The shell is charged with a changing charge density (volumic... if that's how you say it) : P = c/r (r = distance from center, c= given const.)

The shell is coated from the inside *and* from the outside with thin conducting material layers (2-dimentional).

The charge of the outer thin conducting layer is 2*pi*c*a^2
The charge of the inner thin conducting layer is -2*pi*c*b^2

They ask what's the electrostatic energy of the system.

Homework Equations

I don't know how to insert equations here, I'm sorry, but anyhow it's not important because I have a theoratical question.

The Attempt at a Solution

There's an equation tying the enrgy to a 3D intergral on all of "space", of the squared electrostatic field the system creates.
However, I'm having trouble understanding what's the significence of the conducting layers. What's their effect on the problem? What's the difference between them being conducting or not? How would the problem be different if they were not conducting?

If I would attempt to solve it, I would just calculate the field using Gaus' law in the area of the inner vacuum created by the spherical shell (r<a) (0), in the thick shell itself (a<r<b) and on the outside (b<r), and then use the equation. But I have to assume to fact that the layers are conducting has some meaning...

Any hints? Tips? Greatly appreciated!
I hope I wasn't too vauge!

 

[lippyka]

The significance of the conducting layers is that they help to maintain a constant charge distribution on the surface of the shell. Without the conducting layers, the charge would not be uniformly distributed and so the electric field would not be uniform either. This would lead to a higher energy requirement to maintain the charge distribution. The conducting layers also help to prevent the charges from dissipating due to electrical leakage.

 

[Moetasim]

Greetings,

I understand your confusion about the significance of the conducting layers in this problem. Let me explain it to you in more detail.

Firstly, the conducting layers play an important role in this problem because they affect the electric field inside the spherical shell. As you correctly mentioned, the electric field inside the shell is zero, but the conducting layers change this.

When a conductor is placed in an electric field, it redistributes the charges on its surface in such a way that the electric field inside the conductor is zero. This is known as the shielding effect of conductors. In your problem, the conducting layers on both sides of the spherical shell act as shields, and therefore, the electric field inside the shell is zero.

Now, coming to your question about the difference between the conducting and non-conducting layers, if the layers were not conducting, the electric field inside the shell would not be zero. This would significantly change the electric field and hence, the electrostatic energy of the system. Therefore, it is important to consider the conducting layers in this problem.

To solve this problem, as you mentioned, you can use Gauss's law to calculate the electric field in different regions and then use the appropriate equation to calculate the electrostatic energy. However, make sure to take into account the effect of the conducting layers on the electric field.

I hope this helps clear your doubts and gives you a better understanding of the significance of the conducting layers in this problem. Keep up the good work!