# Charge Conservation Violated?

1. Jun 25, 2007

### walkinginwater

hi, guys:
Charge conservation Violated? It seems to be: The charge density inside a spherical volume changes from $$\rho$$ at t=0, after period of time $$\tau$$, the charge density decrease to 0. However, the author claimed that during the processing there is no current density in the material surrounding the initially charged spherical region. Is this possible?

I am now reading a something about Charge Relaxation in a conductor.
You can find the example in the following way:
Then click chapter 7 on the left column , the whole index of chapter 7 will appear on the right;
After that, you click on the section 7.7;
At last, you go to the example 1. where you see what I want to talk about.

Note: Equation (7.15) can be found in the following weblink http://web.mit.edu/6.013_book/www/book.html click on Chapter 7 on the left column, and then click on the section 7.1 on the right column

In the example it states that: " one or both of these migrate in the electric field caused by the net charge[in accordance with (7.15)] while exactly neutralizing each other"

Anybody agree with this? Can he/she give some explanation?

Last edited: Jun 26, 2007
2. Jun 25, 2007

### Meir Achuz

Last edited: Jun 25, 2007
3. Jun 25, 2007

### cesiumfrog

That's interesting. Does it have any application?

4. Jun 26, 2007

### walkinginwater

hi, Meir Achuz:
Thank you very much for your reply. But in fact I am confused over what you have said. In the website of MIT, it states that there is no current density in the material, i.e., there is no $$\vec J$$. But you said
So it seems that your statement doesn't coincide with what from the MIT Website.
Our library doesn't have the book "Classical Electromagnetism" by J. Franklin (AW.com). Would you be so nice to explain in more detail. Or can you scan section 6.93 and email it to me?
p.s.: I make some modification about my post, now you can find the example I mentioned before!

Last edited: Jun 26, 2007
5. Jun 27, 2007

### Meir Achuz

During the decay of the charge distribution, there is an E in the conductor.
Since j=\sigma E, there is a j. That is the problem with trying to learn physics from the web. even MIT.

6. Jun 27, 2007

### walkinginwater

Thanks for your answer! In fact, I continue to read the following sections from http://web.mit.edu/6.013_book/www/book.html and I find in Section 7.8 and 7.9, there are more detailed explanation about this question. The conclusion is that:

• There are current density through the conduction material

• The spatial distribution of the charge density don't change and only the magnitude of the Field decay exponentially.
• The charge will drift to the boundary of the conduction materials

7. Jun 28, 2007

### walkinginwater

This Thread Has been Solved! Thanks for Meir Achuz

This Thread has been Solved! Thanks for the reply of Meir Achuz!!