Griffiths 7.3

You have to get the E-Field involved, you are correct about that.

HINT:

[tex]I=\int \vec{J}\cdot d\vec{a}[/tex]

Start here. Can you get the E-Field involved in this equation from what you know from chapter 7? If so, then what about getting a charge term in the equation?

 

I here is a general current moving between the two metal objects (if I remember the problem correctly).

HINT: Your on the right track with your Gauss's law idea.

 

It is a current that is moving between the two metal objects. There really is nothing more you can say about it. It moves from one object to the other, through the material in between.

Pick any closed surface through which the current either enters or leaves and you'll be able to apply Gauss's Law. Thus, it could contain either object one, or object two.

You also haven't shown ANY work on this problem since I gave you an initial hint. I'm sorry if I'm being vague, but I will not be able to tell you any more about this problem until you show some work. My first hint should have been enough to get you started. For instance, you said:

How about showing me what you will do to solve the problem, once you are sure you can apply Gauss's Law? How do you manipulate the equation i gave you involving J to find the answer using Gauss's Law? Show me some work.

 

There are several problems with your post here, ehrenfest.

First off, I do not have to trust you to do the manipulations. You, on the other hand, DO have to show me your work. You should refresh yourself on the forum rules.

In all honesty, I should not have offered help at all since you did not show ANY work, and still haven't done so. I have seen you around on these forums and, from your other threads I knew you were one to put time into your problems, so I decided to help you.


Secondly, I have offered you a mathematical definition of the current:

[tex]I = \int J \cdot da[/tex]

The problem is so general that you can't apply any more specific definition. This is the best I can do. If this is not specific enough, then there are two options for you.

1)You can assume I'm wrong about there being no other, more specific definition and wait for another homework helper to find the thread. This is very possible. I am not perfect and have already asked some other helpers if there is something I'm missing.

2)You can find a problem with more specific parameters.

Sorry, ehrenfest, but I cannot give you any more specific definition of the current. I just can't. The problem is too general. The definition I gave is the only one that can be applied, since it is the most general expression for any current.

 

This concept is actually not ill-defined at all. The question is specifically asking you to prove something very general, but what you've shown is that you can prove it; therefore it must have been well-defined! There are problems in Jackson that ask you to prove things even more generic than this. But it's always possible to get at them, starting from Maxwell's equations and using vector calculus.

Perhaps what you're confused about is exactly what surface to integrate over. Since you are finding the current "between two objects", you can choose any surface which divides all of space into exactly two regions, one containing Object A and one containing Object B. Because of the conservation of charge, it doesn't make a difference which surface you choose; whatever current flows out of A must flow into B.

 

You got it!