# Current density

Discussion in 'General Electronics Chat' started by antennaboy, Jan 31, 2008.

1. ### antennaboy Thread Starter Active Member

Jan 31, 2008
45
0
Hello All,
I am new to this great forum and have a question about current density and perfect conductors.
If the conductor is perfect, the conductivity is infinite, E is said to be
zero inside.
For a a certain voltage (say 5V) does the current flow inside the conductor or on the surface? why?
For waves traveling in lossy dielectrics (materials with some conductivity) energy is lost. But then I read that a perfect conductor does not dissipate any energy since there is no work to push the charges.
Confused...
thank you

2. ### nomurphy AAC Fanatic!

Aug 8, 2005
567
12
1) If the conductor is perfect, the conductivity is infinite, E is said to be zero inside.

Yes, if the impedance were zero then there would not be a voltage drop across the conductor and no loss (usually radiated heat). But, a perfect conductor does not exist -- there is always some loss, even in super conductors.

2) For a certain voltage (say 5V) does the current flow inside the conductor or on the surface? why?

For AC current there is something called the skin effect -- look it up.

3) For waves traveling in lossy dielectrics (materials with some conductivity) energy is lost. But then I read that a perfect conductor does not dissipate any energy since there is no work to push the charges.

This goes back to question 1, there is no perfect conductor.

3. ### SgtWookie Expert

Jul 17, 2007
22,182
1,728
Current flow is on the surface. Like charges repel each other; opposites attract.

A perfect conductor is an interesting concept. It would have a minimum diameter of one molecule of the conducting material. But to even approach that, you'd have to get the material near absolute zero. If you DID somehow manage to reach absolute zero, all molecular activity would cease. But then, movement of electrons and holes would be molecular activity, right?

4. ### Dave Retired Moderator

Nov 17, 2003
6,960
144
Hi and welcome to All About Circuits!

You need to seperate what appears to be two questions.

If you have a perfect conductor and put 5V (DC) across it you would get an infinite current through the conductor I = V/R 5/0 = infinity. Aside from the impossibilities of this, the current would flow uniformly through the conductor. It might be easier to think of this in terms of a very low resistance conductor - the principles are effectively the same.

For a 5V AC, the current will tend to distribute itself across the conductor because of a phenomenon called the skin effect. The skin depth, d, is dictated by the following equation:

$d =$$\sqrt{\frac{2\rho}{\omega\mu}}$

A perfect conductor will have a resistivity of zero so the skin depth will be zero, i.e. the current will solely be on the surface. Obviously, a conductor msut have a finite resistivity (unless we are looking at super conductivity) and the skin depth will indicate that the current in constrained mainly at the surface but does in reality propagate into the conductor volume.

Note the skin depth implies the depth at which the current density is 1/e of its surface value.

The field inside the conductor is zero, therefore there is no field potential and no losses.

Dave