# Current density

1. Nov 9, 2005

### Tony11235

I know this is a retarted question, I should probably know this, but to the question. Say I have a wire of length L with a small diamter d. It has a current density J. Now say we have another wire of the same length that is hollow. They are both made of the same material. Is the current density for the second wire the same as the first? This is NOT a homework question by the way.

2. Nov 9, 2005

### rbj

is the current, I, the same in both wires? assuming they are and that the outer diameter of both are the same, then the current density of the hollow wire is higher. at least for DC. (AC tends to have this "skin effect". even at 60 Hz, the vast majority of the current in these big power lines is in or near the surface of the conductor.)

3. Nov 10, 2005

### Tony11235

Ok so basically it's ok to say that currently density is related to shape.

4. Nov 10, 2005

### ZapperZ

Staff Emeritus
The question, as it is presented, reads rather vague to me. Whenever something like that happens, then you will get a non-unique answer.

1. "Current density", by definition, is the amount of current flowing per unit cross-section area, i.e. J = I/A in the simplest form. If you keep current I constant, you can already see based from that naive form alone, that changing A will change J. Thus, when you hollow-out the conductor, the cross-sectional area of the conductor that allows current to flow through is reduced. So you will have a different J.

2. On the other hand, the resistivity of a material depends very much on the cross-sectional area. So the assumption of keeping I constant in (1) may not be valid. Reducing the area will increase the resistivity and will cause I to drop. So you now have two competing effects: A is decreasing and would cause J to increase, but I is also decreasing and this would cause J to decrease.

How this works out depends very much on the geometry of the conductor.

Zz.