Why is the Electric Field outside this wire not zero?

[bryanso]

Homework Statement

Not a homework. Just want to understand a (should be simple) example.

Relevant Equations

Why is E not zero?

Not a homework. Just self-studying electromagnetism.

I am stuck at understanding the very beginning of the solution steps in this example:

The E as given in the solution is the field away from a long straight line with charge Lambda. That's clearly not the current configuration.

E should be zero by Gauss law, shouldn't it? ... Net charge is 0.

David Griffiths Electrodynamics 4th Edition, p. 368

 

[Doc Al]

E should be zero by Gauss law, shouldn't it? ... Net charge is 0.

Ask yourself: The field where?

 

[bryanso]

> Ask yourself: The field where?

Outside is 0 from Gauss Law.

Inside conductor is 0 (after equilibrium).

So there are two fields, one on the outer surface and one on the inside contacting surface?

Am I in the right direction?

 

[hutchphd]

The fields are only at the surface?? Please be a little more complete in your description. Electric field lines start on a positive charge and end on a negative charge.

 

[rude man]

> Ask yourself: The field where?

Outside is 0 from Gauss Law.

Inside conductor is 0 (after equilibrium).

So there are two fields, one on the outer surface and one on the inside contacting surface?

Am I in the right direction?

What about E field between a and b? By Gauss' law?

 

[bryanso]

Thank you all. Got it. I knew I missed something very simple. I got misled by the general rule of thumb that there is no E inside a conductor. But this is not a homogenous conductor here. I can proceed now.

Thanks

 

[rude man]

Thank you all. Got it. I knew I missed something very simple. I got misled by the general rule of thumb that there is no E inside a conductor. But this is not a homogenous conductor here. I can proceed now.

Thanks

Right. There can be no E field inside a conductor.
In fact, unless it's a perfect NON-conductor there can be no E field in the steady-state.

UNLESS there is current flow, in which case you have E = ρι where ρ is resistivity and ι is current density.
(Vector equation.)