Why is the Electric Field outside this wire not zero?

In summary: 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.
  • #1
bryanso
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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

Griffiths001.png
Griffiths002.png
 
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  • #2
bryanso said:
E should be zero by Gauss law, shouldn't it? ... Net charge is 0.
Ask yourself: The field where?
 
  • #3
> 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?
 
  • #4
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.
 
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  • #5
bryanso said:
> 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?
 
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  • #6
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
 
  • #7
bryanso said:
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.)

 

1. Why is the electric field outside a wire not zero?

The electric field is not zero outside a wire because charges within the wire create an electric field that extends into the space around the wire. This field can interact with other charges outside the wire, causing a non-zero electric field in that region.

2. How does the electric field outside a wire differ from the electric field inside the wire?

The electric field outside a wire is different from the electric field inside the wire because the distribution of charges is not uniform. Inside the wire, the charges are evenly distributed, resulting in a uniform electric field. Outside the wire, the charges are concentrated along the surface, causing a non-uniform electric field.

3. What factors affect the strength of the electric field outside a wire?

The strength of the electric field outside a wire is affected by the amount and distribution of charges within the wire, the distance from the wire, and the geometry of the wire. The closer the charges are to the surface of the wire and the higher the charge density, the stronger the electric field will be. The shape of the wire also plays a role, as a curved wire will have a different electric field compared to a straight wire.

4. Can the electric field outside a wire be zero at any point?

Yes, the electric field outside a wire can be zero at certain points. This typically occurs at points where the electric field vectors from different parts of the wire cancel each other out. These points are known as electric field null points and can be found at specific distances and angles from the wire.

5. How does the electric field outside a wire relate to the flow of current?

The electric field outside a wire is directly related to the flow of current. Current is the movement of charges, and the electric field is what causes this movement. As such, a non-zero electric field outside a wire indicates the presence of current flowing through the wire. The direction and strength of the electric field can also provide information about the direction and magnitude of the current.

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