[paul cotter (OP)]

A simple setup: two concentric metallic spheres with an internal oscillator powering both, at 180 degrees difference. Will a time varying e field be detected externally to these spheres? Without doing the maths I expect the e field to be restricted to the gap between these spheres.  PS I notice the degree symbol now produces a question mark.

[Bored chemist]

Without doing the maths, I think any field would be contained within the faraday cage consisting of the outer sphere.

[paul cotter (OP)]

Thanks, BC. That's my interpretation too, it being similar to Faraday's ice pail experiments but where inside and outside are relative to where a measurement is taken. The reason for asking is that I am in discussion on another forum where a member expects an external field and I say ,no. I am quite rusty on the relevant maths and can't summon up the required motivation!  Further thoughts: it's analogous to a coax cable which we know has no external field, if it has a decent braid.

[Petrochemicals]

A simple setup: two concentric metallic spheres with an internal oscillator powering both, at 180 degrees difference. Will a time varying e field be detected externally to these spheres? Without doing the maths I expect the e field to be restricted to the gap between these spheres.  PS I notice the degree symbol now produces a question mark.

Concentric? as in within each other

[Bored chemist]

My maths is bad but this looks like a start.
https://en.wikipedia.org/wiki/Faraday%27s_ice_pail_experiment#Proof_induced_charge_is_equal_to_object's_charge

[paul cotter (OP)]

Very informative, BC, thank you. It's 50years since I studied this stuff and I needed a refresh. I may need to recant my position. What I don't understand from that article is if there are alternate charges on opposite sides of the container how can there be no electric field in the metal between these charges? I have always assumed no substantial electric field can exist in a good conductor.

[alancalverd]

A field demands a potential difference, so whilst there will be a field between the concentric spheres, whatever field exists outside will depend on the potential difference between the outer sphere and the point of measurement.

[paul cotter (OP)]

Good evening Alan. I did not describe my difficulty very well( as usual! ). On that wiki article that BC suggested they show opposite charges on opposite sides of a thin metal sheet. I never paid much attention to electrostatics but this description troubles me. How is there not a field between these charges and how are they not neutralised by the expected current one would see in a good conductor? I am getting way too rusty to think about this stuff clearly.

[alancalverd]

I see the logic in the Wiki article after all. If there were no other static field, there would be no net drift of charges across the conductor, but there is indeed an applied field, so charge separation is entirely reasonable since carriers are by definition free to move in a field!

The reason we don't detect a field outside a coax cable is because we usually ground the braid, thus removing any induced charge.  If you leave the braid floating, it will of course follow the charge state of the core conductor.

So if you drive the braid (or your exterior sphere) with respect to ground, an observer outside will see a field corresponding to the instantaneous state of the  braid/shell.   

[paul cotter (OP)]

From a mechanistic analysis the wiki article makes 100% sense to me . What I don't understand is how one can have opposite charges on either side of a thin metal conductor, yet no electric field between these charges. It is an aspect of the ice pail experiments I never thought about before.

[Bored chemist]

So if you drive the braid (or your exterior sphere) with respect to ground

How do you do that from inside the sphere?

If the current flowing in the braid and centre conductor of a coax cable are the same magnitude and in opposite directions, then the fields exactly cancel and you don't get any external field- regardless of which conductor (if any) is grounded.

  If you leave the braid floating, it will of course follow the charge state of the core conductor.

The inside of the braid will react to the charge on the inner wire.
But you won't be able to tell from outside.

That's the magical thing about coax cable, the signal is faraday caged- no interactions (in principle)  in or out.
And faraday cages don't need to be grounded. That's why aircraft antennae are on the outside of the fuselage.

[alancalverd]

From a mechanistic analysis the wiki article makes 100% sense to me . What I don't understand is how one can have opposite charges on either side of a thin metal conductor, yet no electric field between these charges. It is an aspect of the ice pail experiments I never thought about before.

The electric field is that due to the incoming charged body. The confusion (at least the one that used to reside in my brain) is that we deal with current rather than static electricity most of the time, and the whole business  of electrical engineering depends on charge flowing so as to eliminate potential difference and field. We rarely ask what happens if we impose a static field on a conductor - we just take it for granted that charge will move around a closed circuit. But the circuit isn't closed in electrostatics.

[paul cotter (OP)]

Indeed Alan, current in it's various guises is principally what I have dealt with. I only briefly looked at electrostatics in connection with the historical derivation of the Coulomb law.