Poynting proof for a dc current?

[Per Oni]

A comment in another thread led me to think about an experiment which can hopefully test the validity of the pointing vector theory for a dc current.

I’m very unsure of the outcome of this experiment but what the heck. Here it goes: the Poynting theorem states E x H is power per unit surface area.

First consider a single winding with dc current I. We know that H is higher at the surface then at the centre, but E is everywhere the same running length wise. Now think of a coil made out of fairly thick wire say 10mm square with say 20 windings. Similar as with the single wire, a winding in the centre will have a smaller H field then the ones at the outside. Therefore since all winding have the same surface area, current and E field, the outside windings should get hotter than the inside ones. Therefore 2 small thermocouples should be able to pick up the differential.
Note however that the middle one will very quick receive thermal energy from the surrounding wires.

Any thoughts?

 

[Drakkith]

Why would the H field cause heat buildup? I thought it was only resistance of the wire that would cause that.

 

[Per Oni]

Why would the H field cause heat buildup?

The H and E fields together indicate a flow of energy according to Poynting’s theorem.

I thought it was only resistance of the wire that would cause that.

Yeah that’s right. Also, if there was such an effect it would have been noticed a long time ago. So my experiment fails. Where is the flaw? Possible reasons: Poynting vector theorem is applied the wrong way or it doesn’t apply for a dc current. In both cases I’m still intrigued to know how electrical power flows into the coil.

 

[Drakkith]

Perhaps this?

Poynting's theorem takes into account the case when the electric and magnetic fields are coupled – static or stationary electric and magnetic fields are not coupled. In other words, Poynting theorem is valid only in electrodynamics.

I'm not sure if it applies or not, I'm just throwing it out there.

 

[omega_minus]

In both cases I’m still intrigued to know how electrical power flows into the coil.

As you probably know already, the power in the coil is the product of the current in the wire and the voltage dropped across the total winding. The units are [J/C]*[C/s]=[J/s]=[W].
As Drakkith has pointed out the Poynting vector is for EM waves. A unit analysis on that gives its dimensions as [W/m^2], which shows it's useful in calculating the instantaneous power density of a wave, but also in showing the direction of power flow. Since a cross product is involved, the direction of propagation and power flow are both normal to the E and H fields.

 

[Per Oni]

As you probably know already, the power in the coil is the product of the current in the wire and the voltage dropped across the total winding. The units are [J/C]*[C/s]=[J/s]=[W].
As Drakkith has pointed out the Poynting vector is for EM waves. A unit analysis on that gives its dimensions as [W/m^2], which shows it's useful in calculating the instantaneous power density of a wave, but also in showing the direction of power flow. Since a cross product is involved, the direction of propagation and power flow are both normal to the E and H fields.

All you wrote is certainly true but there’s a discussion going on whether the theorem is also valid for dc. I still think it is and that my experiment above is somehow flawed. When I get some more time I'll spend some time on it. Thanks for the input.