# Poynting proof for a dc current?

• Per Oni
In summary, the experiment tries to measure the power flowing into a coil of wire and it seems that there might be a flaw in the methodology.
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?

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

Drakkith said:
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.

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.

Per Oni said:
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.

omega_minus said:
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.

## 1. What is the Poynting proof for a DC current?

The Poynting proof for a DC current is a mathematical expression that describes the flow of energy in a direct current (DC) circuit. It is based on the Poynting vector, which represents the direction and magnitude of energy flow in an electromagnetic field. The Poynting proof is used to calculate the rate of energy transfer in a DC circuit.

## 2. How is the Poynting proof calculated?

The Poynting proof is calculated by multiplying the electric field intensity (E) and the magnetic field intensity (H) at a given point in the circuit. This results in a vector quantity known as the Poynting vector (S). The magnitude of the Poynting vector represents the rate of energy transfer in watts per square meter, while the direction indicates the flow of energy.

## 3. Why is the Poynting proof important in DC circuits?

The Poynting proof is important in DC circuits because it allows us to understand and calculate the flow of energy in these circuits. This is crucial for designing and analyzing electrical systems and ensuring efficient energy transfer. Additionally, the Poynting proof can help identify areas of energy loss or inefficiency in a DC circuit.

## 4. How does the Poynting proof relate to other laws and principles in physics?

The Poynting proof is closely related to other fundamental laws and principles in physics, such as the law of conservation of energy and Maxwell's equations. It is also a crucial component in understanding the relationship between electric and magnetic fields, as described by the electromagnetic wave equation.

## 5. Are there any limitations to the Poynting proof for a DC current?

While the Poynting proof is a useful tool for analyzing DC circuits, it does have some limitations. For example, it does not take into account the effects of resistance, which can significantly impact the flow of energy in a circuit. Additionally, it only applies to steady-state DC circuits and cannot be used to analyze transient or alternating current (AC) circuits.

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