Poynting vector and DC current

In summary, Poynting's Theorem, a fundamental principle in electromagnetism, can be used to calculate energy transferred in both AC and DC systems. This is because DC is essentially just low frequency AC. The proof for this lies in the fact that when electricity was first invented, a transient step occurred that had a continuous Fourier spectrum, covering both nanoseconds and centuries. This means that even in a seemingly DC system, there is still an AC component that can be calculated using Poynting's Theorem.
  • #1
Jackson Lee
77
1
We all know that poynting vector could be used to calculate energy transferred in AC system, but I want to know if that theorem could also be applied to DC current? How to prove this? And how to prove energy transferred in AC system could be calculated via poynting vector?
 
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  • #3
Why should DC be any different to AC?

When electricity was invented and the first contacts closed, a transient step occurred that had a continuous Fourier spectrum, covering periods of a nanosecond out to many centuries.

When you turn a DC LED light on at dusk, then off when you go to bed, that is just a delta function on the scale of the year. If you do it every night of the year, it becomes a year long pulse train, which has an AC component with a real DC component.

DC is really just very low frequency AC.
 

Related to Poynting vector and DC current

What is the Poynting vector?

The Poynting vector is a mathematical quantity that describes the direction and magnitude of the energy flow in an electromagnetic field. It is named after physicist John Henry Poynting and is denoted by the symbol S.

How is the Poynting vector related to DC current?

The Poynting vector is related to DC (direct current) by the fact that it is a measure of the energy flow in a steady-state electromagnetic field. In a DC circuit, the Poynting vector points in the direction of the current flow and is proportional to the square of the current.

What is the significance of the direction of the Poynting vector?

The direction of the Poynting vector represents the direction in which energy is flowing in an electromagnetic field. In a DC circuit, the direction of the Poynting vector is the same as the direction of the current flow, indicating the direction of energy transfer.

How is the Poynting vector calculated?

The Poynting vector is calculated by taking the cross product of the electric field vector and the magnetic field vector, multiplied by the permeability of free space. It is expressed in units of watts per square meter (W/m^2).

What is the practical application of the Poynting vector in DC current?

The Poynting vector is used in DC circuits to calculate the power dissipation in various components, such as resistors. It is also used in understanding the behavior of electromagnetic waves and their interaction with materials in electrical devices.

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