# Energy flow in presence of electric and magnetic field

1. Mar 26, 2013

### nitin_zilch

To mention, i am trying to understand the flow of electromagnetic energy from the roots and only have some basic knowledge. In case i need to refer to some material to get to the answer, kindly provide me the link for the same

In which direction does the energy flow in a region (preferably vacuum) in which electric field is perpendicular to the magnetic field?

The situation is not similar to a travelling electronagnetic wave, in a sense, that the electric field and magnetic field are provided externally.

I have two perceptions about the situation, one is that the electric and magnetic field conditions the space and the motion of the a test particle can be used to see the nature of conditioning.
The second one is that the electromagnetic energy will flow in in a direction perpendicular to the electric and magnetic field.

My second perception is based on the transmission of electromagnetic energy in wires, in which the electric field as potential difference, magnetic field as current, transfer electromagnetic energy from source to bulb and the lines below which i read in a paper about transmission of electromagnetic energy:

"Electromagnetic theory predicts that there will be a flow of energy through any place where electric and magnetic fields both exist and are not parallel to one another."

It is obvious that one would need electrons in wires to produce magnetic field and electric field but in my question i am supplying it externally, therefore i ruled out the need of a medium and the region is assumed to be a vacuum?

please tell me which perception is correct and what is wrong with my perception?

Last edited: Mar 26, 2013
2. Mar 26, 2013

### Simon Bridge

depends on the field and what is happening. For static EM fields with no free charges, there is no movement of energy.

A travelling electromagnetic wave provides its own EM fields from moment to moment.

I don't understand that sentence.
The motion of a test particle can be used to determine the electromagnetic fields.

You mean: in the classical model of an EM wave, the motion of the wavepacket is perpendicular to both the electric and magnetic fields - which are perpendicular to each other?

Which book is that?

Usually we think of a current generating a magnetic field rather than being the field itself.
The B field about a current carrying wire is circular. The electric field points along the wire.
The electrical potential energy is transformed in the motion of charges in the wire, much like gravitational energy flows through the motion of masses.

You do not need to have a medium to have an electric field - you are aware that EM waves can cross space right? You need charges to have an electric current. The charges do not have to be electrons.

I'm unsure of the way you are using some words (like "perception", "flow" and possibly even "energy") though - perhaps English is a second language?

Anyway - I hope this helps.

3. Mar 26, 2013

### nitin_zilch

i know the energy available to the bulb is not derived from the kinetic energy of electrons moving in the wire as their speed under a D.C voltage is of the order of few cm/hour.Therefore this option is ruled out.

in short, the i can reduce my problem to a question

How does electromagnetic energy flows from battery to a bulb in a simple D.C circuit? considering that the majority of extracted energy is not available from the kinetic energy of moving electrons.

4. Mar 26, 2013

### Simon Bridge

That is correct, the simile I used was incomplete.
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/part6/page3.html
... the page before sets it up, this one talks about your question.

5. Mar 26, 2013

### Staff: Mentor

This is given by the Poynting vector, $\mathbf{S}=\mathbf{E}\times\mathbf{H}$:
http://en.wikipedia.org/wiki/Poynting_vector

6. Mar 27, 2013

### nitin_zilch

If i apply this, assume that the axis along the wire is in the plane of paper, then the Electric field is along this axis, the magnetic field perpendicular to it, running into and out of the paper, therefore the pointing vector points normal to the surface of wire.

so the energy flows perpendicular to the surface of wire at evert point, but not in a direction fom battery to bulb, as we would expect.

7. Mar 27, 2013

### nitin_zilch

so this means that if i apply electric field and magnetic field in a region of space the direction in which the energy flow is given by pointing vector.

suppose i have one such region in space, the area of the region is A, the energy flows as per the pointing vector. if the energy is not consumed by any object in that region, then how the energy propogates when it crosses the area A.
if the answer is the same as it was earlier, then there is something peculiar here,

Earlier, in the region of area A, the Elecetric and magentic field were provided externally, but once the energy moves out from that region, there is no external fields. How will the energy propogate here?

8. Mar 28, 2013

### Staff: Mentor

Yes.

Again, the energy flux is always given by the Poynting vector. That follows directly from Maxwells equations, regardless of the details of the fields, as long as they are solutions to Maxwells equations.

If I am correctly understanding your description then the fields you describe are not solutions to Maxwells equations. You cannot have a spatially limited uniform and static E and B, there must either be some time dependence or some end effects.

9. Mar 28, 2013

### nitin_zilch

what i mean to say is if i provide electric and magnetic fields externally in a region, will the poynting theorm still be applicabale ? can i say that the energy moves in a direction perpendicular to both the fields ? if yes, then what do we see in the cycloidal motion of a test charge in these fields?

10. Mar 28, 2013

### Staff: Mentor

I already answered this. The answer, again, is yes. The Poynting theorem is a direct result of Maxwells equations, so it applies any time Maxwells equations apply. Maxwells equations apply to a region where the fields are provided externally.

I am not sure what you are asking here.

11. Mar 28, 2013

### nitin_zilch

how will the energy propogate outside the region, where there is no external magnetic and electric field.

12. Mar 28, 2013

### Staff: Mentor

And I already answered this. The field you are describing is impossible. It is not a solution to Maxwells equations. You cannot have a spatially limited uniform and static field.

13. Mar 28, 2013

### Simon Bridge

@nitin_zilch: are you thinking of the example crossed B and E fields in, say, a cyclotron?
You could produce such fields by, say, getting two large permanent magnets to set up the B field between closely-spaced poles, and a large capacitor to set up the E field perpendicular to this.

The E and B fields set up like this extend through all of space however. There is nowhere where the "external field" does not appear.

One can imagine a charge accelerated by such fields moving into a region where another applied field cancels out the setup above for that region ... that would be very unusual. To understand what happens, you need to consider exactly how this would come about.

In the earlier example of the light-bulb - you don't need the energy flow to be along the wire to make the light bulb glow. You just need energy to flow through the filament of the light bulb. Is it that you want to know how an electric field makes the filament glow?

I think you should stick to one example at a time - understand it, and then move on.

@Dalespam: it is common in class to ask a student to treat some field as if it were spacially limited - as an approximation. A common example of this treatment would be that of a cathode ray tube. This may be a source of confusion. Of course - spacially limiting fields is a common misconception of perpetual motion and over-unity theorists.