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Jeff Root
2014-Jun-28, 05:57 AM
I asked this question before, but the thread got hijacked and
went into three pages without a satisfactory answer.

If a light wave is moving forward, and the positive direction of
the electric field is up, is the positive direction of the magnetic
field to the right or the left? How can that be determined?

I expect that this is the correct answer:



right hand rule

If k is forward and E is up then B is to the right.
However, I'm having a hard time confirming it. I find many
diagrams on the web depicting the electric and magnetic fields
as perpendicular to each other and in phase, but very few show
the direction of propagation AND the positive directions of both
fields. Sometimes the positive directions can be inferred from
arrowheads, and sometimes the positive direction of the electric
field can be inferred to be "up".

This is the least-ambiguous diagram I could find. I found it
before I asked my question originally. Assuming the wave is
travelling in the direction of positive X, away from the viewer,
it shows a left-hand rule, contradicting korjik:

http://www.ch.ic.ac.uk/local/physical/mi_5.html

The diagram at the top of the Wikipedia page on electromagnetic
radiation, as well as the two animations farther down the page,
appear to show a right-hand rule, in agreement with korjik.
I assume that the positive direction of the electric field is up,
as suggested by the blue arrow in the sub-diagram on the right,
and the oblique perspective of the main diagram shows the
positive direction of the magnetic field (red) as coming toward
the viewer as it slants down to the left. That implies that the
view in the sub-diagram is looking at the light coming toward
the viewer, not going away:

http://en.wikipedia.org/wiki/Electromagnetic_radiation

The diagram near the bottom of the Wikipedia page on light
appears to show a left-hand rule, contradicting korjik. I assume
that the positive direction of the magnetic field is up:

http://en.wikipedia.org/wiki/Light

Assuming that the arrows on the y and z axes in this diagram
show the positive directions of the electric and magnetic fields,
respectively, gives a left-hand rule, contradicting korjik:

http://astronomy.swin.edu.au/cosmos/E/electromagnetic+radiation

Assuming that the arrows in the two diagrams on this page show
the positive directions of the fields gives a right-hand rule, in
agreement with korjik:

http://missionscience.nasa.gov/ems/02_anatomy.html

On this page also, assuming the arrows indicate the positive
directions gives a right-hand rule, in agreement with korjik:

http://www.srh.noaa.gov/jetstream/remote/remote_intro.htm

Another diagram where assuming the arrows indicate the positive
directions gives a right-hand rule, in agreement with korjik:

https://www.thermalfluidscentral.org/encyclopedia/index.php/Electromagnetic_waves_and_thermal_radiation

But in this diagram, assuming the arrows indicate the positive
directions gives a left-hand rule, contradicting korjik:

http://www.fao.org/docrep/003/t0355e/t0355e02.htm

Four pages which illustrate a right-hand rule, and four pages
which illustrate a left-hand rule. None which say explicitly.

I agree that the rule for currents in a conductor and the resulting
force is a right-hand rule, but I want better confirmation that the
rule for electromagnetic radiation is also right-handed.

-- Jeff, in Minneapolis

tusenfem
2014-Jun-28, 06:22 AM
The wave vector, or direction of propagation is given by the Poynting flux, i.e. the direction in whicht the energy that is carried by the wave is transported.
The Poynting vector P is given by:


\bf{P} = \bf{E} \wedge \bf{H} = \mu^{-1} \bf{E} \wedge \bf{B}

korjik
2014-Jun-28, 08:40 AM
And the reason he brought it up is that the cross product is right hand rule. If you need a specific cite, try pg 805 of Salas and Hille's Calculus 7th edition, or just the definition of the cross product in the text of your choice.

Reality Check
2014-Jun-30, 03:14 AM
http://en.wikipedia.org/wiki/Electromagnetic_radiation

The equation near the bottom of that Wikipedia page shows that the B field is the cross-product of the unit vector in the direction of propagation and the E field. Thus the right-hand rule (http://en.wikipedia.org/wiki/Right-hand_rule) applies as it does for all cross products:
Using your right hand,
Point your index finger in the direction of the first vector A.
Point your middle finger in the direction of the second vector B.
Your thumb will point in the direction of the cross product C.

The diagrams that you mention may or may not be wrong.

grapes
2014-Jun-30, 12:43 PM
The diagram near the bottom of the Wikipedia page on light
appears to show a left-hand rule, contradicting korjik. I assume
that the positive direction of the magnetic field is up:

http://en.wikipedia.org/wiki/Light

Check that one again, I'm not sure that does contradict:


If k is forward and E is up then B is to the right.


ETA: it's this diagram that you are talking about, right?

http://en.m.wikipedia.org/wiki/File:Light-wave.svg

Jeff Root
2014-Jun-30, 01:13 PM
grapes,

Yes, that's the diagram.

I don't remember writing "I assume that the positive
direction of the magnetic field is up". I'm pretty sure I
meant to say "electric", but typed "magnetic" instead.
However, as it happens, that error doesn't make any
difference because the magnetic field also goes pretty
much "up" in what seems to be its positive direction.
So the diagram appears to show a left-hand rule, as I
said. You check it again, and if it still looks okay to
you, I'll check again.

A possible source of confusion is the poor perspective,
making the orientation of the magnetic component hard
to determine. I see the electric wave as vertical. The
magnetic wave goes into the distance when the electric
wave goes up, and comes into the foreground when the
electric wave goes down.

-- Jeff, in Minneapolis

korjik
2014-Jun-30, 01:51 PM
Check that one again, I'm not sure that does contradict:


ETA: it's this diagram that you are talking about, right?

http://en.m.wikipedia.org/wiki/File:Light-wave.svg

That diagram may not be graphing motion, but just the graph of the wave function. I say this cause it says 'distance' not 'velocity' or some other indication of direction of motion. It may also be supposed to have M out of the screen and it just looks into the screen. That is a common optical illusion with a 3d graph on 2d screen.

EigenState
2014-Jun-30, 04:57 PM
Greetings,


That diagram may not be graphing motion, but just the graph of the wave function. I say this cause it says 'distance' not 'velocity' or some other indication of direction of motion. It may also be supposed to have M out of the screen and it just looks into the screen. That is a common optical illusion with a 3d graph on 2d screen.

The diagram in question certainly fails to explicitly indicate the direction of propagation. The right-hand rule applies only if one is looking along the direction of propagation as already posted by tusenfem.

Best regards,
ES

korjik
2014-Jun-30, 09:17 PM
Greetings,



The diagram in question certainly fails to explicitly indicate the direction of propagation. The right-hand rule applies only if one is looking along the direction of propagation as already posted by tusenfem.

Best regards,
ES

Technically, right hand rule still applies. You just have to get the direction of propagation correct

EigenState
2014-Jun-30, 11:19 PM
Greetings,


Technically, right hand rule still applies. You just have to get the direction of propagation correct

Indeed!

Best regards,
ES