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Forum index » Science and Technology » Physics » Electromagnetics
Circularly polarized beam has torque?
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Tom Ring
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Joined: 06 Jan 2006
Posts: 57

PostPosted: Tue Jun 20, 2006 11:38 pm    Post subject: Circularly polarized beam has torque? Reply with quote

Given that collinear mounted cross (90 degrees) polarized yagi antennas
can produce a circularly beam with proper phasing, how could torque be
produced? Neither beam is producing it individually, the circularity is
all due to phasing between 2 antennas that do not couple.

The antennas also do not need to be collinear, but you need to be a
considerable distance away in that case.

tom
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Tom Ring
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Joined: 06 Jan 2006
Posts: 57

PostPosted: Wed Jun 21, 2006 12:31 am    Post subject: Re: Circularly polarized beam has torque? Reply with quote

Tom Ring wrote:

Quote:
The antennas also do not need to be collinear, but you need to be a
considerable distance away in that case.


Rereading, my second sentence was not very clear, but I will assume that
readers can figure along which axis I meant considerable distance was
needed.

tom
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Timo Nieminen
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Joined: 12 May 2005
Posts: 244

PostPosted: Wed Jun 21, 2006 1:48 am    Post subject: Re: Circularly polarized beam has torque? Reply with quote

On Tue, 20 Jun 2006, Tom Ring wrote:

Quote:
Given that collinear mounted cross (90 degrees) polarized yagi antennas
can produce a circularly beam with proper phasing, how could torque be
produced? Neither beam is producing it individually, the circularity is
all due to phasing between 2 antennas that do not couple.

Start with the simple case first: two crossed centre-fed linear antennas.

Note that for a single linear antenna, H in the near field is 90 degrees
out of phase wrt the current in the antenna (see, eg, Stratton 8.11). Add
a second linear antenna at right angles to the first. If the current in
this is 90 degrees out of phase with the current in the first, it'll be in
phase with H from the first. Just draw the two crossed antenna, the
direction of H from the first, the current in the 2nd, and look at the
direction of the force on each half. Since H is in opposite directions
over each half, the forces on the currents in each half are in opposite
directions. The total force is zero, the torque is non-zero.

Same thing for torque exerted by magnetic field of 2 on current in 1.

Going to a more directional crossed antenna array doesn't make any
fundamental difference to this process.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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Tom Ring
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Joined: 06 Jan 2006
Posts: 57

PostPosted: Wed Jun 21, 2006 3:30 am    Post subject: Re: Circularly polarized beam has torque? Reply with quote

Timo Nieminen wrote:
Quote:

Start with the simple case first: two crossed centre-fed linear antennas.

Note that for a single linear antenna, H in the near field is 90 degrees
out of phase wrt the current in the antenna (see, eg, Stratton 8.11). Add
a second linear antenna at right angles to the first. If the current in
this is 90 degrees out of phase with the current in the first, it'll be in
phase with H from the first. Just draw the two crossed antenna, the
direction of H from the first, the current in the 2nd, and look at the
direction of the force on each half. Since H is in opposite directions
over each half, the forces on the currents in each half are in opposite
directions. The total force is zero, the torque is non-zero.

Same thing for torque exerted by magnetic field of 2 on current in 1.

Going to a more directional crossed antenna array doesn't make any
fundamental difference to this process.


Ok, I think I get this, and I will assume it holds for the whole 360
degrees of excitation. Assuming that, then the torque from the H field
is exerted against what?

Yes I think I know what your answer will be, and in which case, what
happens if the antenna is massless?

tom
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Tom Ring
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Joined: 06 Jan 2006
Posts: 57

PostPosted: Wed Jun 21, 2006 3:38 am    Post subject: Re: Circularly polarized beam has torque? Reply with quote

Timo Nieminen wrote:

Quote:
On Tue, 20 Jun 2006, Tom Ring wrote

Going to a more directional crossed antenna array doesn't make any
fundamental difference to this process.


And another question. What field is the antanna's H field pushing
against to generate the torque?

tom
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Timo Nieminen
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Joined: 12 May 2005
Posts: 244

PostPosted: Wed Jun 21, 2006 3:44 am    Post subject: Re: Circularly polarized beam has torque? Reply with quote

On Tue, 20 Jun 2006, Tom Ring wrote:

Quote:
Timo Nieminen wrote:

Start with the simple case first: two crossed centre-fed linear antennas.

Note that for a single linear antenna, H in the near field is 90 degrees
out of phase wrt the current in the antenna (see, eg, Stratton 8.11). Add
a second linear antenna at right angles to the first. If the current in
this is 90 degrees out of phase with the current in the first, it'll be in
phase with H from the first. Just draw the two crossed antenna, the
direction of H from the first, the current in the 2nd, and look at the
direction of the force on each half. Since H is in opposite directions
over each half, the forces on the currents in each half are in opposite
directions. The total force is zero, the torque is non-zero.

Same thing for torque exerted by magnetic field of 2 on current in 1.

Going to a more directional crossed antenna array doesn't make any
fundamental difference to this process.


Ok, I think I get this, and I will assume it holds for the whole 360
degrees of excitation. Assuming that, then the torque from the H field
is exerted against what?

Yes I think I know what your answer will be, and in which case, what
happens if the antenna is massless?

The radiated field has the equal and opposite angular momentum flux. For
an example of extracting such AM flux from a RF field, P. J. Allen, Am. J.
Phys. 34, 1185-1192 (1966).

As for a massless antenna, build one and see what happens.

If you take the crossed-dipole antenna and put it into space, what
happens? The torque will make it spin faster and faster and, assuming that
it doesn't spin so fast as to fly apart, until the rotational frequency
shift redshifts the emitted frequency to zero. This will happen when the
rotation frequency equals the driving frequency. Note that in this case,
the dipole moment (and higher order multipole moments) of the antenna is
constant, so you get a static dipole field, with no radiation.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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Bergervoet dr. J.R.M.
science forum beginner


Joined: 26 Jun 2006
Posts: 2

PostPosted: Mon Jun 26, 2006 4:52 pm    Post subject: Re: Circularly polarized beam has torque? Reply with quote

Timo Nieminen wrote:
Quote:
On Tue, 20 Jun 2006, Tom Ring wrote:


Given that collinear mounted cross (90 degrees) polarized yagi antennas
can produce a circularly beam with proper phasing, how could torque be
produced? Neither beam is producing it individually, the circularity is
all due to phasing between 2 antennas that do not couple.


Start with the simple case first: two crossed centre-fed linear antennas.

Note that for a single linear antenna, H in the near field is 90 degrees
out of phase wrt the current in the antenna (see, eg, Stratton 8.11).

This is not true. If you are close enough to the current-carrying wire,
H will be almost exactly in phase with the current. At larger distances
it will lag, so you should say that it has a component that is 90
degrees out of phase. (And that's actually enough for your argument.)

-- Jos
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