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riddles >> medium >> The Dodgy Solenoid
(Message started by: THUDandBLUNDER on Oct 9th, 2003, 1:24pm)

Title: The Dodgy Solenoid
Post by THUDandBLUNDER on Oct 9th, 2003, 1:24pm
Imagine that we construct a device like that shown in the figure below. There is a thin, circular plastic disc supported on a concentric shaft with excellent bearings, so that it is quite free to rotate. On the disc is a coil of wire in the form of a short solenoid, concentric with the axis of rotation. This solenoid carries a steady current (I) provided by a small battery, also mounted on the disc. Near the edge of the disc and spaced uniformly around its circumference are a number of small metal spheres insulated from each other and from the solenoid by the plastic material of the disc. Each of these small conducting spheres is charged with the same electrostatic charge (Q). Everything is quite stationary, and the disc is at rest. Suppose now that by some accident (or by prearrangement) the current in the solenoid is interrupted - without, however, any intervention from the outside. So long as the current continued, there was a magnetic flux through the solenoid more or less parallel to the axis of the disc. When the current is interrupted, this flux must go to zero. There will, therefore, be an electric field induced which will circulate around in circles centred at the axis. The charged spheres on the perimeter of the disc will all experience an electric field tangential to the perimeter of the disc. This electric force is in the same sense for all the charges and so will result in a net torque on the disc. From these arguments we would expect that, as the current in the solenoid disappears, the disc would begin to rotate. If we knew the moment of inertia of the disc, the current in the solenoid, and the charges on the small spheres. we could compute the resulting angular velocity.

But we could also make a different argument. Using the principle of the conservation of angular momentum, we could say that the angular momentum of the disc with all its equipment is initially zero, and so the angular momentum of the assembly should remain zero. There should be no rotation when the current is stopped. Which argument is correct? Will the disc rotate or not?

Title: Re: The Dodgy Solenoid
Post by towr on Oct 9th, 2003, 1:41pm
::[hide]It seems the action-force and reaction-force are both from within the same object, and thus cancel eachother out.
So there would be no movement..
(of course it's late and I might have misread it..)[/hide]::

Title: Re: The Dodgy Solenoid
Post by James Fingas on Oct 9th, 2003, 1:46pm
Here's another argument that perhaps shows why it could move even though there appears to be no angular momentum exchange with the rest of the universe:

Since there is the same charge Q on every sphere, there must be a corresponding charge -Q somewhere else in the universe. Therefore, the same electrical fields that cause (or do not cause?) the torque on the disc cause torque in the opposite direction on these -Q charges, causing the universe to gain angular momentum in the opposite direction. So maybe angular momentum is conserved anyways!

Title: Re: The Dodgy Solenoid
Post by aero_guy on Oct 9th, 2003, 1:54pm
Without going back to my physics books I will have to use ENGINEERING INTUITION.  Assuming your electrical engineering is correct, and the change in electric field would induce a force on the charged particles, we know that forces come in pairs and that in all likelihood there would be and induced torque on the wire counter to that given to the particles and as they are on the same disk, no net motion.  If they were on sparate concentric disk we would see counterrotation that would sum to zero angular momentum.

So what is this mystery force?  If the particles themselves were moving I could see them perhaps inducing current in the wire, but they aren't.  Hmm, maybe there is a net motion... equivalent to the angular momentum of the electrons in the wire.  The resistance in the wire is what causes the changing current (for a supeconductor there would be no change).  Maybe this come into play.  Man I need a refresher course on electro magnetism.

Title: Re: The Dodgy Solenoid
Post by James Fingas on Oct 10th, 2003, 8:19am
I've been thinking about this one for a while now, and I can't see the hole in it. The relevant formula is:

curl D = dB/dt (correct to a factor of [mu], [epsilon], or whatever)

This means that as the net flux through the ring of charge particles is decreasing, we get a net circulating electric field. It seems impossible that there wouldn't be a force generated on the charged particles.

The interesting thing about it is that there is no steady-state electric field on the coil, so the coil doesn't even know the particles are there. Therefore, at the moment that the circulating electric field is generated, there can be no angular momentum change on the solenoid (or causality would be violated).

When the electric field reaches the charged particles, presumably it imparts angular momentum on to those particles. At this point, the only way that angular momentum can be conserved is if a reflected or refracted electromagnetic wave carrying angular momentum emanates from the charged particles (again, because of causality).

There is no reason why this angular momentum necessarily has to be transferred back onto the disc, so I say it might just spin! I've never heard of light carrying angular momentum before, but I see no reason why it should be impossible.

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