This is a very interesting experiment with the aim of replicating the experimental work done by Mascart in 1876, in which he said that at a very high speed the disk jumped upwards due to an unknown force. Later on, Dr. Marcel Pagès in 1960, a trained psychiatrist very fond of physics, in particular with antigravity, explained and patented this as the electromagnetic Magnus effect, in which he mentioned the use of this technology for 'cosmic engines', French patent FR1253902 (pdf).
Below is the first test conducted by myself with the aim to reproduce the phenomena described above, and to better understand the mechanisms rotating and levitating the disk.
The experiment is fairly easy to set up. As shown above, all you need is a CD-ROM, two conductive spheres, a couple of insulating supports, some kitchen aluminium foil and a needle for the disc to spin on. Stick the kitchen foil to the upper surface of the CD-ROM as shown in the diagram. (Note the spiral shown above is just painted on the foil for visual purposes, and not required). The spheres should be positioned just a few millimetres below the lower surface of the disc, and connected to an hv supply in the range 30 kV - 60 kV.
As soon as the hv is switched on, the disc rotates really fast, either clockwise or anticlockwise. The initial direction seems to be purely random, and once it starts in a particular direction, it continues to accelerate in the same direction. Air underneath the setup gets ionised, and it is suggested you perform this experiment in a well ventilated room. As the disc accelerates, current consumption increases, until the disc reaches its maximum velocity.
How it works
The dielectric area (CD ROM area) just above the spheres gets polarised and locally charges up with the polarity of the terminal. Since the aluminium foil on the upper surface is at half the hv potential, this generates an asymmetric field between the sphere and the disc, which accelerates the charging up process, by accelerating charged air ions onto the face of the disc. Since the disc is made of insulating material, the charged dielectric particles cannot move over the surface of the disc without the disc itself moving, so a force from the positively charged dielectric area is generated toward the negative sphere, and a similar force from the negatively charged dielectric area is generated toward the positive sphere, thus creating a moment. Charges are thus continuously carried from one side to the other side, the higher the revs, the more charges are carried, and this is reflected in a linear increase in current consumption with speed of rotation. The rotation of this simple device has much in common with the PFT motor described in JLN's PFT MK2 motor. Next we will see the mechanism by which the disc levitates ...
Why should the disc levitate when acted upon by an external magnetic field perpendicular to its plane? We know that when a charged particle (for example an electron beam in a CRT) travels through a magnetic field, it will deflect in a circular path, and if the magnetic field is powerful enough, it will form a spiral path. The centripetal force acting on each particle is governed by Lorentz force:
F= ev x B
Most common applications of this law, normally involve a charged particle travelling at velocity v, across a magnetic field B, which is then acted upon a centripetal force F. However this case is not the unique way to apply the above law. An unconventional setup, such as that done by Marcel Pages (shown at top of page) is to force the charged particles (charged dielectric) in a circular path, and thus providing ourselves the centripetal accelerating force F. Since our disc carrying charged particles is rotating, we can easily find the generated magnetic field:
B = F/ev .......... where F= centripetal force = mv2/r
B = vm/re ........ replacing ω (angular velocity) for v/r
B = ω(m/e) ...... where m and e are the mass and charge of an electron respectively
A multitude of such rotating charges are going round our disc, with the number of charges per second being proportional to the current consumption. One would tend to say, that since the current is in the mA range, the magnetic field will be negligible and may never be enough to generate any usable magnetic field. In a current carrying conductor we usually have a high current with electrons zig-zagging through the metal lattice and drifting along their way at very low speeds. For example, in a copper conductor of radius 1 mm, carrying 1 Amp, the electron drift velocity is of 8.4 cm/hour. This opposition to electron movement results in resistance and heat.
On the other hand in the rotating disk setup, the electron drift velocity is equal to the high angular rotating speed v=ωr=2πfr. In this case, it is the metal lattice that is moving the charges, and their is no relative motion between charges and lattice, thus we have no resistance and heat generation on the metal surface. On a standard CD rom disc (6 cm radius) at 3000 RPM (50 rps), the electron drift velocity at the outer diameter would be equal to (2.π.50)x6 = 1885 cm/sec. Current is defined as charge flow per second, so eventually a high speed rotating charged dielectric could carry the same current as a conductor, even though the conductor has much more mobile electrons per unit volume.
By Lorentz rule, this resulting magnetic field B flows across the disc in the vertical plane, its direction depending on the angular velocity vector. Thus at a high speed, the disc will act as an artificial magnet, or like an electromagnet with no coil, with North pole on one face and South pole on the other face, depending on the direction of rotation. Once this artificial magnet is set up, the disc will react to external magnetic fields in the same way a normal magnet does. So, if a plane coil is energised underneath the disc, generating a pole of similar magnetic polarity as that of the lower face of the disc, the disc will be repelled upwards and away from the energised coil. This works in similar fashion to other levitating mechanisms, including magnetic levitation and superconducting levitation. In magnetic levitation, a magnet floats over another by repulsion of their opposing magnetic fields. In the superconducting levitation experiment (picture below), as the magnet is brought close, induced currents on the surface of the superconductor create an opposed magnetic field that attempts to repel the magnet. When the magnet is close enough, an equilibrium between repulsive force and gravitational force is reached.
Total dipole magnetic moment on charged disk
An amount of charge Q is uniformly distributed over a disk of dielectric material of radius R. The disk spins about its axis with angular velocity ω. To find the magnetic dipole moment of the disk, we first have to determine the dipole moment of a ring of the disk, with radius r and with a width dr, and then integrate over its radius. The amount of charge dq on this ring is equal to:
The angular velocity of the disk is ω, and its period T is equal to:
During one period the charge dq will pass any given point on the ring. The current dI is thus equal to:
The magnetic dipole moment du of the ring is equal to:
The total dipole moment of the disk can be found by integrating du between r = 0 and r = R:
The total magnetic dipole moment is equal to the torque (Nm) exerted on all magnetic dipoles when these are placed in a magnetic field of 1 Tesla. So the torque acting over the whole disc would be:
T= BQωR2/4 ... where B is the external magnetic field acting on the disc
Total levitating force on disc = BQωR/2
So, we see that the levitating force is proportional to the external magnetic field, the angular velocity, the total charge capacity of the disc and radius of disc.
Related EM radiation
What about types of radiation from such a setup? The main radiation one would expect with such a setup is the so called Cyclotron radiation. If you have charged particles flying around in space, they would normally travel undisturbed in straight lines. If, however, a magnetic field is present, they move in spirals around the magnetic field lines, making the magnetic field as their axis of rotation. The reason is that any moving charge is a current, and obeys all known rules for a current, even if there is no conductor / coil to carry the charge.
Charges flying in circles are continually accelerating, with a centripetal acceleration towards the field lines they are spiralling around. This means they are radiating pure sine-wave electric fields polarised perpendicular to the magnetic field lines. What is the spectrum of this radiation? Any given electron radiates a pure sine-wave electric field, so the electromagnetic radiation all comes out at a single frequency: the frequency of the spin of the charge around the field lines, which is equal to the angular velocity of the disk.
f = ω/(2π)
This frequency is quite low as the value will be equal to the disc's RPM, which due to its mechanical limitations cannot go into the Mhz region.