The electron diffraction experiment demonstrates the wave nature of electrons. An electron with momentum p has a de Broglie’s wavelength of λ=h/p. When a beam of electrons is passed through a crystalline structure (such as graphite), an interference pattern of bright and dark rings is formed. If the electrons are accelerated to higher momentum (by turning up the accelerating voltage), the electrons’ wavelength will decrease. The separation between the bright and dark rings will thus decreases. (similar to fringe separation in the double slit experiment being dependent on wavelength Δy=Lλ/d)

–

The sun’s core emits a continuous spectrum of light. However, the gas atoms in the sun’s “atmosphere” are capable of absorbing some of this light. Thanks to the discrete energy levels in gas atoms, these gas atoms can only absorb photons of certain energies (and since E=hc/λ, photons of certain wavelengths) that match the energy gaps in the energy levels of the gas atoms (|E₂-E₁|= hc/λ), resulting in dark lines in the solar spectrum at those wavelengths.

–

–

Out of curiosity, I tried to match the absorption lines in my video to those published on the internet (see http://en.wikipedia.org/wiki/Sunlight). With a little confidence, I think four of the more prominent dark lines (labelled C, D, E and F) in the spectrum are due to absorption by Sodium, Iron, Hydrogen and Iron atoms in the Sun’s atmosphere.

–

P.S.

It came as a surprise to me that the absorption lines of the solar spectrum can be viewed directly with the naked eyes using a grating. Although the video camera tends to over exposure the image (thus resulting in the absorption lines being washed out), the dark lines are clearly visible momentarily when the camera was in the midst of “correcting” the exposure.

–

If the solenoid were powered by a DC current, the ring should only experience a changing magnetic flux only at the instant when the solenoid was turned on. The ring would then have jumped only once, before falling back to the bottom. The fact that it is able to hover tells us that it continuously experiences an upward magnetic force that balances its downward weight.

–

This is possible only if the solenoid is powered by an AC current. We can in fact thinking of the solenoid as the primary coil of a transfomer, and the ring as the secondary coil. The primary and secondary currents are always in-phase (or completely out-of-phase if you choose). So the current in the solenoid and the ring produce magnetic fluxes which are always opposing each other, resulting in a continuous upward magnetic force (a sine-square varying force, to be exact) on the ring, which keeps the ring in the air.

–

The solenoid is the primary coil while the green wire is the secondary.

The video shows clearly how the secondary voltage is proportional to the number of turns in the secondary coil.

Since each additional turn increases the secondary voltage by about 0.064 V, and assuming that the primary coil is 230 V, the number seem to be suggest that the primary coil has about 3600 turns. It does not look like the primary coil has that many turns. So probably there is a lot of flux leakage.

–

The LEDs are powered by a 50 Hz AC supply. Since LEDs are diodes, they light up only during the positive half cycles of the AC supply, but do not light up during the negative half cycles.

This flashing of the LEDs at 50 Hz is revealed if we keep moving the LEDs, as shown in this video.

–

First of all, the street lamps are pulsating because they are powered by an alternating current. Singapore uses 50 Hz AC supply, so the street lamps pulsate 100 times per second.

Some people expect 50 pulsations per second. They have forgotten that a lamp lights up two times in each AC cycle: once during the positive half-cycle, and once more during the negative half-cycle.

–

As the magnet descended, the aluminium beside the descending magnet experiences first an increasing and then a decreasing flux linkage, resulting in induced emf. (E=dΦ/dt)

Since aluminium is conductive, (eddy) currents formed in the blocks, producing their own magnetic field.

The polarity of the induced emf must be such as to produce a induced current and magnetic field that opposes the change that caused the induction in the first place. (Lenz’s Law). This predicts a retarding magnetic force on the descending magnet, bringing it to a (surreally) low terminal velocity.

Since the rods experience a changing magnetic flux as the magnets make their descent, emf is induced in the rods. The resulting eddy current creates a magnetic field that opposes the descent of the magnets, resulting in a retardation force on the magnets.

–

–

Assuming all four magnets are identical, then the induced emf in all the four rods should be exactly the same. However, the induced current is different due to the different resistivities of the four rods. Copper, with the lowest resistivity, has the largest induced current and thus experiences the largest retardation force. Plastic is basically an insulator and has zero induced current (despite the same induced emf). It thus suffers practically no retardation force.

–

Say the north pole of the magnet is facing the ring. Note that the magnetic flux of the magnet is captured by the aluminum ring.

When the magnet is lifted away from the ring, the magnetic flux density at the ring decreases. An emf is induced around the ring since the ring experiences a change in flux linkage (Faraday’s Law, ε=-dΦ/dt). The direction of the induced emf (and current) should be such as to produce an effect to oppose the change that resulted in the induced emf in the first place (Lenz’s Law). Since the ring experiences a decreasing downward magnetic flux, the direction of induced current must be to produce a downward magnetic flux as well (in an attempt to arrest the decreasing magnetic flux). Since the magnetic field of the magnet and the ring are in the same direction, the ring experiences an attractive magnetic force that lifted the ring off the table.

When the solenoid was energized, it produces a magnetic field. The ring thus experienced an increase in magnetic flux linkage. This results in an induced emf around the ring. (Faraday’s Law: emf=dΦ/dt)

The magnetic flux captured by all three rings are exactly the same. (It’s is the same solenoid, so B is the same. The rings have the same circular area, so A is the same. And Φ=BA) Clearly, all three rings experienced the same change in magnetic flux linkage. This leads to the conclusion that the induced emf in all three rings are exactly the same!

So why do they jump to different heights?

Firstly, they jump because the induced current (caused by the induced emf) produces its own magnetic field. The interaction of the magnetic field of the ring and the magnetic field of the solenoid leads to a mutually repulsive force. (This outcome is predicted by Lenz’s Law). Note that the effect of the induced emf is felt only when it results in an induced current.

The solid ring presents the largest cross sectional area, and thus smallest resistance to the induced emf. (R=ρL/A) The induced current is the largest, hence it jumped the highest. The holes in the second ring confines the current to the edges of the ring. With a larger resistance, the induced current is less (despite the same induced emf), hence it jumped less high. As for the broken ring, there was practically zero induced current (despite the same induced emf) thanks to the infinite resistance presented by the air gaps.