Author: mrchuakh

161 Magnet and Coil

The easiest way to make sense of the induced voltages is to first figure out the how the magnetic flux linkage (of the coil) varies with time. Obviously, the flux linkage is strongest when the magnet is centred with the coil.

1 Fall Through

(a) magnet approaching coil
(b) magnet is centred with coil
(c) magnet left coil

2 Bungee Dip

(a) magnet at the top
(b) magnet at the bottom
(c) magnet at the top

3 Aligned

(a) magnet at the top
(b) magnet centred with the coil
(c) magnet at the bottom
(d) magnet centred with the coil
(e) magnet at the top

4 Cross-over

(a) magnet at the top
(b) magnet centred with coil
(c) magnet at the bottom
(d) magnet centred with coil
(e) magnet at the top

159 Fundamental and Harmonics

Can you differentiate between the sounds of sinusoidal, saw-tooth and square waves? Only the sinusoidal wave is monotonic. It truly consists of one single pitch. The saw-tooth and square waves are actually the superposition of many sinusoidal waves of different frequencies. So they contains higher harmonics on top of the fundamental. While they all sound like the same pitch to us, they also sound different because of the different (amplitudes) of the harmonics they contain.

The sound produced by the guitar (string) and the recorder (open pipe) are also not monotonic. It takes a bit of imagination to realize that the standing waves formed on the string and the air in the pipe actually consists of many frequencies at the same time. But that’s what allows the sound produced by different instruments to have different timbres.

153 Transformer Electric Shock

I take a standard step-down transformer and flip it around to use it as a step-up.

Instead of feeding a AC voltage, as is standard for a transformer, I connect a 9-V DC battery across the lower-turn coil. There is no output voltage across the higher-turn coil, except at the instants when the 9-V battery is connected or disconnected.

The voltmeter seems to suggest a much larger (induced) output voltage upon disconnection. I am not sure if I can trust the >1000 V reading. But I usually make my students (typically about 13) join hands to take the place of the voltmeter. They sure enjoyed the electric shocks when I connected/disconnected the circuit.

153 Non Conservative Field

The following diagrams summarise some interesting measurements, the outcome of which will probably surprise many people. (the red circle represents the region of alternating magnetic field)

nonConservative1

Note that the voltmeters give different readings even though they are connected across the same two points.

nonConservative2

This is due to the fact that the electric field generated by a changing magnetic field is fundamentally different from the so-called coulomb fields. In an non-coulomb field, where the field is not set up by electrical charges, the field is non-conservative. So moving a charge round one complete circuit actually does not return the charge to the original potential.

It is also useful to note that the “surprising” readings all have the voltmeter forming a loop that encloses the changing magnetic field itself.

152 Transformer

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.

 

Upthrust: Floating Golf Ball — xmdemo 077

 

When there is only the brine (see Figure 1), the weight of the brine displaced (labelled A) is equal to the weight of the golf ball.

Capture

Let’s imagine the golf ball floating at the same level as before after oil has been added on top (see Figure 2). Since the golf ball now displaces oil as well, it must receive an additional upthrust that is equal to the weight of the displaced oil (labelled B). This means that at this level, there is a net upward force acting on the the golf ball. So surely the golf ball will float higher until the weight of the displaced brine plus oil equals the weight of the golf ball again (see Figure 3).

Wait, are we certain that the Archimedes Principle is applicable even when an object is submerged in two different fluids? Let’s use the “water banana” trick again.

Capture

Imagine a golf ball that is made of oil above the fluid boundary, and brine below. (Basically, this imaginary golf ball is the displaced fluids.) Since such a golf ball will be at neutral buoyancy, it must be experiencing an upthrust that is equal to its weight, which is the weight of the displaced fluids. So Archimedes Principle works even there are two (or more) layers of fluids.

Still, how does the oil, which clearly exerts only downward pressure forces on the golf ball, results in additional upthrust? This is easily explained if we use a cube instead.

Capture

When there is only brine (see Figure 4), the cube receives only upward pressure forces1. When oil is added (see Figure 5), besides resulting in downward pressure forces, it also results in an increase in the pressure in the brine. While the pressure at the top of the cube is increased by h1ρg, the pressure at the bottom of the cube is increased by h2ρg, resulting in a net increase in upthrust. Get it?

  1. Let’s ignore atmospheric pressure since it will be cancelled out when we take the difference of upward and downward pressure forces.

 

900 Magnetic Pump

We have current flowing across the mercury (from one ring to the other), which is sitting in a magnetic field. So there is a F=BIL magnetic force. Or we can think the moving electrons (that constitute the current) experience a F=Bqv magnetic force. This force is directed perpendicular to the current (and magnetic field), which turns out to be along the circumference of the ring. The mercuy is thus pumped in a merry-go-round fashion.

Why should the metal lattice chase after/get dragged by the electrons?

147 Stirling Engine

a

The construction of this stirling engine is quite simple. The acrylic container holds the working air. The air pushes the piston. The piston rotates the fly wheel. The fly wheel in turn pushes the displacer (the Styrofoam piece). The piston and the displacer are connected to the fly wheel in such a way that they are always out of phase by a quarter cycle. This automatically synchronizes the displacer to fulfill the important function of pushing the air to the hot end when it’s the air’s turn to push, and pushing the air to the cold end when it’s the fly wheel’s turn to push.

a

b

c

d

The diagrams above show the positions of the piston and the displacer at four stages. During abc, the displacer moves the air towards the hot end so that the air is heated up. This is when we extract work done by the air. During cda, the displacer moves the air towards the cold end so that the air is cooled down. This is when work is done by the piston. Since abc occurred at higher temperature and pressure, in one complete cycle, net work done is by the air.