## Using a datalogger to measure induced emf

This video tutorial is a guide for next week's practical for CG18/12.

## Boyle's Law

Using a hand-operated vacuum pump, we can demonstrate the relationship between pressure and volume of a gas. According to Boyle's law, the pressure of a gas of constant mass and temperature will be inversely proportional to its volume.

In our demonstration, we will reduce the ambient pressure within the sealed container, hence allowing the higher internal pressure of a balloon to cause it to expand. When the volume within the balloon increases, the internal pressure can be observed to decrease until it is in equilibrium with the surrounding pressure.

While the relationship between pressure and volume is not exactly obeying Boyle's law due to additional factors such as the tension due to the elastic property of the balloon, it does demonstrate an inverse relationship.

## Polarization with 3 Filters

In what seems like a counter-intuitive demonstration, we can place a polarizing filter in between two other filters which do not transmit light in order to cause light to pass through again.

This is because each filter will permit the components of electric field vectors of the electromagnetic waves that are parallel to its axis of polarization according to the equation $A = A_o \cos{\alpha}$ where $A_o$ is the original amplitude of the unpolarized wave incident on the filter and $\alpha$ is the angle between the electric field vector and the axis of polarization. Each time the wave passes through a filter, it undergoes a reduction in amplitude according to the equation so that by the third filter, its resultant amplitude is
$A = A_o \cos{\alpha_1} \cos{\alpha_2}cos{\alpha_3}$
where $alpha_i$ is the angle between the axis of polarization of the ith filter and the electric field vector direction of the incident light on the ith filter.

According to Malus' law, which applies to two filters with an angle of $\theta$ between their axes of polarization, the resulting intensity for light that passes through 3 filters is given by
$I=I_o \cos^2{\theta_1}\cos^2{\theta_2}$
where $\theta_1$ is the angle between the axes of the first and second filters and $theta_2$ is the angle between the axes of the second and third filters.

## Polarization Using Sunglasses and a Computer Screen

Using a pair of polarizing sunglasses, you can demonstrate the effects of polarization together with a computer screen which is also polarizing. When the axes of polarization of the two polarizing screens are rotated, the brightness alternates between bright and dark.

Light coming from a computer screen is usually polarized. In the video below, when polarized light passes through another polarizer, the intensity of the light is given by Malus' law:

$I = I_o cos ^2{\theta}$

where $\theta$ is the angle between the two axes of polarization and $I_o$ is the original intensity of the unpolarized light.

Only the components of electric field vectors in electromagnetic radiation that are parallel to the axis of polarization of a polarizing filter will be permitted through. Those electric field components that are perpendicular to the polarization axis are blocked by the filter.

Hence, the amplitude of a vector A that passes through is given by $A = A_o \cos{\theta}$. Since intensity is proportional to the square of amplitude ($I \propto {A^2}$), we have Malus' law.

The purpose of having polarizing filters in sunglasses and computer screens is to cut out glare due to light from other sources.

## Boiling under Reduced Pressure

With the help of a simple manual vacuum pump that is used to keep food fresh, we can demonstrate the effect of a reduced pressure on the boiling point of water. This leads students to a discussion on what it takes to boil a liquid and a deeper understanding of the kinetic model of matter.

Materials

1. Vacuum food storage jar with hand-held vacuum pump
2. Hot water

Procedure

1. Boil some water and pour them into the jar such that it is half filled. This is necessary as hand-held vacuum pumps are not able to lower pressure enough for boiling point to drop to room temperature.
2. Cover the jar with the lid and draw out some air with the vacuum pump.

Explanation

When water boils, latent heat is needed to overcome the intermolecular forces of attraction as well as to overcome atmospheric pressure. Atmospheric air molecules would prevent a significant portion of the energetic water molecules from escaping as they will collide with one another, and cause them to return beneath the liquid surface.

Removal of part of the air molecules within the jar lowers the boiling point of water because less energy is needed for molecules to escape the liquid surface.

In a previous demonstration, we put a boiled egg into a flask with a mouth narrower than the egg. The challenge is now to remove the egg from the flask without breaking it.

Materials

2. Egg
3. Water
4. Bunsen burner or candle

Procedure

1. Pour some water into the conical flask.
2. Invert the flask quickly over a tray such that the egg seals the mouth of the flask, preventing the water from coming out.
3. Light a flame and place the part of the flask with water over the flame. This will help prevent the heat from cracking the flask.
4. Place a tray under the mouth of the flask as the egg slides out to prevent a mess.

Explanation

The flame heats up the air and the water in the flask. The heated air expands while some of the water vapourizes. With the increase in amount of gas and temperature, the pressure within the flask increases.

This classic physics demonstration is used to show the effects of pressure difference between the atmosphere and a cooling volume of air. With a set of clean apparatus, you can even have the egg for a snack after that.

Materials

1. Hard-boiled Egg
2. Flask or glass bottle with mouth smaller than the egg
3. Paper measuring about 2 cm by 5 cm
4. Lighter

Procedure

1. Peel the hard-boiled egg.
2. Light the piece of paper and drop it into the flask.
3. Place the peeled egg on the mouth of the flask such that the egg seals the flask.
4. Observe the egg being sucked in while the flame dies.

Explanation

When the burning paper enters the flask, it causes the air within the flask to heat up and expand, with some escaping from the flask. When the egg seals the flask, the flame dies as the paper is about to be burned up while oxygen is also running out.

The air then cools down and the pressure within the flask drops. The pressure due to the atmosphere acting downward on the egg is then greater than that acting upward due to the pressure of the cooling air. This pushes the egg into the bottle.

## Single Slit Diffraction using Fingers

This demonstration requires no material other than your own fingers. Hold your index and middle fingers close to each other, leaving a small slit between them about 1 mm in width.

Look through the slit into a source of light such as the window or a lamp. You will need to look with one eye up close to the slit. Warning: do not look directly at the sun.

You will be able to see a number of vertical dark lines between the fingers.

Science Explained

So where do these vertical lines come from? They are dark fringes caused by destructive interference of light when it diffracts through your finger tips.

This phenomenon can be explained using Huygens' principle. Huygens pictures every point on a primary wavefront as a source of secondary wavelets and the sum of these secondary waves determines the form of the wave at any subsequent time. Hence, each of these secondary wavelets can interference with one another.

Constructive interference takes place when the difference in path lengths between two coherent waves is an integer multiple of the wavelength. This is when the resultant wave is the brightest. Destructive interference occurs when that difference in path length is a half-integer of the wavelength (e.g. $\frac{1}{2}\lambda$$\frac{3}{2}\lambda$$\frac{5}{2}\lambda$, etc.) and gives a dark fringe.

The alternating bright and dark fringes is a diffraction pattern, which becomes observable by the eye looking through the slit.

## Ionisation of Air to Remove Static Electric Charges

Materials

1. Wool
2. PVC pipe or plastic comb
3. String
4. Lighter

Procedure

1. Hang the string from an elevated position. Leave the bottom end free.
2. Rub the PVC pipe with wool. This deposits negative charges, or electrons, onto the surface of the PVC pipe.
3. Place the side of the pipe that is rubbed near the string. You should notice the string being attracted  towards the PVC pipe.
4. Holding the PVC pipe still while attracting the string, light a flame using the lighter and place it in between the string and pipe. You should observe the string falling back to its original position.

Science Explained

When air is ionised with the help of a flame, it serves as a conducting medium through which static electric charges can escape from a surface.

## Magnetic Shielding

Materials

1. Bar magnet
2. Paper clip (stainless steel)
3. Plastic clipboard
4. Steel bookend

Procedure

1. Before the demonstration, make sure that the paper clip is not already magnetised by touching it with the steel bookend. If it gets attracted to the bookend, get a new paper clip.
2. For the demonstration, first show that the paper clip can be picked up by a bar magnet in direct contact.
3. Next, place the bar magnet on the plastic clipboard and try to pick up the paper clip with the clipboard in between them. Show the audience that the paper clip is attracted.
4. Finally, place the bar magnet on the steel bookend and attempt to pick up the paper clip with the bookend between them. The paper clip will not be picked up.

Science Explained

Iron and steel are examples of ferromagnetic materials that have their magnetic domains aligned with an external magnetic field when placed in that field. This strengthens the magnetic field but also serves to concentrate the field lines within the ferromagnetic material itself, such that very little of the magnetic field penetrates the "shield".