# Useful Resources

I will be adding resources here as I find them – mostly Maths and Physics themed.

## Online Mathematics Course

Loughborough’s Mathematics Education Centre runs a free, three-week MOOC – Getting a Grip on Mathematical Symbolism – designed for those students aspiring to become scientists or engineers but who lack mathematical confidence.

It will run again on the FutureLearn platform starting May 8th. Registration is open now:

https://www.futurelearn.com/courses/mathematical-symbolism

The course is designed for students who have some engineering or science knowledge gained through vocational qualifications or through workplace experience but who perhaps have not studied mathematics formally since leaving school. It will be appropriate for those who lack confidence but who need to establish a bedrock of knowledge in order to further their education.
This is a foundation, entry-level course and is not intended for those who already possess recent post-GCSE mathematics qualifications. It is highly recommended for those students going to university who have not studied maths beyond GCSE. Please share when appropriate.

Note that it is planned to run this course again shortly before the start of the new academic year in September.

Magnet Academy is an online resource provided by the National High Magnetic Field Laboratory — the largest, most high-powered magnet lab in the world. It has a wide selection of useful tutorials about electromagnetism for ages 5 upwards.

Interactive Magnetic Tutorials

# British Science Week

As part of British Science Week, Loughborough University hosts a ‘Community Day’ event where Loughborough locals are invited on campus to take part in various ‘science based’ activities.

This year it falls on 25th March I will be:

• Coordinating an Electrodough workshop – for which we’re looking for student ambassadors.
• Running a ‘Cold Science’ demonstration with liquid nitrogen.
• Working with the East Midlands Institute of Physics to deliver several ‘busking’ activities –  for which I’m looking for student ambassadors.

If you’re interested in getting involved please let me know.

# Liquid nitrogen

Roughly the same cost (weight for weight) as a pint of milk, it’s a common feature in science fiction films: the nitrogen dewar in the background that might at some point be used to freeze that alien chasing you down the corridor…

But how much liquid nitrogen would it actually take to do this?

Hint: Assume the creature weighs about 50kg and has a heat capacity of 2000 J/K/kg. Liquid nitrogen has a temperature of 77K and latent heat of 199 kJ/kg. For arguments sake, let’s say the creature becomes vulnerable at 250K…

Now let’s add another complication: the Leidenfrost effect. As a coolant, the low boiling point of liquid nitrogen (77K) typically means that it will boil off so fast on contact with another object much hotter than it, that a ‘protective’ layer of air is formed. This will insulate said object from the cooling effects of the liquid nitrogen, for example preventing cold burns for anyone crazy enough to stick their hand in a bucket of liquid nitrogen for a second or two. CAUTION: This effect will not stop you from getting burnt as more nitrogen is added.

For more see Wikipedia entry for liquid nitrogen

# Fleming’s Left Hand Rule

Any charged particle moving through a magnetic field will experience a force that will cause it to move in a particular direction. An easy way to remember the direction of this force is Fleming’s Left Hand Rule (where the direction of current is the direction in which positive charges move).

Illustration of Fleming’s Left Hand Rule

So for the example above, a positive particle moving into a uniform magnetic field experiences a force that pushes it up away from the magnetic field. This “motion” of the charged particle is due to the magnetic field that the moving charge makes, interacting with the magnetic field it is moving through (just like two magnets can repel each other).

We can use this rule to figure out the direction in which the rotating arm of a motor will move.

Factoid:

This effect is used to define the standard international (S.I.) unit of magnetic field – the Tesla.

1 Tesla = the value of magnetic field (B) that causes a force of 1 Newton to act on a 1 meter length of conductor (i.e. copper) carrying a current of 1 Ampere at right angles to the magnetic field.

# The invisible rod

Challenge: How can you make a quartz rod invisible with some water, sugar and a beaker?

If we take something that is typically transparent (i.e. the quartz rod) you can normally see it quite clearly when placed in a liquid, by the way in which light is bent as it passes through.

This ‘bending’ of light – refraction – can be described by Snell’s law:

$n_{1}sin(\theta_{1})=n_{2}sin(\theta_{2})$

where ‘n’ is the refractive index of the material.

So you might imagine that if we can change the rod, or the liquid itself, so that light entering from behind the beaker does not refract further on entering the quartz rod, we can effectively make the quartz rod invisible. To do this we want to match up the refractive indices ($n_{1}, n_2$).

With water, as you add more and more sugar the refractive index increases, until finally it approaches that of quartz ~1.46.

# Homopolar motors

A simple motor that doesn’t need commutators or brushes, only:
– An AA battery
– Some disc-shaped strong magnets
– Some wire and wire cutters and/or pliers

The aim is to bend the wire in a roughly heart shaped design so that the top just touches the + end of the battery and the bottom curls around the base (i.e. magnet). It needs to be close enough so that a current will flow but not so close that friction stops it from moving.

When a current flows through the wire a force is exerted on it due to the magnetic field of the magnet at the bottom of the battery. (The direction of this can be determined using Fleming’s left hand rule.) This produces a torque on the wire that results in it rotating about the battery: in the example above the wire would rotate clockwise.

# The “Energy Crisis”

We are constantly being told that oil and gas reserves are running out, or that our dependence on fossil fuels is driving climate change but what are the alternatives?

– Nuclear fission
– Nuclear fusion
– Solar panels
– Tidal power
– Wind turbines
– Thermal storage and conversion
– Hydrogen storage
– Biofuels
– Shale gas