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:
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.
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…
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.
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.
Challenge: How can you make a quartz rod invisible with some water, sugar and a beaker?
Answer: Snell’s Law
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:
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 ().
With water, as you add more and more sugar the refractive index increases, until finally it approaches that of quartz ~1.46.
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.
If you’ve ever had a chance to play with ferrofluid then you’ll be familiar with the typical picture of a ‘flower-like’ pattern.
A ferrofluid is a suspension of tiny magnetic (iron) particles, covered in a substance called a surfactant (e.g. oleic or citric acid) that is mixed with oil.
The combination of these 3 substances leads to an animated response to magnetic fields:
1) The iron particles are attracted to the magnet.
2) The surfactant binds the iron particles and oil limiting how far the iron particles are pulled towards the magnet thus leaving it slightly mobile.
3) A combination of the magnetic field and surface tension of the ferrofluid mixture results in patterns that follow the direction of magnetic field lines.
1) Yes, you can make a simple ferrofluid suspension with laserjet toner and oil, but it will never result in the patterns seen above unless a surfactant has been added. (This typically involves more detailed steps that I will not outline here but might be a great question/project for a chemistry teacher…)
There are several videos online (YouTube is a big culprit here) that suggest otherwise but I can only assume that they switch to storebought ferrofluid when they start the demonstrations. If anyone disagrees with this send me your recipe! I’d be happy to be proven wrong.
2) One of the YouTube videos above also suggests that you can mix the ferrofluid with water to create a more fluid mix. Again, this is pure myth. For a short term solution you could mix it with a water:propanol solution but this will slowly breakdown the ferrofluid itself and likely would not last more than a few weeks. If you want something more long term then you may need to buy it from a specialised company.
*Non-technical description of a surfactant: A chemical with ‘arms’ that can grab onto other substances.