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February 2015 Archives

I've spent most of today thinking Google's image-of-the-day is a wicket, but have just realized it is in honour of Alessandro Volta.



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In January I had a go at the 2014 Scholarship Physics Exam, as I've done for the last couple of years. Sam Hight from the PhysicsLounge came along to help (or was it laugh?) The idea of this collaboration is that I get filmed attempting to do the Scholarship paper for the first time. This means, unlike some of the beautifully explained answers you can find on YouTube, you get my thoughts as I think about the question and how to answer it. Our hope is that this captures some of the underlying thinking behind the answers - e.g. how do you know you're supposed to start this way rather than that way? What are the key bits of information that I recognize are going to be important - and why do I recognize them as such? So the videos (to be put up on PhysicsLounge) will demonstrate how I go about solving a physics problem (or, in some cases, making a mess of a physics problem), rather than providing model answers, which you can find elsewhere. We hope this is helpful. 

One of the questions for 2014 concerned friction. This is a slippery little concept. Make that a sticky little concept. We all have a good idea of what it is and does, but how do you characterize it? It's not completely straightforward, but a very common model is captured by the equation f=mu N, where f is the frictional force on an object (e.g. my coffee mug on my desk), N is the normal force on the object due to whatever its resting on, and mu (a greek letter), is a proportionality constant called the coefficient of friction. 

What we see here is that if the normal force increases, so does the frictional force, in proportion to the normal force. In the case of my coffee mug on a flat desk*, that means that if I increase the weight of the mug by putting coffee in it, the normal force of the desk holding it up against gravity will also increase, and so will the frictional force, in proportion.

Or, at least, that's true if the cup is moving. Here we can be more specific and say that the constant mu is called 'the coefficient of kinetic friction': kinetic implying movement.  But what happens when the cup is stationary? Here it gets a bit harder. The equation f=mu N gets modified a bit: f < mu N. In other words, the maximum frictional force on a static object is mu N. Now mu is the 'coefficient of static friction'. Another way of looking at that is that if the frictional force required to keep an object stationary is bigger than mu N, then the object will not remain stationary. So in a static problem (nothing moving) this equation actually doesn't help you at all. If I tip my desk up so that it slopes, but not enough for my coffee mug to slide downwards, the magnitude force of friction acting on the mug due to the desk is determined by the component of gravity down the slope. The greater the slope, the greater the frictional force. If I keep tipping up the desk, eventually, the frictional force needed to hold the cup there exceeds mu N, and off slides the cup. 

What this means is that we when faced with friction questions, we do have to think about whether we have a static or kinetic case. Watch the videos (Q4) you'll see how I forget this fact (I blame it on a poorly written question - that's my excuse anyway!). 


*N.B. I have just picked up a new pair of glasses, and consequently previously flat surfaces such as my desk have now become curved, and gravity fails to act downwards. I expect this local anomoly to sort itself out over the weekend. 

P.S. 17 February 2015. Sam now has the videos uploaded on physicslounge  

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Not so long ago, a tennis ball appeared in our garden. It's a rather distinctive red one. It doesn't belong to us. It was lying close by to the (low) fence between us and our neighbour, so I just chucked it back. 

Next morning, it was there again. I threw it back.

And, more or less immediately, it was back with us. Evidently, it didn't belong to next door. They were working on the assumption it belonged to us. The next-likely suspect was the house at the back of us, which has some rather energetic children. Over went the ball into their garden. 

Next day it was back with us. Not their ball, either. Suddenly, this ball has become highly mobile. It flits from garden to garden, and doesn't appear to be finding a home anywhere? Where did it come from?

I can't help thinking that this is a good analogy with conduction of electrons in n-type semiconductors. Although silicon underlies so much of modern electronics, it comes as a real surprise to many students to learn that silicon is really quite a lousy electrical conductor. That's unsurprising when you look at its structure - the silicon atoms are locked in a lattice, with each atom bonded by strong covalent bonds to four other atoms. There are no free electrons - all the outermost electrons that would contribute to conduction are tightly bound in chemical bonds. Without free, or losely bound, electrons, there's not going to be much electrical conduction. 

So how come silicon devices are at the heart of modern electronics? The key here (in the case of n-type silicon) is that extra electrons have been put into the lattice. This is done by adding impurity atoms with five, not four, electrons in their outer shell (e.g. phosphorus). These electrons aren't involved with bonding, and become extremely mobile, because none of the silicon atoms finds it favourable to take them on. They flit from atom to atom, finding a natural home nowhere, as does our tennis ball. Unlike a tennis ball, however, electrons are charged particles. Apply an electric field, and they have a purpose, and we suddenly have movement of electrical charge (which is simply what an electrical current is).

There's a second way to make silicon conduct, and that's the reverse. Rather than adding in electrons, we take them away. How does that work? Introduce now an atom into the lattice that only has three outer-shell electrons (e.g. boron). It is likely to grab one from a neighbour, to allow itself to make four covalent bonds. But now its neighbour is devoid of an electron. It will grab one from one of its neighbours. And so on. Now the 'lack of an electron', or 'hole', as its known in semiconductor physics, is what is mobile. Since electrons are positively charged, the lack of an electron (i.e., a hole) is positively charged. Apply an electric field and the hole moves - and we have electrical current again. This is 'p-type' silicon ('p' for positive, since conduction is through positively charged holes; contrast 'n' for negative, where conduction is through movement of negatively charged electrons). 

In our tennis ball analogy, the p-type lattice corresponds to a less desirable neighbourhood - someone on discovering that one of their tennis balls is missing makes up a complete set by sneaking round into the next-door garden to steal one, thus transferring the problem elsewhere. 

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