Here's a man, you will probably not recognize. This man is Sir Joseph Larmor. In 1919, he was the first to propose the mechanism which is now widely accepted for generating the Earth's magnetic field. He proposed that it was possible for electrical currents to account for the magnetic field necessary to regenerate electrical currents. In other words, a mechanism of instability in which the current stem cell would provide the field that would provide the currents and so on. Let me show you a very simple model for a dynamo. This one is not a model for the Earth, it's rather a model for the dynamo you could have on a bicycle. It's something that converts kinetic energy into electrical energy. In this model, we have a disk, say of copper, something conducting, which we will rotate and within a magnetic field, so with a permanent magnet. If we do that, we can compute the electromotive force by integrating from the axis to the rim of the disk, and we have an electromotive force that will drive currents and turn the light bulb on, if you rotate fast enough. Now, this model is not a self-excited dynamo because it relies on a permanent magnet. Let us now turn to self exciting dynamo action, that's the homopolar disk dynamo. It was introduced in 1955 by Sir Edward Bullard. In this model, we just suppress the magnet and replace it with a coil, just a wire that spirals and therefore produces a magnetic field like this whenever a current goes through it. If we assume that there is a current to start with in this model, then there is a magnetic field, and so the coil will act just to replace the magnet that we used in the first experiment. We can write down equation to convince ourselves of that. It's not very difficult, but we have to go through that step by step. First, we need to write down the electromotive force E. It will depend on the flux of magnetic field through the disk, of the rotation of the disk, that's the E. And the flux depends on the mutual inductance between the disk and the coil, which depends on the number of spires of the coil, also the relative position of the coil to the disk, so that will define the magnetic flux through the disk. Then we know the electromotive force and we can write down the equation governing the evolution of currents relying on L and R. Where L is the self-inductance of the circuit and R is the resistance of the complete circuit. That's this equation which I've written here. We can easily see here that the system will go unstable only if the right-hand terms become large enough. The first term describes the evolution of the electrical currents in the circuit. The second term is the resistance. You can see if you move this term to the right, it's a negative term always. So all it can do is dissipate electrical currents whereas the term on the right of our equation is a positive term. It can actually yield growth of the magnetic field and the electrical currents. So the currents in the circuit will grow and together of course, the magnetic field in the coil, they will both grow together provided Omega is large enough. Well, that's a very funny system because one is a bit worried of the problem of the chicken and the egg. Was there a current first that drives the magnetic field or was there a magnetic field first? And the motion of the conductor in this magnetic field will drive the currents? It's a puzzling question. And just like the question of the chicken and the egg, it has no answer. What we have described here is just an instability. The system becomes unstable, the currents will grow exponentially if the rotation is large enough. Think of it, there's an easy instability. You experiment very often it's the Larsen effect. Ever been to a rock concert where the sound was too loud and a very acute sound would grow and be almost unbearable. Larsen effect. Nobody ever in the concert has played this note, played this tune. It's just that the configuration of the amplifier, microphone, and loudspeaker is such that this note is unstable. It just grows out of nowhere, out of a tiny, tiny perturbation. If there was no noise to start with, there would be no Larsen effect, but there's always a bit of noise. In the same way in the experiment we've shown. If there was no current, no magnetic field, there would be nothing, but there's always a bit of noise, so if it's unstable, it will just grow. To illustrate how the electrical currents built on the kinetic energy, how they drive their energy from the kinetic energy, we can use the same pendulum as were using before. We know it's a good pendulum and it will work for a long time because it has a kinetic energy which is converted to potential energy back to kinetic, potential and so on. It just oscillates. It's constant. If we now place a magnet, it stops abruptly and you've heard no noise. Whereas it would have provided a noise if it was just mechanical. What happens is that the motion of this aluminum within the magnetic field drives electrical currents. These currents are then dissipated by resistance to heat. But of course to drive currents, you need to take the energy from somewhere and you take it from the motion of the pendulum. That's why it stops almost instantly. It's important to notice that aluminum is non-magnetic. Otherwise it would jump on the magnet. I'll show you a second experiment that demonstrates the same effect. If we use plastic, PVC like this, and a strong magnet, it just slides on the plastic. If we now do the same with copper, copper is non-magnetic, so there's no actual magnetic strength here. However, the motion of the magnet on the cooper will drive currents, and these currents dissipate energy. And so the magnet dissipated kinetic energy as it slides. And so it's much harder for the magnet to slide down than it was with plastic, it goes really slowly. So that shows that the electrical energy is built at the expense of the kinetic energy. If we now turn back to the Earth's core, what happens is that the Earth generates a magnetic field driven by electrical currents within the Earth. This energy is taken away from the kinetic energy of convection of the Earth's core. As the Earth is cooling down, the liquid iron is in motion, and this kinetic energy is then transformed to electrical currents, which we can measure the trace of at the surface with a compass needle.
