Magnetic Field LinesMagnetic field is always very intriguing, probably because it acts at a distance.
We can visualise the magnetic field lines using iron filling or iron bids. These lines, either visualised in a plan or in 3D space, indicate the local direction of the magnetic field. This is also the direction indicated by the compass needle. |
 
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Magnetic Field Strength The magnetic field does not only have a direction, it also has a strength. This strength can be measured by counting the beats of a compass needle placed in the magnetic field. The beats are clearly faster (stronger magnetic field) when the magnet is closer to the needle. The compass measures here the strength of the magnetic field in a very similar way as a pendulum with moderate amplitude can be used to measure the strength of the gravity field (which is pretty much constant at the Earth surface, providing the underlying idea of pendulum clocks).
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Curie TemperatureAs we know that in the absence of nearby magnets, the compass needle approximately indicates the geographic north, it is tempting to speculate that the Earth is a big magnet. Indeed, we know that the Earth core, 3000 km below our feet, is mainly composed of liquid iron.
However it is not possible to assume that the Earth is just a big magnet: the temerature rises rapidly deep in the Earth. At the depth of the Earth core, the temperature reaches a few thousand of degrees. Heating a magnet destroys it magnetic properties (thermal agitation prevents the ordering necessary for matter to be magnetic). This phenomenon, which occures at much more moderate temperatures, is here demonstrated by heating a magnet with a welding torch. The magnet falls when it looses its magnetic properties. |
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Oersted's Experiment
Magnetism can however be generated, in the absence of any permanent magnet, by electrical currents. This was pointed out by Hans Christian Oersted in 1820. A current in a wire affects the compass needle just as a magnet. In fact by winding the wire in a coil, we produce a field very similar to that of a bar magnet.
This experiment establishes a direct connection between electricity and magnetism. |
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The Bicycle Dynamo The difficulty of dynamo theory is then to understand the origin of the electrical currents. When we think of "dynamos", we usually think of the bicycle dynamo.
This experiment illustrates the principle of the bicycle dynamo. A magnet rotating in front of a coil induces an alternative electrical current in the circuit (usually used to power the bike's light). Mechanical energy is thus converted to electrical energy (motion & magnetic field yield electrical currents). This is the basic principle of dynamo action. The electrical currents (and thus the magnetic field) produced by such dynamos however rapidly oscillates in time. |
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The Faraday Disc DynamoA modified version, introduced by Michael Faraday, allows to produce a continuous electrical current (and thus a non-oscillating magnetic field). A conducting (but non-magnetic) copper disc is rotated in a strong horse-shoe magnet.
Electrical contacts allowing motion of the disc are established both on the axis and at the rim of the disc. As the disc rotates, a difference of potential (or an electrical current) is measured in the wire.
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Principle of the Bullard DynamoThe Faraday disc dynamo, presented above, generates a continuous current, and thus a steady magnetic field, but it suffers from a strong limitation if we want to think of it as a model for electrical current generation in the Earth core: it relies on the use of a permanent magnet. We have seen before that permanent magnetism does not survive at high temperatures. Sir Bullard introduced in 1955 a modification of the above setup which qualifies as a "self-excited dynamo" (i.e. a dynamo which does not rely on the use of a permanent magnet).
As we know that electrical currents in a coil produce a dipolar magnetic field (see "Oersted's Experiment" above), the basic idea is to suppress the magnet and replace it by a coil. If the disc is rotated rapidly enough, so that the generation mechanism examplified in "The Faraday Disc Dynamo" is strong enough to counteract ohmic resistivity, then any seed of electrical current will be amplified and grow. The system will then act as a self-excited dynamo. Note however that the movie here is purely illustrative of the principle of this dynamo as dynamo action would in fact require a much faster rotation of the disc than can be achieved with this setup. |
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The Lorentz forceWe have now established the basic principle of self-excited dynamo action. One problem however immediatly springs to mind: if we rotate the disc rapidly enough, an electrical current will grow. We therefore produce electrical energy. Where does this energy come from? Do we get it for free?
Of course, not! In fact this energy builds at the expense of mechanical energy. Which means that as the electrical currents grow, there should be a braking force acting on the disc to slow it down. In fact such a force, present when there are electrical currents and magnetic fields, exists and is known as the Lorentz force (Laplace force in french!). It is examplified by sliding two powerful magnets on an inclined slide. One slide is conducting, but non-magnetic (copper), the other one is insulationg (PVC). The motion of the magnet drives current in the copper plate, which interact with the magnetic field to provide a magnetic braking through the Lorentz force. The fall of the magnet on the copper plate is clearly slower! Similarly an aluminium pendulum (non-magnetic) is very efficiently slowed down when passing through the magnetic field of a horse-shoe magnet. It is thus clear that electrical energy is created at the expense of mechanical energy. |
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Barlow's wheel
If all this is correct, we should be able to drive the rotation of the disc used in the Farady disc dynamo by imposing both the magnetic field and the electrical current. Indeed,
Peter Barlow proposed this experiment, known as Barlow's wheel, to demonstrate the force acting on matter in the presence of an imposed electrical current and an applied magnetic field.
A potential difference is maintained between the center and the rim of the disc, resulting in a predominantly radial electrical current in the disc. An horizontal magnetic field is localy applied using a horse-shoe magnet. The resulting lorentz force is orthogonal to both the current and the field, it is thus vertical in the region of interest and yields a rotation of the disc. |
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Lorentz Force in a FluidWe can examplify the same force in a fluid. We use here salted water. We apply an horizontal electrical current using two electrodes. A magnet is used to locally apply a vertical magnetic field. The resulting force is orthogonal to both the field and the current. Its effect on the fluid flow is visualised using black ink. The flow driven by the Lorentz force is quite clearly visible. When we flip the magnet upside-down (thus reversing the direction of the applied magnetic field) the direction of the flow is reversed.
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Thermal convectionIf electrical energy builds up at the expense of mechanical energy, we need to think of something that will maintain motions within the Earth core. In all the dynamo experiments presented above, we provide energy by "rotating the handle" of the disc. Which effect could play a similar role in the Earth core? If nothing drives the motions of the liquid iron, surely the motions will stop as the magnetic field grows...
The most obvious (but not the only) mechanism for maintaining motions within the Earth core is thermal convection. As the Earth cools down a strong temperature difference is maintained across its core. Such a temperature jump can drive motions similar to that of water in a boiling pan. These are illustrated here using sugar syrup and an ombroscopy technic (the optical index of the fluid varies with temperature). |
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The Lowes and Wilkinson dynamoThe Bullard dynamo (see "Principle of the Bullard Dynamo" above) examplifies the basic principle of self-excited dynamo acion. It relies however on a good arrangement of electrical wires. Nothing like that is expected within the Earth core!
Lowes and Wilkinson constructed in 1963 at the University of Newcastle an experiment to demonstrate self-excited dynamo action in a conducting volume (without wires). This is here a replica of their experiment built in Paris by Nicolas Mordant and Christophe Gissinger in Paris. In this setup, two cylinders, in soft iron, are placed at an angle and are rotated. They are both placed in a conducting bloc, also of soft iron. To ensure that the electrical currents can flow across the entire volume, a metal liquid at ambient temperature is placed between the rotating cylinders and the blocs: Galinstan (a mixture of Gallium and Indium). In such a configuration the magnetic field is advected by motion and additional field is created in the sheared region. The setup is designed so that the field created by the shear at the boundary of one cylinder acts as a seed field to the other cylinder. |
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Emmanuel Dormy