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### Kelvin and Atmospheric Electricity

June 19, 2013

William Thomson (1824-1907), also known as Lord Kelvin, was a British physicist. Kelvin is best known for determining that -273.15 Celsius is the value of absolute zero on the temperature scale. For this work, we've named the temperature unit, the kelvin, in his honor.

Like most physicists, Kelvin's interests went beyond a single topic area. Kelvin's analysis of the fundamental problem of the age of the Earth was interesting as being correct, given all the facts known at the time, but incorrect in the end. Kelvin calculated the likely lifetime of the Sun, based just on its generating heat by gravitational collapse, only, and he got a number too small to allow Darwinian evolution.

(Wikimedia Commons image.

Kelvin also calculated the time it would have taken for the Earth's crust to have cooled from the temperature of its core, and he got 20-40 million years. He had much greater success when he moved into applied studies, especially on the topic of the first transatlantic telegraph cable.

Experiments by foremost electrician, Michael Faraday, showed that the data rate of such cables diminished with length. The cause of this was the distributed capacitance of the cable, where the cable conductor and the sea water act as plates of a capacitor for which the cable cladding was the dielectric. Kelvin rightly saw that a reduction in cable resistance by using a larger diameter conductor, and a reduction in the capacitance by using thicker insulation, would improve the data rate,

The modern solution to this problem, before the invention of electronic amplifiers, is the dispersal of loading coils along the length of the cable. These are inductors that balance the cable capacitance. In the cable's original state, the only solution was a very sensitive detector, the mirror galvanometer. Even with that, the data rate was excruciatingly slow.

A recent arXiv paper by Karen Aplin of the Physics Department, Oxford University, and Giles Harrison of the Department of Meteorology, University of Reading, recalls another of Kelvin's scientific interests; namely, atmospheric electricity.[1] The electrical potential increases with altitude above Earth's surface by a surprisingly high value, 100 volts per meter (30 volts per foot), increasing with the approach of thunderstorms.

So, why aren't we all walking around in a frenzied and perpetual bad hair day? The voltages may be high, but the currents, which are carried by a few ionized molecules in the air, are very small. We can only see such potential differences if we have a really high impedance voltmeter, or an electrometer.[2]

One of the most common such field measuring devices is the field mill, which combines an electrostatic shutter and an alternating current amplifier, as shown in the figure. Since alternating currents are easier to amplify than direct currents, a motor periodically shields the sensing electrode from the Earth's field. Not surprisingly, a MEMS field mill was demonstrated more than a decade ago.[3]

Schematic diagram of a simple field mill.

If the motor shaft is not grounded, as would be the case when it spins on a nylon bearing, a conducting brush is needed to ground the shaft.

(Illustration by the author, using Inkscape.)

Kelvin, who became interested in atmospheric electricity in 1859, did not have the advantage of modern electronics for his studies. The first practical amplifier, Lee de Forest's Audion, wasn't invented until 1906. As one who commonly jumped from one physics area to another, Kelvin discontinued his atmospheric electrical studies just two years later, in 1861.[1]

Although the existence of an atmospheric potential, even in fair weather, was know for many decades before Kelvin's time, he was the first to offer quantitative data.[1] Kelvin invented a novel water spray electrometer for measuring the atmospheric potential gradient; and, for his time, the extremely novel use of photography as a means for data logging.

Rather than measuring the potential of the air, directly, Kelvin's water spray electrometer measured the potential of an insulated tank spraying water into the air. The potential of the tank equilibrates to that of the air at the altitude where the water spray become droplets that are no longer electrically connected to the tank. The water tank equilibrates to this potential because of charge transfer by the water drops.[1]

The equilibration occurs since any potential difference between the tank and the air will transfer charge to, or from, the water tank, which acts as a capacitor. You can calculate all this from the list of capacitor equations in a previous article (Carbon Nano-Onion Supercaps, August 26, 2010).

Kelvin's water spray electrometer, as illustrated in his notebook schematic, below, included photographic recording of the data from the mirror electrometer, and a battery reference. In the figure, B = battery, C = driving clock for the data recorder, D = a cylinder coated with a photosensitive medium, M = electrometer mirror (illuminated by a gas light), and I = Insulators.

Kelvin's water spray electrograph.

A portion of Fig. 2 of Ref. 1, modified for contrast, via (arXiv.)[1)]

As a true scientist, Kelvin realized that his photographic data wiggles needed a reference, so he used zinc-copper cells, which generate 1.08 volts. In one measurement, Kelvin related the atmospheric potential to the equivalent of a series connection of 115 of these cells, or 124.2 volts. For his vertical distance from the ground of three feet, this gives a voltage gradient of 137 volts/meter.[1] Kelvin thought that such potential measurements would help in weather forecasting.[1] Indeed, field mills are now used to give warning of impending thunderstorms.

In some of his measurements, Kelvin may have detected changes in the atmospheric potential gradient from the Carrington Event, a solar storm that continued from August 28, 1859, until September 2, 1859.[1] This caused the largest recorded geomagnetic storm ever recorded, with auroral lights of extreme intensity. The electrical disturbance from this geomagnetic storm caused problems for the primitive telegraph circuits of the time, and a similar event would likely disrupt modern civilization for many months.

### References:

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