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Conventional means of measuring high voltages and currents rely on the measurement consuming a (hopefully) small amount of the power from the system. For instance, a resistive divider does draw some small amount of current. In power engineering, this small power is called the "burden".
Instead of directly measuring the quantity of interest, you can measure the changes in properties of some material as a result of the surrounding electrical or magnetic field. The power required for making the measurement is provided by the measuring equipment itself. One family of these techniques relies on the changes in optical properties of certain materials in electrical and magnetic fields: the Kerr effect, the Pockels effect, and the Faraday effect.
All of these techniques rely on various mechanisms by which a material rotates the polarization of light passing through. The amount of rotation depends on the electric or magnetic field. The performace is determined largely by how well you can measure the change in polarization of the light. High quality polarizing film has a transmission ratio of 1000:1 between aligned and crossed.
If one wanted to measure the E field around an operating Tesla coil, as well as the waveforms, the electro-optic sensorl could be mounted on a long insulated rod with fiber optic cables to send the light to and from the measuring cell. An alternate scheme could be to use a laser and appropriate prisms or mirrors to send the light out to the cell along the support and to return it to a detector. In the latter case, the sensor itself could be mounted to the high voltage terminal, with the laser and detector mounted at some distance away.
Often used to create extremely high speed shutters, the Kerr effect is an anisotropic change in the index of refraction of a substance in response to an electric field. A practical implementation has the Kerr substance (often nitrobenzene, which has a very high Kerr Constant) between two crossed polarizers. The polarization of the light is rotated in proportion to the square of the E field, allowing some light to pass through the polarizers. As a shutter, the response time of the Kerr Cell is limited mainly by how fast the E field can be changed.
The problems with a Kerr Cell are: nitrobenzene is a volatile solvent which is remarkably toxic; the effect is proportional to the square of the E-field, which is no problem for a shutter application, but not as appropriate for a measurement application.
The Pockels effect is similar to that of the Kerr effect, except that the change in index is linearly proportional to the electric field. Substances such as KDP (Potassium Dihydrogen Phosphate), KD*P (Deuterated KDP) and LiNbO3 (Lithium Niobate) show large Pockels effects and are very popular as electro-optic modulators for laser work.
One problem with Pockels sensors is the cost of the crystals, particularly in large sizes. A small 1 cm diameter crystal suitable for turning on and off a laser beam isn't particularly expensive (several hundreds of dollars), but a larger one for use as a photographic shutter would be prohibitively expensive. For a HV measuring application, the cell could be on the scale of millimeters, particularly if fiberoptic cables are used.
Faraday rotation is a magnetic effect. Notable in high density lead glass, the rotation is proportional to the magnetic field. A chunk of lead glass 1" thick and 2" in diameter would need a field of .5 Tesla (5000 Gauss) to rotate the polarization 90 degrees. (This is about 10,000 ampere turns for that physical size). The rotation is proportional to the length of the optical path and to the magnetic field, so a longer piece of glass makes a more sensitive detector.
Faraday rotation does provide a handy way to measure the current in EHV or UHV power lines. A piece of lead glass (which can be quite long) is placed near the power cable and a polarized laser is used to measure the rotation. In a Tesla coil application, lead glass sensors connected by fiber optic cables could be used to measure the current at various parts of the coil. For that matter, a glass fiber of the appropriate material could be used as the sensor itself.
There have been some Scientific American "Amateur Scientist" columns dealing with Kerr Cells and Faraday modulators.
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