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What is the best way of generating strong, steady, electric fields (E) using the tools and voltages available to the home hobbyist? Is it better to using electrostatic sources like a Van de Graaff generator, or can high strength fields be obtained using electrical circuits in some way?

In addition, is there a way of generating such strong field while still making them "accessible"? That is, having a strong field which instruments and equipment can be brought close to to take advantage of the field strength?

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Remember that the strength of a electric field is voltage over distance. That means decreasing the distance makes the field stronger as much as increasing the voltage. Also keep in mind that what you seem to be talking about is lethal voltages. These can seriously hurt or worse with just a few pF between them and ground.

In college one of my frieds had a neon sign transformer. That put out around 6 kV if I remember right, and was useful for all sorts of messing about with high voltage. We made a Jacob's ladder with it, and used it to make the anode voltage of a old TV tube we repurposed into sortof a oscilloscope.

Starting with a transformer is probably the best way. You get to high voltages quickly, and it's inherently isolated. The isolated part makes it a little more difficult to kill yourself. The output is also AC, so you can use a diode/capacitor ladder to step up the voltage easily.

To make a volume with your strong E field, put the high voltage on two opposite plates of some conductor, space them apart, and your high E field will be in the middle. Beware that there will be a force pulling the plates together proportional to the E field strength.

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Another way is to make or buy a Tesla coil. But FIRST, study up on Tesla coils and all the dangers of very high voltage they make. Once you are fully aware of the safety precautions to take, you can utilize the Tesla coil to generate a strong electric field. Now, the spark that the Tesla coil generates will be utilizing AC current, and you can feed the two plates to generate a strong electric field between them. But remember, the spark will be based on AC current, which you will most likely be tapping from your house current, and this means that the plate circuit will be "closed" or circular. To make the spark a "one way", open spark, simply attach a high voltage rectifier diode to the input to the plates. This way, the plates will have a steady, powerful electric field between them, and you can even generate the field with only one plate, since the field is technically an "open", d.c. current-based. But PLEASE PLEASE get fully educated on the dangers and safety precautions of Tesla coils.

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