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Do magnetic fields have any effect on dielectric breakdown

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Would a magnetic field have any effect on the dielectric breakdown of insulators? For example, the dielectric breakdown of air is 3 Mega volts per meter at a gap of one meter; if you applied a magnetic field to that breakdown, would it help guide the electrons along the path and therefore reduce the amount of power needed to cause the dielectric breakdown or would it have no effect? Or just require too much power to generate a magnetic field strong enough to make a difference?

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