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The key to understanding EMP is that this is an induced effect, so you need rapid changes in magnetic field, $\frac{dB}{dt}$. In order to generate a rapidly changing field, you have to have a rapidly changing current in an inductor - as you may recall, $$V = -L \frac{dI}{dt}$$ For this rapid change in current you not only need a high voltage - you need a low ...

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