What is a typical ("maximum") non-relativistic speed ?
You mean, before the effects of relativity become significant? I guess it depends how much error you're willing to accept in the Newtonian calculation. If you give a specific example of a case where relativity's prediction about something would be different from the Newtonian prediction, someone can give you the amount the two predictions would be different as a function of speed.
With no additional information about the error tolerance or the exact application, I would would use .14c as a general cutoff. That gives you a 1% time dilation.
Electrons in a metal wire travel at a few mm/s...
Edit: ...and you know that magnetic field that current generate is due to a relativistic effect of electric field.
Well, I'm limited to 55 mph where I live, but I confess that I sometimes exceed that limit ...
So, be careful not to be electrically charged, or you have to say you are going at relativistic speeds
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