Ah, that rule always confused me in school, but my sons explained it to me again when they were studying! For a straight wire, the magnetic field forms circles around it, like the rings around a tree trunk. To find the direction, you use your right hand: hold the wire with your thumb pointing in the current's direction, and your curled fingers will show the field's direction.
I remember this only because my abbayi drew it on my kitchen notepad, saying "Amma, even your coil of suture thread on the table shows a similar circular pattern!" It made me smile — who knew my nursing supplies could teach physics?
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