The Field Around a Current-Carrying Wire

Moving charge makes a magnetic field, and a current is just charge on the move. Around a long straight wire, that field doesn't shoot outward like an electric field does from a charge. Instead it wraps around the wire in complete circles, like rings stacked around a pole. Point your right thumb in the direction of the current and your fingers curl the way the field circles - that's the right-hand rule, and it tells you the field's direction at any point around the wire.

The strength of that field follows B = mu0·I/(2·π·r), where mu0 is the permeability of free space (4·π x 10⁻⁷ T·m/A), I is the current, and r is the distance from the wire. Because r sits in the denominator, the field thins out fast as you move away - double the distance, and the field is half as strong. Close to the wire the circles are tight and the field is intense; farther out, the same total field spreads over a bigger circle, so each point feels less of it. This is why a compass needle near a wire swings the instant current flows: it's reacting to a real magnetic field circling the wire, not some electric effect.

This field is the building block for everything else in the unit. Two wires carrying current create fields that push or pull on each other - that's the force between parallel conductors. Wrap the wire into a loop or a coil and those circular fields stack up inside to make a much stronger, more useful field, which is how solenoids and electromagnets work. Reverse the current direction and the whole field pattern flips, circling the opposite way, which is exactly how you'd use the right-hand rule to predict the new field.