Current Loops and Solenoids

A single loop of current makes a magnetic field that loops around the wire and threads through the loop's center, like a weak donut of field. Bend the wire into many loops stacked side by side, a solenoid, and something better happens: inside the coil, the field from each loop points the same direction and adds up. Outside the coil, the fields from neighboring loops mostly cancel. The result is a strong, almost uniform field running straight down the solenoid's axis, dropping to nearly zero outside.

The crowding effect depends only on how densely the loops are packed, not on the total length or total turns separately. That ratio, turns per length, is written n = N/L. The field inside a long solenoid is B = mu0·n·I = mu0·(N/L)·I, where mu0 = 4·π x 10⁻⁷ T·m/A. Double both N and L together and n does not change, so B does not change either; stretch the same coil without adding turns and the field weakens because the loops are now spread thinner.

Outside the solenoid, the field looks just like a bar magnet's: it loops from one end, curves around the outside, and returns to the other end. One end acts like a north pole, the other like a south pole, and which end is which flips if you reverse the current direction. This is the link between electromagnetism and permanent magnets: a bar magnet's field comes from countless tiny current loops, electrons circulating and spinning inside its atoms, all lined up the same way a solenoid's loops are.