18.2 Magnetic Fields from Magnets and Currents

Permanent magnets create magnetic fields due to microscopic electron motion and alignment inside materials. Electric currents also create magnetic fields, which is the crucial bridge to electromagnetism. The historical observation that a current deflects a compass needle is conceptually as important as any formula in this section.

Field lines for magnetic systems are continuous closed loops. For bar magnets, external lines run from north to south and return through the interior. For current-generated fields, the geometry depends on current path: circular around straight wires and loop-like around coils and solenoids.

A long straight current-carrying wire produces concentric circular field lines centered on the wire. A single circular loop creates a dipole-like field pattern. A solenoid approximates a bar magnet: field inside is relatively uniform and strong, while outside it spreads and weakens.

Two notation conventions are used constantly: a dot means vector out of the page toward you, and a cross means vector into the page away from you. These symbols encode three-dimensional direction on two-dimensional diagrams and are essential for force-direction questions.

For current-generated fields, point the right thumb in current direction; curled fingers show magnetic-field direction around the conductor. For solenoids, curled fingers follow current around turns and the thumb points to the solenoid's north side. Use one consistent hand rule through the full problem to avoid accidental direction flips.