\section{Magnetism: Forces, Fields, and Sources}

This unit develops the magnetic interaction, beginning with the force a magnetic field exerts on a moving charge — the vector cross-product law $\vec{F} = q\vec{v}\times\vec{B}$ — and the circular or helical motion that follows. In AP Physics C: Electricity and Magnetism, magnetic force is introduced as a velocity-dependent, perpendicular force that changes the direction of motion but does no work.

From particle motion the unit extends to macroscopic currents: the force and torque on current-carrying conductors and loops placed in a magnetic field. That current viewpoint then flips to its source side — the Biot–Savart law and Ampère's law — which let you calculate the magnetic field produced by steady currents using symmetry. The unit closes with solenoids, parallel currents, and magnetic dipoles as canonical configurations.

\input{concepts/em/u12/e12-1-magnetic-force-charge.tex}

\input{concepts/em/u12/e12-2-particle-motion-in-b.tex}

\input{concepts/em/u12/e12-3-force-on-current.tex}

\input{concepts/em/u12/e12-4-biot-savart.tex}

\input{concepts/em/u12/e12-5-ampere.tex}

\input{concepts/em/u12/e12-6-solenoids-dipoles.tex}
