checkpoint 1

units/em/unit-10.tex

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+\section{Capacitance, Dielectrics, and Energy Storage}
+
+This unit shifts the focus from electric fields and potentials produced by isolated charge distributions to systems designed to store electric energy: capacitors. The central idea is that a conductor (or pair of conductors) can hold charge and associated electric potential energy in a controlled geometry, and that the ability to store charge at a given voltage is quantified by the capacitance $C$.
+
+The flow begins with conductors in electrostatic equilibrium, where charge resides entirely on surfaces and the interior field vanishes. It then covers charge redistribution through contact, induction, and grounding. Next, capacitance and the standard capacitor geometries (parallel-plate, spherical, cylindrical) are introduced, followed by the energy stored in capacitor electric fields. The unit concludes with dielectrics, showing how inserting an insulating material increases capacitance through polarization.
+
+\input{concepts/em/u10/e10-1-conductors.tex}
+
+\input{concepts/em/u10/e10-2-charge-redistribution.tex}
+
+\input{concepts/em/u10/e10-3-capacitance.tex}
+
+\input{concepts/em/u10/e10-4-capacitor-energy.tex}
+
+\input{concepts/em/u10/e10-5-dielectrics.tex}

units/em/unit-11.tex

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+\section{Direct-Current Circuits}
+
+This unit develops the circuit viewpoint for electric charge motion. In AP Physics C: Electricity and Magnetism, the central idea is that steady currents through resistive elements obey precise relationships between current, voltage, and resistance. The treatment is restricted to direct-current (DC) circuits — configurations where sources are ideal constant-voltage batteries and fields have settled so that charge flows at a constant rate.
+
+The flow begins with the microscopic description of current, including drift velocity and current density, then introduces resistance, resistivity, and Ohm's law at both macroscopic and microscopic levels. It continues with electric power dissipation in resistors, then builds up to multi-resistor circuits through equivalent resistance for series and parallel combinations. Kirchhoff's junction and loop rules are introduced as the systematic tool for analyzing complex networks. RC transients with a time constant and internal resistance, which affects real batteries and measurement devices, round out the unit.
+
+\input{concepts/em/u11/e11-1-current-density.tex}
+
+\input{concepts/em/u11/e11-2-resistance-ohm.tex}
+
+\input{concepts/em/u11/e11-3-power.tex}
+
+\input{concepts/em/u11/e11-4-equivalent-resistance.tex}
+
+\input{concepts/em/u11/e11-5-kirchhoff.tex}
+
+\input{concepts/em/u11/e11-6-rc-circuits.tex}
+
+\input{concepts/em/u11/e11-7-internal-resistance.tex}

units/em/unit-12.tex

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+\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}

units/em/unit-13.tex

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+\section{Electromagnetic Induction}
+
+This unit introduces the phenomena where changing magnetic conditions produce electric effects. In AP Physics C: Electricity and Magnetism, the core ideas begin with magnetic flux — a scalar measure of how much magnetic field penetrates a surface — and then culminate in Faraday's law, which quantifies how a time-varying magnetic flux induces an electromotive force. These concepts are the gateway from electrostatics to the full unification of electricity and magnetism.
+
+The flow starts with magnetic flux and Faraday's law, then addresses the direction of induced currents through Lenz's law. From there, the unit covers motional emf (emf generated by conductors moving through a field), inductance and the magnetic energy stored in fields, and finally the transient behavior of LR circuits and the harmonic oscillations of LC circuits.
+
+\input{concepts/em/u13/e13-1-magnetic-flux.tex}
+
+\input{concepts/em/u13/e13-2-faraday.tex}
+
+\input{concepts/em/u13/e13-3-lenz.tex}
+
+\input{concepts/em/u13/e13-4-motional-emf.tex}
+
+\input{concepts/em/u13/e13-5-inductance.tex}
+
+\input{concepts/em/u13/e13-6-lr-circuits.tex}
+
+\input{concepts/em/u13/e13-7-lc-circuits.tex}

units/em/unit-8.tex

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+\section{Electrostatics: Charge, Field, Flux}
+
+This unit develops the core ideas of electrostatics by starting with charge as a conserved quantity and then building the interaction model for stationary charges. In AP Physics C: Electricity and Magnetism, the emphasis is on careful charge bookkeeping, Coulomb's law, superposition, and the interpretation of the electric field vector $\vec{E}$ as a map of the force per unit charge that space assigns to a test charge.
+
+From there, the unit extends point-charge reasoning to standard continuous charge distributions, then introduces electric flux as a measure of how much electric field passes through a surface. That flux viewpoint leads naturally to Gauss's law, especially for highly symmetric charge distributions and Gaussian surfaces that make the field easy to determine.
+
+\input{concepts/em/u8/e8-1-charge-conservation.tex}
+
+\input{concepts/em/u8/e8-2-coulomb-superposition.tex}
+
+\input{concepts/em/u8/e8-3-electric-field.tex}
+
+\input{concepts/em/u8/e8-4-continuous-distributions.tex}
+
+\input{concepts/em/u8/e8-5-electric-flux.tex}
+
+\input{concepts/em/u8/e8-6-gauss-law.tex}

units/em/unit-9.tex

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+\section{Electric Potential and Energy}
+
+This unit develops the energy viewpoint for electrostatics. In AP Physics C: Electricity and Magnetism, the central idea is that electric interactions can be described not only with the vector field $\vec{E}$ but also with the scalar quantities electric potential energy $U$ and electric potential $V$. That scalar viewpoint often makes multi-charge systems and energy changes easier to analyze.
+
+The flow begins with electric potential energy for charge configurations, then defines electric potential and voltage, connects potential to the electric field, and finishes with equipotentials and the energy changes of moving charges. The scope here is electrostatics only, so the field remains conservative and no induction-related electric fields are considered yet.
+
+\input{concepts/em/u9/e9-1-electric-potential-energy.tex}
+
+\input{concepts/em/u9/e9-2-potential-voltage.tex}
+
+\input{concepts/em/u9/e9-3-field-potential.tex}
+
+\input{concepts/em/u9/e9-4-equipotentials.tex}