AP Physics C: Electricity and Magnetism

Units

1. 1

   Electric charges, fields, and Gauss's law

   6 lessons

   1. Electric charge and Coulomb's lawUse Coulomb's law F = kq₁q₂/r² to find the size and direction of the force between point charges, and add the forces from several charges as vectors in components.
   2. Conservation of charge and the process of chargingKeep a ledger of charge that only moves and never appears, tell polarization from charging, share charge between identical conductors, and charge a sphere by induction with a ground.
   3. Electric fieldsDefine the electric field as force per unit charge, find the field of one or several point charges as a vector sum, read a field map, and find the acceleration of a charge in a field.
   4. Electric fields of charge distributions by integrationSet up and evaluate dE = k dq/r² as an integral for a ring on its axis, a rod and a semicircular arc, using symmetry to drop the components that cancel and the limits to check the answer.
   5. Electric fluxFind the flux of a uniform field through a flat surface as Φ = EA cos θ with θ from the normal, sum the outward flux over a closed surface, and see that flux through spheres round a charge does not depend on radius.
   6. Gauss's lawState Gauss's law, ∮E·dA = Q_enc/ε₀, choose a Gaussian surface from the symmetry of the charge, and use it to find the field of spheres, lines and planes, with the enclosed charge found by integration when the density varies.
2. 2

   Electric potential

   3 lessons

   1. Electric potential energyFind the electric potential energy U = kq₁q₂/r of a pair, add one term per pair for several charges, and use conservation of energy to find the speed of charges released from rest.
   2. Electric potential and its relation to the fieldDefine potential as energy per unit charge, add the potentials of point charges and distributions as scalars, and move between V and E with E_x = −dV/dx and ΔV = −∫E·dl.
   3. Conservation of electric energyUse ΔU = qΔV and the conservation of K + qV to find the energy and speed of a charge moved through a potential difference, and the distance of closest approach of a charge fired at a fixed one.
3. 3

   Conductors and capacitors

   4 lessons

   1. Electrostatics with conductorsState and justify the rules for a conductor in electrostatic equilibrium, that E = 0 inside, excess charge sits on the surface, the body is one potential and E = σ/ε₀ just outside, and apply them to spheres, shells with cavities and joined conductors.
   2. Redistribution of charge between conductorsFind how charge divides between conductors in contact from the condition of equal potentials, find the charge a grounded conductor takes near another charge, and account for the energy lost.
   3. Capacitors and capacitanceDefine capacitance C = Q/ΔV, derive it for parallel plates, concentric spheres and coaxial cylinders with Gauss's law and integration, find the stored energy U = ½CΔV², and predict what changes when a capacitor is altered with a battery attached or removed.
   4. DielectricsExplain how a dielectric polarizes and weakens the field by the factor κ, and predict the change in C, Q, ΔV, E and U when a slab fills a capacitor that is isolated and when it stays connected to a battery.
4. 4

   Electric circuits

   8 lessons

   1. Electric current and current densityUse I = dq/dt, I = nqv_dA and J = I/A, find charge by integrating a changing current, and integrate a current density that varies across a wire.
   2. Simple circuitsFind the closed path in a schematic, tell closed, open and short circuits apart, and predict the current, the potential differences and the brightness of bulbs when a switch changes or a wire bypasses one.
   3. Resistance, resistivity and Ohm's lawUse R = ΔV/I and Ohm's law, find the resistance of a wire from R = ρL/A, integrate a resistivity that changes along a bar, and tell an ohmic element from a nonohmic one on an I–V graph.
   4. Electric powerUse P = IΔV = I²R = ΔV²/R and E = Pt, choose the form of P that uses the quantity that is the same, and decide which of two bulbs is brighter in series and in parallel.
   5. Compound DC circuits, internal resistance and metersReduce a circuit of series and parallel parts to one resistor and work back to every current and potential difference, include a battery's internal resistance, and place ammeters and voltmeters, ideal and real.
   6. Kirchhoff's loop ruleApply ΣΔV = 0 round a closed loop with the right signs for batteries and resistors, find the current in a single loop with one or two batteries, draw the potential round the loop, and check the answer with a power ledger.
   7. Kirchhoff's junction rule and multi-loop circuitsApply ΣI_in = ΣI_out at a junction, write enough independent junction and loop equations for a multi-loop circuit, solve for every branch current, and check the answer with the loop rule and a power ledger.
   8. Resistor-capacitor (RC) circuitsCombine capacitors in series and parallel, derive and use q = Cℰ(1 − exp(−t/RC)) and the decay on discharge from the loop rule, read the time constant τ = RC, and track where the energy goes.
5. 5

   Magnetic fields and electromagnetism

   4 lessons

   1. Magnetic fields, dipoles and materialsDescribe a magnetic field as a vector field made by dipoles and moving charges, explain why magnetic field lines close on themselves and why the net flux through a closed surface is zero, and say which materials a magnet attracts.
   2. Magnetic force on moving charges and the fields they makeUse F = qv × B for its size and direction, show that the magnetic force does no work, find the radius and period of circular motion, handle crossed E and B fields and the Hall effect, and write the field of a moving charge.
   3. Magnetic fields of current-carrying wires: the Biot-Savart lawUse the Biot-Savart law to find the field of a long straight wire, a circular loop and an arc, add the fields of several currents, and find the force on a current in a field and between parallel wires.
   4. Ampère's lawUse ∮B·dℓ = μ₀I_enc with a loop that follows the symmetry to find B for a long wire, a wire with varying current density, and a solenoid.
6. 6

   Electromagnetic induction

   6 lessons

   1. Magnetic fluxCompute Φ_B = BA cos θ for a flat loop in a uniform field, integrate ∫B·dA when B varies, and explain why the net flux through a closed surface is zero.
   2. Faraday's law and Lenz's lawUse ε = −N dΦ/dt to find an induced emf from a changing flux, find its direction with Lenz's law, and apply it to a changing field, a moving rod and a rotating coil.
   3. Induced currents and magnetic forcesFind the current, retarding force and power for a conductor moving in a magnetic field, say where the energy goes, and solve for a falling rod's speed with Newton's second law.
   4. Inductance and magnetic energyDefine L = NΦ/I, derive L = μ₀N²A/ℓ for a solenoid, use ε = −L dI/dt for the back emf, and use U = ½LI² for the energy stored in the magnetic field.
   5. Circuits with resistors and inductors (LR circuits)Solve a series LR circuit with the loop rule, find the exponential growth and decay of the current with time constant τ = L/R, and describe the inductor at the start and after a long time.
   6. Circuits with capacitors and inductors (LC circuits)Show that an ideal LC circuit oscillates, find q(t), I(t), ω = 1/√(LC), the maximum current and the quarter-cycle phase from the loop rule and energy conservation, and map the circuit onto a spring-mass system.
7. 7

   Exam skills: the four free-response types

   4 lessons

   1. Mathematical routines: deriving fields, potentials and circuit responsesWrite a derivation the way the exam scores it: name the principle and the surface or loop, solve in symbols with definite integrals, and finish with an expression checked by units, a limit and a sign.
   2. Translation between representationsMove one electrostatic or circuit situation between field lines, V(x) and E(x) graphs, a circuit schematic, graphs against time and an equation, and write the sentence that links two of them.
   3. Experimental design, linearization and analysisWrite a procedure with its variables, instruments and trials, choose axes that make a law a straight line, read the slope and intercept from the best-fit line, and name errors and improvements.
   4. Qualitative/quantitative translation: claims, evidence and equationsAnswer the exam's argument question in three parts: commit to a claim with physical reasoning beyond the algebra, derive the result in the question's symbols, and connect the result back to the claim.