AP-PHYSCEM
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AP® Physics C Electricity and Magnetism
The AP-PHYSCEM exam assesses mastery of calculus‑based electricity and magnetism, covering electrostatics, conductors, capacitors, circuits, magnetic fields, and electromagnetism, preparing students for AP Physics C and introductory college physics.
90
Minutes
40
Questions
3/5
Passing Score
$98
Exam Cost
Who Should Take This
High‑school juniors or seniors who have completed or are enrolled in a calculus‑based physics curriculum and aim to earn college credit should take the AP-PHYSCEM exam. It also benefits aspiring engineering or physics majors seeking to demonstrate strong analytical skills in electromagnetism before college.
What's Covered
1
All five units of the AP Physics C: Electricity and Magnetism course framework (College Board, effective 2024-present): Unit 1 Electrostatics
2
, Unit 2 Conductors, Capacitors, Dielectrics
3
, Unit 3 Electric Circuits
4
, Unit 4 Magnetic Fields
5
, Unit 5 Electromagnetism
What's Included in AccelaStudy® AI
Adaptive Knowledge Graph
Practice Questions
Lesson Modules
Console Simulator Labs
Exam Tips & Strategy
20 Activity Formats
Course Outline
60 learning goals
1
Unit 1: Electrostatics
3 topics
Charge, Force, and Electric Field
- State the fundamental properties of electric charge including conservation, quantization, and the superposition principle for electrostatic forces.
- Apply Coulomb's law to calculate the vector force between point charges and use superposition to find the net force on a charge due to multiple source charges.
- Define the electric field as force per unit positive test charge and calculate the field due to one or more point charges using vector superposition.
- Calculate the electric field due to continuous charge distributions (infinite lines, rings, disks, and arcs) by integrating Coulomb contributions from differential charge elements.
- Sketch electric field line patterns for point charges, dipoles, and combinations of charges, and explain the relationship between field line density and field magnitude.
- Describe the behavior of an electric dipole in a uniform external field, calculating the torque and potential energy of the dipole as functions of angle.
Gauss's Law
- Define electric flux as the surface integral of E dot dA and calculate flux through planar and curved surfaces in both uniform and non-uniform fields.
- State Gauss's law in integral form and explain its equivalence to Coulomb's law for electrostatic fields produced by enclosed charge distributions.
- Apply Gauss's law with appropriate Gaussian surfaces to determine the electric field of spherically symmetric, cylindrically symmetric, and planar charge distributions.
- Evaluate the conditions of symmetry required for Gauss's law to yield a closed-form electric field and contrast this approach with direct Coulomb integration.
Electric Potential
- Define electric potential as the negative line integral of the electric field (V = -integral E dot dl) and distinguish potential from potential energy and electric field.
- Calculate the electric potential due to point charges using V = kq/r and extend to continuous distributions by integrating scalar potential contributions.
- Determine the electric field from a known potential function using E = -grad V and interpret equipotential surfaces in relation to electric field lines.
- Calculate the potential energy of a system of point charges by summing pairwise contributions and relate the result to the work required to assemble the configuration.
- Derive the energy density of an electric field (u = epsilon_0 E^2 / 2) and use it to calculate the total energy stored in a specified region of space.
2
Unit 2: Conductors, Capacitors, Dielectrics
2 topics
Conductors in Electrostatic Equilibrium
- Describe the defining properties of conductors in electrostatic equilibrium: zero internal field, surface-only charge, equipotential volume, and perpendicular surface field.
- Apply Gauss's law to determine the electric field just outside a conductor surface and the induced charge on inner and outer surfaces of conducting shells.
- Explain electrostatic shielding by Faraday cages and analyze how charges redistribute on nested conducting shells with enclosed point charges.
Capacitance and Energy Storage
- Define capacitance (C = Q/V) and derive the capacitance of parallel-plate, cylindrical, and spherical geometries using Gauss's law and potential integration.
- Calculate equivalent capacitance for capacitors connected in series and parallel and determine the charge and voltage across each capacitor in a network.
- Explain how inserting a dielectric between capacitor plates increases capacitance by the factor kappa and reduces the internal electric field through polarization.
- Calculate the energy stored in a capacitor using U = (1/2)CV^2 = (1/2)Q^2/C = (1/2)QV and relate it to the electric field energy density between the plates.
- Analyze how connecting or disconnecting a charged capacitor from a battery before inserting a dielectric changes the charge, voltage, field, and stored energy differently.
3
Unit 3: Electric Circuits
3 topics
Current and Resistance
- Define electric current as rate of charge flow (I = dQ/dt), describe current density J = nqv_d, and distinguish conventional current from electron drift direction.
- Explain the microscopic model of resistance in terms of electron collisions with the lattice and apply the resistivity relationship R = rho L/A to calculate resistance.
- Apply Ohm's law (V = IR) and calculate power dissipated in resistive elements using P = IV = I^2R = V^2/R for steady-state DC circuits.
- Describe the effect of temperature on the resistivity of metallic conductors and semiconductors and explain the difference in their resistance-temperature behaviors.
DC Circuit Analysis
- Calculate equivalent resistance for complex resistor networks involving nested series and parallel combinations, including Wheatstone bridge configurations.
- Apply Kirchhoff's junction rule (charge conservation) and loop rule (energy conservation) to set up and solve systems of linear equations for multi-loop circuits.
- Analyze circuits containing real batteries with internal resistance to determine terminal voltage and the effect of load on current delivery.
- Explain the proper connection of ammeters (in series) and voltmeters (in parallel) and predict how their finite resistance affects the measured values in a circuit.
RC Circuits
- Derive the first-order differential equation governing RC charging circuits and solve it to obtain Q(t), I(t), and V_C(t) as exponential functions of time.
- Derive and solve the differential equation for RC discharging circuits, obtaining exponential decay expressions for charge, current, and voltage.
- Interpret the time constant tau = RC physically and calculate the fraction of final charge reached after integer multiples of the time constant.
- Analyze the energy budget of an RC circuit by calculating energy stored in the capacitor, energy dissipated by the resistor, and energy supplied by the battery.
- Design an experiment to measure the time constant of an RC circuit using voltage-time data and linearization of the exponential decay to extract R or C.
4
Unit 4: Magnetic Fields
2 topics
Magnetic Force on Charges and Currents
- State the expression for the magnetic force on a moving charge (F = qv x B) and use the right-hand rule to determine the direction of the force.
- Derive the radius and period of circular motion for a charged particle in a uniform magnetic field and explain why the magnetic force does no work.
- Analyze the helical trajectory of a charged particle entering a magnetic field at an angle to the field direction, separating parallel and perpendicular velocity components.
- Calculate the force on a straight current-carrying wire in a uniform magnetic field using F = IL x B and determine the torque on a rectangular current loop.
- Explain the operation of a velocity selector and a mass spectrometer by combining electric and magnetic forces on charged particles.
Sources of Magnetic Fields
- State the Biot-Savart law and apply it to calculate the magnetic field at a point due to a straight wire segment, a circular loop at its center, and at a point on the axis.
- Apply Ampere's law (integral B dot dl = mu_0 I_enc) to determine the magnetic field inside and outside infinitely long straight wires, solenoids, and toroids.
- Calculate the force per unit length between two long parallel current-carrying wires and predict whether they attract or repel based on current directions.
- Evaluate the symmetry requirements for Ampere's law to yield a closed-form result and contrast situations where the Biot-Savart law must be used instead.
- Describe the magnetic dipole moment of a current loop and compare the far-field pattern of a magnetic dipole to that of an electric dipole.
5
Unit 5: Electromagnetism
3 topics
Electromagnetic Induction
- Define magnetic flux as the surface integral Phi_B = integral B dot dA and calculate flux through planar loops in uniform and non-uniform magnetic fields.
- Apply Faraday's law (EMF = -d Phi_B / dt) to calculate the induced EMF when flux changes due to time-varying fields, moving loops, or rotating coils.
- Apply Lenz's law to determine the direction of induced current and explain how it ensures that electromagnetic induction conserves energy.
- Analyze motional EMF for conducting bars sliding on rails in a magnetic field, determining the induced current, force on the bar, and power dissipated.
- Calculate the EMF induced in a generator (rotating coil in a uniform field) as a function of time and relate peak EMF to angular velocity and coil parameters.
Inductance and LR Circuits
- Define self-inductance (L = N Phi_B / I) and calculate the inductance of a solenoid from its geometric properties and number of turns per unit length.
- Derive the differential equation for current growth in an LR circuit and solve it to obtain I(t) = (V/R)(1 - e^(-Rt/L)) with time constant tau = L/R.
- Analyze the current decay in an LR circuit when the EMF source is removed, deriving the exponential decay I(t) = I_0 e^(-Rt/L).
- Calculate the energy stored in an inductor (U = (1/2)LI^2) and derive the magnetic energy density u = B^2 / (2 mu_0) from the solenoid inductance expression.
- Define mutual inductance (M = N_2 Phi_21 / I_1) and explain how a changing current in one coil induces an EMF in a nearby coil through shared magnetic flux.
Maxwell's Equations and Synthesis
- List the four Maxwell's equations in integral form and identify the physical law each represents: Gauss (E), Gauss (B), Faraday, and Ampere-Maxwell.
- Explain Maxwell's displacement current term (epsilon_0 d Phi_E / dt) added to Ampere's law and describe how it resolves the charging-capacitor inconsistency.
- Construct an integrated argument tracing the unification of electricity and magnetism from Coulomb through Gauss, Faraday, and Ampere-Maxwell to the prediction of electromagnetic waves.
- Design an experiment to quantitatively verify Faraday's law using a solenoid and search coil, and evaluate measurement accuracy against theoretical predictions.
Scope
Included Topics
- All five units of the AP Physics C: Electricity and Magnetism course framework (College Board, effective 2024-present): Unit 1 Electrostatics (26-34%), Unit 2 Conductors, Capacitors, Dielectrics (14-17%), Unit 3 Electric Circuits (17-23%), Unit 4 Magnetic Fields (17-23%), Unit 5 Electromagnetism (14-20%).
- Electrostatics: Coulomb's law, electric field and field lines, electric flux and Gauss's law, electric potential as a line integral of electric field, potential due to continuous charge distributions, and energy stored in electric fields.
- Conductors, capacitors, and dielectrics: electrostatic properties of conductors, capacitance of parallel-plate and spherical capacitors, capacitor combinations in series and parallel, dielectrics, and energy stored in capacitors.
- Electric circuits: current density and drift velocity, resistance and resistivity, Ohm's law, Kirchhoff's rules, RC circuits with calculus-based analysis of charging and discharging, and power dissipation.
- Magnetic fields: magnetic force on moving charges and current-carrying conductors, Biot-Savart law, Ampere's law, magnetic field of solenoids and toroids, and force between parallel current-carrying wires.
- Electromagnetism: electromagnetic induction, Faraday's law with calculus, Lenz's law, inductance and LR circuits, energy stored in magnetic fields, and Maxwell's equations in qualitative form.
- Calculus-based problem solving including vector calculus, line integrals, surface integrals, and differential equations applied to electromagnetic systems.
- Laboratory skills including experimental design, data analysis, linearization, and error analysis in the context of electrostatics and circuit experiments.
Not Covered
- Mechanics topics (kinematics, dynamics, energy, momentum, rotation) covered in AP Physics C: Mechanics.
- Electromagnetic wave propagation, waveguides, antenna theory, and radiation beyond qualitative discussion of Maxwell's equations.
- Advanced electrodynamics, relativistic electromagnetism, and quantum electrodynamics beyond the AP framework.
- AC circuit analysis, impedance, resonance, and phasor methods not covered in the AP Physics C: E&M curriculum.
Official Exam Page
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