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AP Course

AP Physics 2

Study AP Physics 2 Units 9–15, with the Fall 2026 radioactive-decay clarification applied and official exam updates linked separately.

Study Units 9–15 through original models, derivations, experiments, quizzes, and practice sets.

Lessons
Particle Motion Behind Temperature and PressureConnecting Gas Variables with the Ideal-Gas ModelHeat Flow and the Approach to Thermal BalanceEnergy Accounting for Thermodynamic ProcessesMaterial Response to Heating and Heat ConductionEntropy, Probability, and the Direction of Thermal ChangeCharge Interactions and Coulomb-Force ModelsTracking Charge During Contact and InductionMapping Electric Fields from Source ChargesEnergy of Configurations of ChargesElectric Potential and Equipotential ReasoningCapacitance and Energy Stored in Electric FieldsConserving Energy in Charged-Particle MotionCharge Flow and Conventional CurrentModeling Sources, Wires, and Loads in Simple NetworksHow Geometry and Material Set ResistanceElectrical Energy Transfer and PowerReducing Series-Parallel DC NetworksLoop Equations from Energy ConservationJunction Equations from Charge ConservationTransient Charging and Discharging in RC NetworksSources, Direction, and Strength of Magnetic FieldsMagnetic Forces and Curved Paths of ChargesForces Between Fields and Current-Carrying ConductorsChanging Magnetic Flux and Induced EMFReflection and Absorption at Material BoundariesLocating Images with Mirror Ray ModelsRefraction, Index, and Total Internal ReflectionLocating Images with Thin-Lens ModelsPulses, Wave Types, and Propagation SpeedPeriodic-Wave Measures and GraphsBoundary Changes and PolarizationElectromagnetic-Wave BehaviorFrequency Shifts from Relative MotionSuperposition, Interference, and Standing WavesDiffraction from Openings and EdgesTwo-Slit and Grating Pattern GeometryPhase Change and Thin-Film ColorQuantum Models and Dual Wave-Particle EvidenceEnergy Levels in a Hydrogen-Like AtomConnecting Spectral Lines to Energy TransitionsThermal Spectra and Blackbody CurvesPhoton Thresholds in the Photoelectric EffectPhoton-Electron Scattering and MomentumMass-Energy Accounting in Fission and FusionRandom Nuclear Decay, Activity, and Half-Life
Quizzes
Practice Problems Formula notes, diagrams, and practice sets will be added here.

AP Physics 2 · Unit 14 · Topic 14.4

Electromagnetic-Wave Behavior

Superposition, boundary conditions, diffraction, and phase explain sound and physical-optics patterns.

1. Topic Lens

Electromagnetic-Wave Behavior is studied through waves, sound, and physical optics. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[v=f\lambda\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. A repeating wave advances one wavelength during one period T.
  2. Speed is distance over time, so v=λ/T.
  3. Frequency is 1/T, giving v=fλ.
\[\lambda=\frac{v}{f}\]

3. Detailed Visual Model

Pixel diagram for Electromagnetic-Wave BehaviorOriginal schematic connecting Electromagnetic-Wave Behavior to Waves, Sound, and Physical Optics.NS
Electromagnetic-Wave Behavior: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

A 340 Hz tone travels at 340 m/s. Find its wavelength.

Answer: λ=v/f=1.00 m.

Investigation idea: Measure standing-wave nodes in an air column or string and compare allowed wavelengths with boundary conditions.

Common trap: Wave speed is determined by the medium; changing frequency usually changes wavelength, not the medium's speed.

Expanded Topic 14.4 Lesson

5. Learning Targets

  • Explain how accelerating charges and time-varying fields produce electromagnetic radiation.
  • Use the mutually perpendicular directions of \(\vec E\), \(\vec B\), and propagation to analyze an electromagnetic wave.
  • Relate speed, frequency, wavelength, electric-field amplitude, magnetic-field amplitude, and intensity.
  • Organize the electromagnetic spectrum without treating its named bands as different kinds of waves.
  • Distinguish classical wave intensity from the energy of one photon and predict common interactions with matter.

6. A Wave Made of Fields

An electromagnetic wave is a traveling disturbance of electric and magnetic fields. It does not require matter: sunlight crosses the near-vacuum between the Sun and Earth.

  • The electric field \(\vec E\) and magnetic field \(\vec B\) oscillate in phase.
  • Each field is perpendicular to the other and to the propagation direction.
  • Because both field oscillations are transverse, electromagnetic waves can be polarized.
  • The wave transfers energy and momentum even though no material particle travels with it from source to receiver.

At any instant in an ideal plane wave, the propagation direction follows \(\vec E\times\vec B\).

7. How Radiation Is Produced

A charge at rest creates an electric field, and a steady current creates a magnetic field. Radiation is associated with accelerating charge or a time-varying current. In a transmitting antenna, charges oscillate; the changing electric field is linked to a changing magnetic field, and the disturbance propagates outward.

Near an antenna, stored near-fields can have a complicated geometry. Far enough away, a small part of the outgoing radiation can be modeled locally as a transverse plane wave. The simple wave equations below refer to that radiation-zone model.

8. Original Field-Orientation Model

Electric and magnetic fields in a traveling electromagnetic wave The wave travels to the right. A sinusoidal electric field oscillates vertically. Magnetic-field symbols alternate out of and into the page so that the cross product of electric and magnetic fields points along propagation. electric field EE oscillationpropagation: E × BB outB in
The dots and crosses represent magnetic field out of and into the page. They are sample directions, not particles. Use the right-hand rule on \(\vec E\times\vec B\) to check the energy-flow direction.

9. Maxwell's Speed Prediction

In vacuum, the field equations predict a propagation speed set by the electric and magnetic constants:

\[c=\frac{1}{\sqrt{\mu_0\epsilon_0}}\approx2.998\times10^8\,\mathrm{m/s}\]

Like every periodic wave, an electromagnetic wave also satisfies

\[c=f\lambda_0\]

In a simple transparent medium with refractive index \(n\), use \(v=c/n\) and \(v=f\lambda_{\mathrm{medium}}\). At a stationary boundary, the source-set frequency remains the same, so a lower speed means a shorter wavelength.

10. Electric and Magnetic Amplitudes

For an electromagnetic plane wave in vacuum, the instantaneous field magnitudes and their amplitudes obey

\[\frac{E}{B}=c,\qquad E_0=cB_0\]

A large numerical ratio does not mean the electric field contains all the energy; volts per meter and teslas are different units. In a material, do not automatically substitute \(c\): the corresponding field ratio depends on the medium.

11. Energy Flow and Intensity

Intensity is average power delivered per perpendicular area. For a sinusoidal plane wave in vacuum,

\[I_{\mathrm{avg}}=\frac{P_{\mathrm{avg}}}{A}=\frac12c\epsilon_0E_0^2=\frac{cB_0^2}{2\mu_0}=\frac{E_0B_0}{2\mu_0}\]
Amplitude scalingDoubling \(E_0\) also doubles \(B_0\), but makes average intensity four times as large.
Geometric spreadingAn isotropic source distributes power over \(4\pi r^2\), so \(I=P/(4\pi r^2)\).
Field falloffFor ideal spherical spreading, intensity falls as \(1/r^2\), while field amplitude falls as \(1/r\).

Real antennas have directional radiation patterns, and absorption can remove energy. Use the inverse-square model only when the source and surroundings justify it.

12. Worked Field-and-Intensity Example

A sinusoidal plane wave in vacuum has electric-field amplitude \(E_0=300\,\mathrm{V/m}\).

\[B_0=\frac{E_0}{c}=\frac{300}{3.00\times10^8}=1.00\times10^{-6}\,\mathrm T\]
\[I_{\mathrm{avg}}=\frac12(3.00\times10^8)(8.85\times10^{-12})(300)^2\approx1.20\times10^2\,\mathrm{W/m^2}\]

If \(E_0\) decreases to \(150\,\mathrm{V/m}\), the new intensity is one quarter as large, about \(29.9\,\mathrm{W/m^2}\).

13. Worked Geometric-Spreading Example

An ideal isotropic source radiates \(60\,\mathrm W\). Ignoring absorption, at \(r=3.0\,\mathrm m\),

\[I=\frac{60}{4\pi(3.0)^2}=0.53\,\mathrm{W/m^2}\]

At \(6.0\,\mathrm m\), the distance doubles, so the intensity becomes \(0.53/4\approx0.13\,\mathrm{W/m^2}\). The power is not lost; the same total power is spread over four times the spherical area.

14. One Spectrum, Many Frequency Ranges

All electromagnetic waves share the same basic field structure and vacuum speed. The familiar band names identify useful, overlapping frequency ranges rather than sharp changes in the laws of physics.

RegionTypical production or useCommon interaction or detection idea
RadioOscillating currents in antennas; communicationDrives charges in a resonant receiving antenna
MicrowaveRadar, communication, heating applicationsAbsorption depends strongly on material and frequency
InfraredThermal emission, remote controls, sensingOften excites molecular vibration or is detected thermally
VisibleLamps, lasers, sunlightTriggers retinal receptors and many electronic sensors
UltravioletHot sources, discharge lamps, sunlightCan drive photochemical change; effects depend on wavelength and dose
X-ray / gammaRapid electron processes or nuclear transitionsHigh photon energy can ionize matter; shielding and exposure matter

15. The Photon-Energy Bridge

Classical wave equations describe fields and intensity. When energy exchange occurs in discrete quanta, the energy of one photon is

\[E_\gamma=hf=\frac{hc}{\lambda_0}\]

At fixed frequency, greater intensity generally means more energy arriving per area per time, often modeled as more photons arriving—not a larger energy for each photon. Raising frequency increases each photon's energy while leaving the vacuum wave speed unchanged.

16. Frequency and Wavelength Example

A transmitter operates at \(2.45\,\mathrm{GHz}\). Its vacuum wavelength is

\[\lambda_0=\frac{c}{f}=\frac{3.00\times10^8}{2.45\times10^9}=0.122\,\mathrm m\]

If the wave enters a simple medium with \(n=1.50\), then \(v=2.00\times10^8\,\mathrm{m/s}\) and \(\lambda=0.0816\,\mathrm m\), while \(f=2.45\,\mathrm{GHz}\) remains unchanged.

17. What Matter Can Do to an EM Wave

ReflectThe wave returns into the first region; conductors often reflect strongly over selected frequency ranges.
Transmit / refractThe wave continues into the material, usually with a new speed and wavelength.
AbsorbField energy is transferred to internal degrees of freedom and may become thermal or chemical energy.
ScatterIrregularities, particles, or induced charges redirect energy into other directions.
Diffract / interfereWave components spread around openings and superpose, especially when dimensions are comparable to \(\lambda\).
PolarizeAn anisotropic material or reflection can preferentially select electric-field orientations.

“Transparent” is frequency-specific. A material can transmit visible light but absorb infrared or ultraviolet. Predict behavior from the wave's frequency, the material response, geometry, and thickness—not from the spectrum label alone.

18. Evidence-Building Investigation

A. Source and receiver
  1. Open PhET Radio Waves & Electromagnetic Fields.
  2. Move the transmitter electron once, then oscillate it repeatedly. Compare what reaches the receiver.
  3. Change the oscillation frequency and amplitude separately. Record which visible features and receiver responses change.
  4. Use observations to defend the claim that accelerating charge, not charge position alone, launches the traveling disturbance.
B. Model audit
  1. Sketch \(E\), \(B\), and propagation directions at three locations.
  2. For each sketch, verify the direction of \(\vec E\times\vec B\).
  3. Predict how doubling source amplitude affects field amplitude and intensity.
  4. State two ways the simulation or plane-wave sketch simplifies a real antenna.

19. Common Reasoning Traps

  • “Higher frequency travels faster.” All frequencies have speed \(c\) in vacuum; in matter, dispersion can make speed frequency-dependent.
  • “The fields are parallel.” In a plane EM wave, \(\vec E\perp\vec B\perp\) propagation.
  • “Doubling amplitude doubles intensity.” Intensity is proportional to amplitude squared.
  • “Frequency changes at a boundary.” A stationary boundary preserves frequency; speed and wavelength can change.
  • “Every high-frequency label guarantees the same biological effect.” Interaction depends on photon energy, intensity, exposure, and material.

20. AP-Style Reasoning Checks

  1. An EM wave travels in \(+x\). At one instant \(\vec E\) points \(+y\). Which way must \(\vec B\) point?
  2. If \(B_0\) triples in a vacuum plane wave, by what factor do \(E_0\) and intensity change?
  3. A wave enters glass and slows. State what happens to frequency and wavelength.
  4. Two sources emit the same frequency. Source A has twice the electric-field amplitude at a detector. Compare intensities and photon energies.
  5. Why may a window be transparent to visible light but not to another spectrum region?

Answers: \(+z\), because \(+y\times+z=+x\); \(E_0\) triples and intensity becomes nine times as large; frequency stays fixed and wavelength decreases; A has four times the intensity but the same photon energy; material response depends on frequency and its available charge or molecular excitations.

Checkpoint · Topic 14.4

Explain how electromagnetic-wave behavior supports or limits this conclusion: λ=v/f=1.00 m.

Official curriculum reference: College Board AP Physics 2 course page. The explanation and worked example are independently written for this study site.