Netherlands VWO 6 (eindexamenjaar) Physics

Chapters: 4

1. Charge and field (part 2)

Electric and magnetic fields

Electric Charges and Fields – Charge comes in two kinds, is conserved and comes in whole-number packets of e = 1.6 × 10⁻¹⁹ C. Two point charges push or pull with F = kq₁q₂/r² (k = 9 × 10⁹ N m² C⁻²). Forces and fields from many charges add as vectors (superposition). The field E = F/q₀ of a point charge is kq/r²; field lines show it. A dipole (±q a distance 2a apart) has moment p = q·2a; in a uniform field it feels zero net force but a torque τ = pE sinθ. Electric flux Φ = E·A, and Gauss's law says the flux out of any closed surface is q_enclosed/ε₀, which quickly gives E for a long wire (λ/2πε₀r), a plane sheet (σ/2ε₀) and a thin spherical shell (kq/r² outside, 0 inside).

Electromagnetic radiation and matter

Towards Bohr's Model: Light, Photons, Spectra and Bohr's Atom – Light is an electromagnetic wave: c = νλ, and wavenumber ν̄ = 1/λ. But some facts need particles: Planck said energy comes in packets (quanta) E = hν. Einstein used photons to explain the photoelectric effect: an electron comes out only if hν is above the work function W₀ = hν₀, and its kinetic energy is hν − hν₀. Atoms give line spectra, which means electron energies are fixed. Bohr put the electron on fixed orbits with angular momentum nh/2π; energy Eₙ = −2.18 × 10⁻¹⁸ Z²/n² J, radius rₙ = 52.9 n²/Z pm. A jump between orbits gives a photon, and 1/λ = R_H(1/n₁² − 1/n₂²) gives the Lyman, Balmer, Paschen, Brackett and Pfund series. Bohr works only for one-electron species.

Quantum world

Matter Waves and the de Broglie Relation – Light behaves like a wave and a particle. In 1924 Louis de Broglie said matter does the same: every moving particle has a wave with wavelength λ = h/p = h/mv. For a body of kinetic energy K, λ = h/√(2mK); for an electron accelerated through V volts, λ = 1.227/√V nm. Everyday objects have far too tiny a λ to notice, but electrons have λ about the size of atoms.

Laws of nature and models

Model Evaluation: How Good Is a Model? – A model is a simple copy of the real world that makes predictions. To evaluate it, we compare its predictions with the real answers. In machine learning we split data into a training set (to learn) and a test set (to check on new data). A confusion matrix counts true positives (TP), false positives (FP), false negatives (FN) and true negatives (TN). Accuracy = (TP + TN) ÷ total. Precision = TP ÷ (TP + FP). Recall = TP ÷ (TP + FN). F1 = 2PR ÷ (P + R). Science models (like the inverse-square law or the particle model) are judged the same way: do predictions match measurements, and where does the model stop working?