South 고등학교 2학년 Electromagnetism and Quantum

Chapters: 3

1. Electromagnetic interaction

Electric fields quantitatively · Induction and dielectric polarisation · Magnetic fields of currents · Lorentz force · Faraday's law · R, C, L in circuits · Diodes and transistors

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).
Electrostatics: Induction, Polarisation and Sharing of Charge – Electrostatics is the study of charges at rest. Objects get charged by friction (rubbing), by contact (conduction) or by induction (bringing a charge near, without touching). In a conductor, free electrons move: a nearby charge pushes them to one side (induction), and earthing then leaves the conductor with the opposite charge. In an insulator (dielectric), electrons cannot travel, but each molecule stretches into a tiny dipole and lines up with the field (polarisation); that is why a charged comb attracts neutral paper. When charged conductors are joined by a wire, charge flows until their potentials are equal. For spheres far apart, V = kq/r, so the charge divides in the ratio of the radii: q₁/q₂ = r₁/r₂, and the smaller sphere has the larger surface charge density. Total charge is always conserved.
Magnetic Field due to a Current: Biot-Savart Law and Ampere's Law – A current makes a magnetic field around it (Oersted, 1820). The Biot-Savart law gives the field of a tiny piece of wire: dB = (μ₀/4π)·I dl sinθ / r². Adding all pieces of a circular loop gives B = μ₀NI / 2R at the centre and μ₀NIR² / 2(R² + x²)^{3/2} on the axis. Ampere's circuital law ∮B·dl = μ₀I gives B = μ₀I / 2πr for a long straight wire. A long solenoid has a strong, uniform field B = μ₀nI inside and almost none outside.
Lorentz Force, Torque on a Loop and the Moving Coil Galvanometer – A charge q moving with velocity v feels F = q(E + v × B), the Lorentz force. The magnetic part qvB sinθ is at right angles to v, so it bends the path into a circle (r = mv/qB) without changing speed. A wire feels F = IL × B. Parallel wires attract if the currents are in the same direction: F/L = μ₀I₁I₂/2πd. A loop in a field feels a torque τ = m × B with magnetic moment m = NIA, so a loop acts as a magnetic dipole. A moving coil galvanometer uses this torque: its deflection φ = (NAB/k)I. A small shunt turns it into an ammeter; a large series resistance turns it into a voltmeter.
Electromagnetic Induction – When the magnetic flux through a coil changes, an emf is produced in it: ε = −N dΦ/dt (Faraday). The minus sign is Lenz's law: the induced current always opposes the change that made it. Moving a rod in a field gives motional emf ε = Blv. A changing current makes an emf in its own coil (self-induction, L) and in a nearby coil (mutual induction, M).
Force on a Current-Carrying Conductor, Motor and Induction – A wire carrying current inside a magnetic field feels a push. The push is biggest when the wire is at 90° to the field and zero when it is parallel. Fleming's left-hand rule gives its direction. A motor uses this push to spin a coil; a generator does the reverse and makes current by moving a coil or magnet.
Alternating Current – An alternating current (AC) changes size and direction again and again: I = I₀ sin ωt. Its rms value is I₀/√2, the steady DC that gives the same heating. A resistor keeps V and I in step; an inductor makes I lag by 90° (Xʟ = ωL); a capacitor makes I lead by 90° (Xᴄ = 1/ωC). In a series LCR circuit Z = √(R² + (Xʟ − Xᴄ)²), resonance happens when Xʟ = Xᴄ, and average power is P = Vrms Irms cos φ.
Semiconductors and the p-n Junction Diode – A semiconductor has a small energy gap (about 1 eV), so a little heat frees some electrons. Pure silicon is intrinsic (electrons = holes). Adding a 5-valence atom makes n-type; a 3-valence atom makes p-type. Joining p and n makes a junction with a depletion layer and a barrier (about 0.7 V for Si). The diode conducts in forward bias, almost not in reverse bias, so it can change AC into one-way DC (rectifier).

2. Light and communication

Interference, diffraction, holograms · Optical instruments · Polarisation · Photoelectric effect · Lasers

Interference (Young's Double Slit) and Single Slit Diffraction – Two coherent sources (same frequency, fixed phase difference) make a steady pattern of bright and dark fringes. At a point on the screen the path difference is Δ = yd/D: bright where Δ = nλ, dark where Δ = (n + ½)λ. All fringes have equal width β = λD/d. A single slit of width a gives diffraction: a bright central maximum of width 2λD/a, with first minima where a sin θ = λ, and weaker side maxima.
Optical Instruments: Microscopes and Telescopes – How big a thing looks depends on the angle it makes at the eye. A simple microscope (one convex lens) gives m = 1 + D/f (image at D) or D/f (image at infinity). A compound microscope uses a short-focus objective and an eyepiece: m = mₒ × mₑ ≈ (L/fₒ)(D/fₑ). An astronomical telescope uses a long-focus objective and short-focus eyepiece: m = fₒ/fₑ in normal adjustment, with tube length fₒ + fₑ. Reflecting telescopes use a concave mirror as objective.
Polarisation of Light – Light is a transverse wave: its electric field shakes at right angles to the direction it travels. In ordinary light the shaking happens in all directions. A polaroid lets through only one direction, so the light becomes plane polarised and half as bright. A second polaroid at angle θ lets through I = I₀cos²θ (Malus's law). Polarisation proves light is transverse and is used in sunglasses, LCD screens, cameras and 3D films.
Photoelectric Effect and Einstein's Equation – When light of high enough frequency falls on a metal, electrons jump out at once. Light comes in packets called photons, each with energy E = hν. One photon gives all its energy to one electron: hν = φ + KEmax, where φ is the work function. Below the threshold frequency ν₀ = φ/h no electron comes out, however bright the light.
Lasers: How Stimulated Emission Makes a Beam of Light – LASER stands for Light Amplification by Stimulated Emission of Radiation. A pump lifts atoms to a higher energy level. When a photon of the right energy passes an excited atom, the atom gives out a second, identical photon. With more atoms excited than unexcited (population inversion) and mirrors at each end, the light builds up into a narrow, single-colour, coherent beam. X-rays are also high-energy light, made when fast electrons hit a metal target.

3. Quantum and the micro world

Single-quantum double-slit experiment · Superposition and measurement · Tunnelling · Modern atomic model and uncertainty · Nuclear fusion in stars

Quantum Physics Basics: Double Slit, Superposition and Measurement – Tiny things like photons and electrons are "quantum objects". Each one is detected as a single dot (like a particle), but where the dots land follows a wave of probability, which makes stripes. Before we measure, a quantum object can be in a superposition of possibilities. If we find out which path it took, the stripes disappear. Quantum computers and quantum cryptography use these rules.
Nuclear Fusion – In nuclear fusion, light nuclei join to make a heavier nucleus and release energy. In the Sun's core, at about 15 million °C, four hydrogen nuclei join in steps (the proton–proton chain) to make one helium nucleus. The helium weighs about 0.7% less than the four hydrogens; that missing mass becomes energy by E = mc². Gravity squeezing in and fusion heat pushing out keep a star steady for billions of years.