A-Level Physics Revision: Electrons, Waves, and Particles

Electric current

The rate of flow of charge.

Elementary charge

e = 1.6 × 10^−19 C, where n = number of electrons.

Mean drift velocity

Average velocity of electrons: I = nAve.

Potential difference

Work done per unit charge to move charge between two points.

Resistance

Opposition to current, R = V/I.

Electrical power

P = IV = I^2R = V^2/R.

Resistivity

ρ = RA/L, where R = resistance, A = cross-sectional area, L = length.

I-V characteristics

Ohmic conductor: straight line through origin; Filament lamp: curve due to increasing resistance; Diode: conducts after threshold in forward direction only.

Thermistors and LDRs

Thermistor resistance decreases with temperature; LDR resistance decreases with light intensity.

Kirchhoff's First Law

Total current entering a junction equals total current leaving it (conservation of charge).

Kirchhoff's Second Law

Sum of emfs equals the sum of pd around a closed loop (conservation of energy).

Internal resistance

Resistance inside a source of emf, modeled as E = I(R + r).

Power affected by internal resistance

Useful power: P = I^2R; Lost power: P = I^2r.

Wave speed

v = fλ.

Longitudinal and transverse waves

Transverse: oscillations perpendicular to direction of energy transfer; Longitudinal: oscillations parallel to direction of energy transfer.

Superposition

The net displacement is the vector sum of individual displacements.

Stationary waves

Formed by superposition of two progressive waves of same frequency and amplitude travelling in opposite directions.

Polarisation

Restriction of oscillations to one plane, used in sunglasses, stress analysis, and LCDs.

Intensity and amplitude

Intensity is directly proportional to the square of amplitude, I ∝ A^2.

Fringe spacing equation

w = λD/s, where w = fringe spacing, D = distance to screen, s = slit separation.

Conditions for observable interference

Coherent sources (constant phase difference) and similar amplitude.

Photoelectric equation

hf = ϕ + (1/2)mv^2, where ϕ = work function.

Electronvolt

Energy gained by an electron when it moves through 1V: 1 eV = 1.6 × 10^−19 J.

Wave-particle duality

Light and particles exhibit both wave-like and particle-like properties.

de Broglie wavelength

λ = h / mv

Capacitance

Capacitance is the charge stored per unit potential difference. Units: Farads (F)

Energy stored in a capacitor

E = 1/2 CV^2

Time constant

Time constant = resistance × capacitance. τ = RC

Exponential decay equations for discharge

Voltage: V = V0 e^(-t/RC)

Fully charged/discharged capacitor

After 5RC (~99.3% charged/discharged)

Electric field strength

E = F / Q

Field due to a point charge

E = (1 / (4πϵ0)) * (Q / r^2)

Electric potential energy

W = (1 / (4πϵ0)) * (Qq / r)

Uniform electric field

Constant E, parallel field lines (e.g. between plates)

Radial electric field

Field lines from a point charge

Electric potential

Work done per unit charge to move a charge from infinity to a point in the field

Force on a moving charge in magnetic field

F = Bqv sin θ

Magnetic flux

Φ = BA cos θ

Flux linkage

NΦ = N * Φ

Faraday's Law

Induced emf is equal to the rate of change of flux linkage. E = -d(NΦ)/dt

Lenz's Law

Direction of induced current opposes the change causing it (conservation of energy)

Velocity selector

Uses crossed electric and magnetic fields so only particles with specific velocity pass through undeflected

Field around a wire

Concentric circles

Field around a solenoid

Uniform field inside, similar to bar magnet

Mass defect

The difference between the mass of an atomic nucleus and the sum of the masses of its individual nucleons

Binding energy

Energy required to split a nucleus into free nucleons. E = Δmc^2

Activity

A = λN

Decay law

N = N0 e^(-λt)

Half-life

Time taken for half the nuclei to decay: T1/2 = (ln 2) / λ

PET scanning

Uses positron-emitting tracers. Annihilation produces gamma rays detected in coincidence

MRI scanner

Uses strong magnetic fields and radio waves to align and manipulate nuclear spins of hydrogen nuclei

Gamma camera principle

Gamma rays from tracer pass through collimator, hit scintillator, generate light photons → photomultiplier tubes → electrical signal → image

Comparison of PET, CT, and MRI scans

PET: functional info, expensive, radioactive. CT: structural, uses X-rays, good resolution. MRI: soft tissue detail, no ionising radiation