PAU Physics (Andalusia) flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Gravitational field strength

Force per unit mass at a point, g = F/m = GM/r². It is a vector pointing toward the source mass and equals the local free-fall acceleration.

Gravitational potential

Work per unit mass to bring a small mass from infinity to a point: V = −GM/r. It is a negative scalar, zero at infinity, and measured in J/kg.

Escape velocity

Minimum launch speed for a projectile to escape a body's gravity without further propulsion: v = √(2GM/R). It is independent of the projectile's mass and launch angle.

Orbital speed of a satellite

For a circular orbit of radius r around mass M, gravity provides the centripetal force, giving v = √(GM/r). Larger orbits correspond to slower orbital speeds.

Kepler's third law

The square of the orbital period is proportional to the cube of the semi-major axis: T² = 4π²a³/(GM). The constant depends only on the central mass.

Total energy in orbit

For a satellite in a circular orbit, E = K + U = GMm/(2r) − GMm/r = −GMm/(2r). Bound orbits always have negative total mechanical energy.

Geostationary orbit radius

A satellite with period equal to one sidereal day (about 86 164 s) must orbit at r = (GMT²/4π²)^(1/3), roughly 4.2×10⁷ m from Earth's centre.

Electric field of a point charge

E = kQ/r², directed radially away from positive charge and toward negative charge. The constant k = 1/(4πε₀) ≈ 9×10⁹ N·m²/C².

Electric potential of a point charge

V = kQ/r, a scalar that is zero at infinity and positive near positive charge. Potential energy of a charge q placed there is U = qV.

Uniform field between parallel plates

Two plates separated by d with potential difference V produce E = V/d, uniform and directed from the positive to the negative plate. A charge q feels constant force qE.

Gauss's law

Electric flux through any closed surface equals the enclosed charge divided by ε₀. It yields E = σ/ε₀ for a conductor surface and E = λ/(2πε₀r) for a line charge.

Relation between field and potential

Electric field is minus the potential gradient, E = −dV/dr. Field lines point toward decreasing potential and cross equipotential surfaces at right angles.

Capacitor energy storage

A capacitor stores charge Q at voltage V with C = Q/V. Stored energy is U = ½CV² = ½QV = Q²/(2C), held in the electric field between the plates.

Magnetic force on a moving charge

F = qv×B, magnitude qvB sinθ. The force is perpendicular to velocity, so it does no work and only changes direction, not speed.

Radius of a cyclotron orbit

A charge moving perpendicular to a uniform field follows a circle of radius r = mv/(qB). The period T = 2πm/(qB) is independent of speed.

Magnetic flux

Φ = B·A·cosθ, where θ is the angle between the field and the surface normal. Measured in webers; flux through a loop changes when B, A or orientation changes.

Lenz's law

The induced current flows in the direction that opposes the change in magnetic flux producing it. This is the origin of the minus sign in Faraday's law.

Motional emf

A conducting rod of length L moving at speed v perpendicular to field B develops emf ε = BLv. If it slides on rails forming a circuit of resistance R, current is BLv/R.

Solenoid magnetic field

Inside a long solenoid with n turns per metre carrying current I, the field is B = μ₀nI, uniform and parallel to the axis. Outside it is approximately zero.

Wave speed relation

For any periodic wave, speed equals frequency times wavelength: v = λf. Equivalently v = ω/k, with ω = 2πf and k = 2π/λ.

Standing wave on a string

With both ends fixed, allowed frequencies are f_n = n·v/(2L), n = 1, 2, 3… Adjacent nodes are separated by half a wavelength.

Closed pipe harmonics

A pipe closed at one end supports only odd harmonics: f_n = n·v/(4L) with n = 1, 3, 5… The closed end is a node, the open end an antinode.

Sound intensity level

β = 10 log(I/I₀) decibels, with I₀ = 10⁻¹² W/m². A tenfold increase in intensity adds 10 dB; doubling distance from a point source cuts about 6 dB.

Doppler effect for sound

Observed frequency shifts upward when source and observer approach and downward when they recede. The shift depends on the speeds of both source and observer relative to the medium.

Critical angle

For light travelling from a denser medium of index n₁ to a less dense one n₂, total internal reflection begins at sinθ_c = n₂/n₁. It requires n₁ greater than n₂.

Double-slit interference

Constructive interference occurs when d·sinθ = mλ. On a distant screen the fringe spacing is Δy = λD/d, where D is the slit-to-screen distance.

Lorentz factor

γ = 1/√(1 − v²/c²), always at least 1 and growing without limit as v approaches c. It multiplies time intervals and momentum in relativistic formulas.

Time dilation

A clock moving at speed v relative to an observer runs slow: Δt = γ·Δt₀, where Δt₀ is the proper time measured in the clock's own rest frame.

Relativistic energy-momentum

Total energy satisfies E² = (pc)² + (m₀c²)². Rest energy is m₀c², and kinetic energy is (γ − 1)m₀c², not ½mv² at high speed.

Photoelectric threshold

Electrons are emitted only if photon energy hf exceeds the work function W. The threshold frequency is f₀ = W/h and maximum kinetic energy is hf − W.

de Broglie wavelength

Any particle with momentum p has an associated wavelength λ = h/p. For a non-relativistic particle this is h/(mv), explaining electron diffraction by crystals.

Radioactive half-life

Time for half the nuclei in a sample to decay: T½ = ln2/λ, where λ is the decay constant. Activity A = λN also halves in each half-life.