PAU Physics (Castilla y León) flashcards

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

Gravitational potential

Work per unit mass needed to bring a small mass from infinity to a point, V = −GM/r. It is always negative, zero at infinity, and a scalar, so potentials from several masses add algebraically.

Escape velocity

Minimum launch speed for a body to escape a planet's gravity without further propulsion: v = √(2GM/R). It depends only on the planet's mass and radius, not on the projectile's mass.

Kepler's third law

For bodies orbiting the same central mass, the square of the orbital period is proportional to the cube of the semi-major axis: T² = (4π²/GM)·a³. It follows from equating gravitational and centripetal force.

Geostationary orbit

A circular equatorial orbit with a 24-hour period and the same sense as Earth's rotation, so the satellite stays above one point. Its radius, about 4.2×10⁷ m from Earth's centre, follows from Kepler's third law.

Gravitational field strength

Force per unit mass at a point, g = GM/r², directed towards the attracting mass. Outside a uniform sphere it equals the field of a point mass at the centre; its SI unit is N/kg or m/s².

Coulomb's law

The electrostatic force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation: F = k·q₁·q₂/r², attractive for opposite signs, repulsive for like signs.

Electric potential of a point charge

V = k·Q/r, a scalar that keeps the sign of Q. Positive charges create positive potential; the potential energy of a test charge q placed there is U = q·V, measured in joules.

Uniform electric field between plates

Between parallel plates the field is uniform, E = V/d, running from the positive to the negative plate. A charge q there feels a constant force qE, so its motion is uniformly accelerated.

Gauss's law

The electric flux through any closed surface equals the enclosed charge divided by ε₀. It shows the field inside a conductor in electrostatic equilibrium is zero and gives E = σ/ε₀ near a conducting surface.

Equipotential surfaces

Surfaces on which the electric potential has the same value everywhere. They are always perpendicular to field lines, and moving a charge along one requires no work.

Capacitance and stored energy

Capacitance is charge per unit potential difference, C = Q/V, measured in farads. A charged capacitor stores U = ½CV² = Q²/(2C); for parallel plates C = ε₀ε_r·A/d.

Magnetic force on a moving charge

F = q·v×B, with magnitude qvB·sinθ where θ is the angle between velocity and field. The force is always perpendicular to v, so it changes direction but never does work or changes speed.

Radius of a cyclotron orbit

A charge moving perpendicular to a uniform magnetic field follows a circle of radius r = mv/(|q|B). The period T = 2πm/(|q|B) does not depend on speed, which is the basis of the cyclotron.

Magnetic flux

Φ = B·A·cosθ, where θ is the angle between the field and the surface normal. Measured in webers (Wb); flux changes when field strength, area, or orientation changes.

Faraday and Lenz laws

Induced emf equals the negative rate of change of magnetic flux linkage: ε = −N·dΦ/dt. The minus sign means the induced current opposes the change producing it, conserving energy.

Motional emf

When a conductor of length L moves at speed v perpendicular to a magnetic field B, an emf ε = BLv appears across it. Connecting it to a resistance R gives a current I = BLv/R.

Wave equation for a stretched string

The speed of a transverse wave on a string is v = √(T/μ), where T is tension and μ the mass per unit length. Wave speed also equals λ·f for any periodic wave.

Sound intensity level

β = 10·log(I/I₀) decibels, with reference intensity I₀ = 10⁻¹² W/m². Because intensity falls as 1/r² from a point source, the level drops about 6 dB each time distance doubles.

Doppler effect for sound

The observed frequency shifts when source and observer move relative to each other: f' = f(v ± v_o)/(v ∓ v_s). It rises on approach and falls on recession; no shift occurs for purely transverse motion.

Harmonics of a closed pipe

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

Critical angle and total reflection

Light travelling from a denser to a less dense medium is totally internally reflected beyond the critical angle, given by sinθ_c = n₂/n₁. It requires n₁ greater than n₂ and is used in optical fibres.

Thin lens equation

1/f = 1/s' − 1/s in the Cartesian convention, with magnification m = −s'/s. A positive image distance means a real image on the opposite side for a converging lens.

Lens power in dioptres

Power is the reciprocal of focal length in metres, P = 1/f, measured in dioptres. Converging lenses have positive power, diverging lenses negative; powers of thin lenses in contact add.

Telescope magnification

For an astronomical telescope focused at infinity, angular magnification M = f_o/f_e, the ratio of objective to eyepiece focal length. A long objective and short eyepiece give high magnification but a narrow field.

Time dilation

A clock moving at speed v relative to an observer runs slow by the factor γ = 1/√(1 − v²/c²): Δt = γ·Δt₀, where Δt₀ is the proper time measured in the clock's rest frame.

Photoelectric effect equation

Einstein's relation hf = W₀ + K_max, where W₀ is the work function. Emission occurs only above the threshold frequency f₀ = W₀/h; increasing intensity raises current, not maximum kinetic energy.

de Broglie wavelength

Every particle has an associated wavelength λ = h/p, where p is its momentum. It is measurable for electrons and neutrons and explains electron diffraction by crystals.

Bohr energy levels of hydrogen

E_n = −13.6 eV/n². Photons are emitted or absorbed when electrons move between levels, with energy equal to the difference; transitions to n = 1 give the ultraviolet Lyman series.

Radioactive half-life

The time for half the nuclei in a sample to decay, related to the decay constant by T½ = ln2/λ. Activity A = λN decays exponentially as N = N₀e^(−λt).

Mass defect and binding energy

The mass of a nucleus is less than the sum of its separate nucleons; the difference Δm corresponds to binding energy E_b = Δm·c². Higher binding energy per nucleon means greater nuclear stability.

Propagation of uncertainty in products

When quantities are multiplied or divided, their fractional uncertainties add: Δz/z = Δx/x + Δy/y. For a power xⁿ, the fractional uncertainty becomes n times that of x.

Systematic versus random error

Systematic errors shift all readings the same way, as with a zero error or miscalibration, and are not reduced by averaging. Random errors scatter both ways and are reduced by repeated measurements.