Basque PAU Physics flashcards

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

Newton's law of gravitation

The gravitational force between two point masses is F = G m1 m2 / r², attractive and directed along the line joining them. G = 6.674×10⁻¹¹ N·m²/kg².

Gravitational potential

The gravitational potential at a point is the work done per unit mass to bring a small mass from infinity to that point: V = -G M / r. It is zero at infinity and negative everywhere finite.

Kepler's third law

The square of the orbital period is proportional to the cube of the semi-major axis: T² = (4π²/GM) a³. For circular orbits, a is the orbital radius.

Escape velocity

The minimum speed needed to escape a body's gravitational field from its surface: v_esc = √(2GM/R). For Earth it is about 11.2 km/s.

Geostationary orbit

A circular equatorial orbit with a period of 24 hours, so the satellite appears fixed above one point on Earth's equator. Its radius is about 4.22×10⁷ m from Earth's center.

Coulomb's law

The electrostatic force between two point charges is F = k q1 q2 / r², with k = 1/(4π ε0) ≈ 8.99×10⁹ N·m²/C². It is repulsive for like charges and attractive for opposite charges.

Electric field of a point charge

The electric field at distance r from a point charge Q is E = k Q / r², directed radially outward for positive Q and inward for negative Q. The force on a charge q is F = qE.

Gauss's law

The net electric flux through any closed surface equals the enclosed charge divided by ε0: Φ = ∮ E·dA = Q_enclosed / ε0. It simplifies fields of symmetric charge distributions.

Electric potential

The electric potential at a point is the work per unit charge needed to bring a positive test charge from infinity to that point: V = k Q / r for a point charge. It is a scalar.

Uniform field between plates

Two parallel conducting plates with potential difference V separated by distance d produce a uniform electric field E = V/d, directed from the positive to the negative plate.

Magnetic force on a charge

A charge q moving with velocity v in a magnetic field B experiences force F = q v × B, magnitude q v B sinθ. The force is perpendicular to v and does no work.

Biot–Savart law

The magnetic field due to a current element is dB = (μ0 I / 4π) (dl × r̂)/r². For a long straight wire it gives B = μ0 I / (2π r).

Ampère's law

The line integral of B around a closed loop equals μ0 times the net current enclosed: ∮ B·dl = μ0 I_enclosed. It is useful for highly symmetric current distributions.

Faraday's law of induction

The induced emf in a circuit equals the negative rate of change of magnetic flux through it: ε = -dΦ/dt. For a coil of N turns, ε = -N dΦ/dt.

Lenz's law

The direction of an induced current is such that it opposes the change in magnetic flux that produced it. This is a consequence of conservation of energy.

Motional emf

A conducting rod of length L moving with speed v perpendicular to a magnetic field B develops an emf ε = B L v, which can drive a current in a closed circuit.

Wave equation

A harmonic wave is described by y(x,t) = A sin(ωt - kx + φ), where ω = 2πf, k = 2π/λ, and the wave speed is v = λf = ω/k.

Standing waves on a string

For a string of length L fixed at both ends, standing waves have wavelengths λ_n = 2L/n and frequencies f_n = n v/(2L), where n = 1, 2, 3, ...

Doppler effect for sound

The observed frequency changes when source and observer move relative to each other: f' = f (v ± v_o)/(v ∓ v_s). The frequency is higher when they approach and lower when they recede.

Sound intensity level

The intensity level in decibels is β = 10 log10(I/I0), where I0 = 10⁻¹² W/m² is the threshold of hearing. Doubling the distance from a point source reduces the level by about 6 dB.

Snell's law

When light passes from medium 1 to medium 2, n1 sinθ1 = n2 sinθ2, where n = c/v is the refractive index. Light bends toward the normal when entering a denser medium.

Total internal reflection

When light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle θc = arcsin(n2/n1), it is totally reflected at the boundary.

Thin lens equation

For a thin lens, 1/f = 1/s + 1/s', where s is the object distance and s' is the image distance. Magnification is m = -s'/s. f is positive for converging lenses.

Magnifying glass

A converging lens of focal length f used as a magnifier gives an angular magnification M = 25/f (with f in cm) when the image is at infinity. The near point is taken as 25 cm.

Young's double-slit interference

Two coherent slits separated by d produce bright fringes at d sinθ = nλ and dark fringes at d sinθ = (n + ½)λ. Fringe spacing on a screen at distance L is Δy = λL/d.

Photoelectric effect

Electrons are emitted from a metal surface when light of frequency above a threshold strikes it. The maximum kinetic energy is K_max = hf - Φ, where Φ is the work function.

Photon energy

A photon of frequency f has energy E = hf = hc/λ, where h = 6.63×10⁻³⁴ J·s. Its momentum is p = h/λ. hc = 1240 eV·nm is a useful conversion.

de Broglie wavelength

A particle with momentum p has an associated wavelength λ = h/p = h/(mv). For an electron accelerated through V volts, λ ≈ 1.23 nm / √V.

Bohr model energy levels

In the Bohr model of hydrogen, the energy levels are E_n = -13.6 eV / n². A transition between levels emits or absorbs a photon of energy equal to the energy difference.

Time dilation

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

Mean and standard deviation

The best estimate from repeated measurements is the mean x̄ = Σx_i/n. The standard deviation s measures the spread of the data, and the uncertainty of the mean is s/√n.

Propagation of uncertainties

For sums or differences, absolute uncertainties add: Δ(x ± y) = Δx + Δy. For products or quotients, relative uncertainties add: Δ(xy)/(xy) = Δx/x + Δy/y.