Canary PAU Physics 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 = G M/r², directed toward the attracting mass; units N/kg or m/s². Inside a uniform sphere, g is proportional to r.

Gravitational potential

Work done per unit mass to bring a small mass from infinity to a point, V = -G M/r. It is always negative and zero at infinity; potential energy U = m V.

Escape speed

Minimum launch speed for an object to escape a body's gravity without further propulsion: v_esc = √(2 G M/R). It is independent of the object's mass and launch direction.

Kepler's third law

For circular orbits, the square of the period is proportional to the cube of the orbital radius: T² = (4π²/G M) r³. This follows from equating gravitational and centripetal forces.

Coulomb's law

The electrostatic force between two point charges is F = k q1 q2/r², along the line joining them, repulsive for like charges and attractive for unlike. k = 8.99×10^9 N·m²/C².

Electric potential of a point charge

V = k Q/r, the work per unit positive charge to bring it from infinity to distance r from charge Q. Potential is a scalar and is positive near a positive charge.

Capacitance

Ratio of stored charge to potential difference: C = Q/V. For a parallel-plate capacitor, C = ε0 A/d; inserting a dielectric of constant κ multiplies C by κ.

Gauss's law

The net electric flux through a closed surface equals the enclosed charge divided by ε0: ∮E·dA = Q_enclosed/ε0. It is useful for highly symmetric charge distributions.

Magnetic force on a moving charge

F = q v × B, with magnitude q v B sinθ. The force is perpendicular to both velocity and field, so it does no work and changes only the direction of motion.

Radius of a cyclotron orbit

A charge moving perpendicular to a uniform magnetic field follows a circle of radius r = m v/(|q|B). The period T = 2πm/(|q|B) is independent of speed.

Magnetic field of a long wire

B = μ0 I/(2π r), where r is the perpendicular distance from the wire. Field lines are concentric circles around the wire, with direction given by the right-hand grip rule.

Magnetic flux

Φ = B·A = B A cosθ, where θ is the angle between the field and the area normal. The SI unit is the weber (Wb), equal to one tesla square meter.

Faraday's law of induction

The induced emf in a circuit equals the negative rate of change of magnetic flux linkage: ε = -N dΦ/dt. The minus sign expresses Lenz's law.

Lenz's law

An induced current flows in the direction that opposes the change in magnetic flux that produced it. This is a consequence of energy conservation and gives the minus sign in Faraday's law.

Motional emf

A conducting rod of length L moving at speed v perpendicular to a uniform magnetic field B develops an emf ε = B L v between its ends, because charges experience a magnetic force q v × B.

Speed of electromagnetic waves

In vacuum, c = 1/√(μ0 ε0) ≈ 3.00×10^8 m/s. In a medium, the speed is v = c/n, where n is the refractive index.

Wave speed equation

For any periodic wave, speed equals frequency times wavelength: v = f λ. Frequency is set by the source and does not change when the wave enters a new medium; speed and wavelength do.

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). Approaching motion raises the observed frequency; receding motion lowers it.

Standing waves on a string

For a string of length L fixed at both ends, allowed frequencies are f_n = n v/(2L), n = 1, 2, 3, ... The fundamental has one antinode and two nodes.

Sound intensity level

β = 10 log10(I/I0) decibels, with reference intensity I0 = 1×10^-12 W/m². An increase of 10 dB corresponds to a tenfold increase in intensity.

Snell's law

n1 sinθ1 = n2 sinθ2 at an interface between media with refractive indices n1 and n2. Light bends toward the normal when entering a medium with larger n.

Total internal reflection

Occurs when light travels from a higher-index to a lower-index medium at an angle exceeding the critical angle θ_c = arcsin(n2/n1). No refracted ray emerges.

Thin lens equation

1/f = 1/d_o + 1/d_i, with magnification m = -d_i/d_o. Real images have positive image distance and are inverted; virtual images have negative image distance.

Double-slit interference

Constructive interference occurs when d sinθ = m λ, giving bright fringes. On a distant screen, fringe spacing is Δy = λ L/d, where L is the slit-to-screen distance.

Lorentz factor

γ = 1/√(1 - v²/c²). It equals 1 at rest and grows without limit as v approaches c, quantifying time dilation, length contraction, and relativistic mass increase.

Time dilation

A clock moving relative to an observer runs slow: Δt = γ Δt0, where Δt0 is the proper time measured in the clock's rest frame. The effect is symmetric between inertial frames.

Length contraction

An object moving relative to an observer is shortened along the direction of motion: L = L0/γ, where L0 is the proper length measured in the object's rest frame.

Relativistic energy-momentum relation

E² = (p c)² + (m c²)², where E is total energy and m is rest mass. For a photon, m = 0, so E = p c; for a particle at rest, E = m c².

Photoelectric equation

Maximum kinetic energy of emitted electrons is K_max = h f - φ, where φ is the work function. Emission requires f above the threshold f0 = φ/h, regardless of light intensity.

de Broglie wavelength

A particle with momentum p has an associated wavelength λ = h/p = h/(m v). It explains electron diffraction and is measurable for electrons accelerated through a few tens of volts.

Radioactive half-life

The time for half of the nuclei in a sample to decay: T½ = ln2/λ, where λ is the decay constant. The number remaining after time t is N = N0 e^(-λt).

Mass defect and binding energy

The mass of a nucleus is less than the sum of its constituent nucleons; the missing mass Δm corresponds to binding energy ΔE = Δm c². One atomic mass unit equals 931.5 MeV/c².