PAU Physics (Andalusia) study plan

Derive the gravitational field of a point mass and of a uniform spherical shell using Gauss's law for gravitation, and state where the shell theorem fails.

Compute gravitational potential energy and escape velocity for a planet, keeping sign conventions explicit throughout.

Apply Kepler's three laws quantitatively to elliptical orbits, calculating period from semi-major axis and locating periapsis and apoapsis speeds via conservation of angular momentum and energy.

Solve at least eight PAU-style problems on satellite energy, orbital transfer, and geostationary orbit conditions, writing each answer with units and significant figures.

Derive the electric field of discrete charge distributions and of continuous ones (rod, ring, infinite sheet) by integration and by Gauss's law.

Calculate electric potential from a field by line integration and verify consistency by taking the gradient back to the field.

Apply Gauss's law to spherical, cylindrical, and planar symmetry, and explain why it gives no shortcut for a finite rod.

Solve six PAU-style problems combining field, potential, and work done moving a charge between two points.

Draw side-by-side comparisons of gravitational and electrostatic fields: inverse-square form, sign of the source, superposition, and potential reference point.

Solve problems where a charged particle moves in combined gravitational and electric fields, such as Millikan-type and orbiting-charge setups.

Re-derive the most-missed results from weeks 1 and 2 from memory in under 15 minutes each.

Complete a timed 45-minute mixed set of gravitational and electrostatic questions and classify every mistake as conceptual, algebraic, or unit-related.

Apply the Lorentz force to charged particles in uniform magnetic fields, deriving the radius and period of circular motion and the helix pitch for a velocity with a field-parallel component.

Compute the magnetic field of straight wires, loops, and solenoids using Biot-Savart and Ampere's law, and find the force between parallel currents.

State Faraday's and Lenz's laws precisely and determine induced current direction in changing-flux scenarios, including a bar sliding on rails and a rotating coil.

Calculate motional emf and the mechanical power needed to maintain constant speed in an induced-current circuit.

Derive the emf of a rotating coil and connect it to the sinusoidal form of alternating current, identifying peak and rms values.

Write and apply the wave equation for a traveling harmonic wave, extracting amplitude, wavelength, frequency, and phase from a given expression.

Analyze standing waves on strings and in open and closed pipes, and compute beat frequencies from two superposed waves.

Solve problems on the Doppler effect for moving source and moving observer, including the supersonic case and shock-wave geometry.

Apply Snell's law, total internal reflection, and the thin-lens and mirror equations to locate images and state whether they are real, virtual, inverted, or upright.

Explain and compute interference and diffraction effects: Young's double slit, single-slit minima, and thin-film interference with the correct phase-shift rule.

Describe polarization and Malus's law, and compute transmitted intensity through one or two polarizers.

Solve a mixed set of six optics problems, at least two requiring a ray diagram drawn to scale.

Apply the postulates of special relativity to compute time dilation, length contraction, and relativistic momentum and energy, including rest energy and total energy.

Solve two-body and decay problems using mass-energy equivalence and conservation of momentum in the relativistic regime.

Apply the photoelectric effect equation to find threshold frequency, work function, and stopping potential, and interpret intensity versus frequency graphs.

Use de Broglie wavelength, Bohr energy levels, and the uncertainty principle to compute transitions and spectral lines.

Write balanced nuclear equations for alpha, beta, and gamma decay and compute activity and half-life from decay data.

Complete two full timed mock exams under PAU conditions, one at the start of the week and one at the end, and compare scores item by item.

Re-solve every problem missed in weeks 1 to 7 without notes, and confirm each is now correct on the first attempt.

Recite from memory the ten formulas most likely to be needed across all five domains, with units and sign conventions.

Review exam technique: showing intermediate steps, stating the physical principle invoked, and reporting answers with correct significant figures and units.