PAU Physics (Castilla y León) study plan

Derive Kepler's third law from Newton's law of gravitation and state the conditions under which it holds.

Compute gravitational field and potential for point masses and for a uniform spherical shell, distinguishing inside and outside regions.

Calculate escape velocity and orbital energy for circular orbits, and relate total energy to the semi-major axis for elliptical orbits.

Solve at least 10 PAU-style problems on satellites, geostationary orbits and energy changes between orbits.

Apply superposition to find the net field and potential of discrete point-charge configurations in two dimensions.

Use Gauss's law to derive the field of spheres, infinite lines and infinite planes of charge.

Compute electric potential energy of assembled charge systems and the work needed to move a charge between points.

Convert fluently between field, potential and potential-energy language in written answers.

Describe the motion of a charged particle entering a uniform electric field, including parabolic deflection and velocity selection.

Solve capacitor problems: capacitance of parallel plates, stored energy, and the effect of inserting a dielectric.

Explain electrostatic shielding and the field inside a conductor in equilibrium.

Answer conceptual short questions in the exact phrasing PAU expects, with justification in two or three sentences.

Compute magnetic force on moving charges and current-carrying wires, including direction rules.

Apply the Biot-Savart law and Ampere's law to straight wires, loops and solenoids.

Derive the radius and period of circular motion of a charge in a uniform magnetic field.

Explain the operation of a mass spectrometer and a velocity selector quantitatively.

State and apply Faraday's and Lenz's laws to changing flux through loops, including rotating coils and moving rods.

Compute induced emf and current direction in at least 8 varied induction scenarios.

Distinguish transverse from longitudinal waves and write the equation of a harmonic wave from given parameters.

Apply the wave equation, superposition and standing-wave conditions for strings and pipes.

Solve sound problems using the Doppler effect, intensity levels in decibels, and resonance in open and closed pipes.

Apply Snell's law and total internal reflection, and compute critical angles and apparent depths.

Construct ray diagrams for mirrors and thin lenses and verify them with the thin-lens and mirror equations.

Analyse simple optical instruments such as the magnifying glass and the compound microscope.

Apply time dilation, length contraction and relativistic mass-energy relations to numerical problems.

Compute photon energy, work function, stopping potential and de Broglie wavelength in photoelectric and matter-wave problems.

Balance nuclear equations and calculate mass defect, binding energy and activity with half-life decay.

State the postulates of special relativity and of Bohr's model and use them to justify quantitative results.

Propagate uncertainties through sums, products and powers, and report results with correct significant figures.

Interpret linearised graphs, extract slopes with units, and judge whether a fit supports a hypothesis.

Identify apparatus, control variables and sources of systematic error in standard PAU laboratory scenarios.

Complete two full past-paper simulations under exam conditions and mark them strictly.