Basque PAU Physics common mistakes
Basque PAU Physics · Understand the traps and how to avoid them.
In orbital-mechanics problems, writing the centripetal condition as GMm/r² = mv²/r and then solving for speed while forgetting that r must be measured from the centre of the planet (r = R + h), not from the surface.
Candidates memorise the formula with a bare 'r' and substitute the altitude h directly, because the problem statement often gives h prominently and R only in a data table. The symbol r looks like a single quantity, so the addition is skipped under time pressure.
What to do instead
Before substituting, always draw the orbit and label the radius explicitly as r = R_planet + h, writing this line on paper. Check the answer dimensionally and numerically: a satellite at 400 km altitude around Earth must give r ≈ 6.77×10⁶ m, not 4×10⁵ m. Keep a habit of writing 'r = R + h' as a fixed first step in every satellite problem.
Treating gravitational potential V = -GM/r as a positive scalar and then adding it directly to kinetic energy without the negative sign, or confusing potential with field magnitude when comparing two points.
Students conflate the field (which points toward the mass and has magnitude GM/r²) with the potential (a negative scalar with 1/r dependence). The minus sign is easy to drop because many textbook exercises focus on magnitude only, and the inverse-square versus inverse-first-power distinction blurs.
What to do instead
Memorise the pair as a table: field g = -GM/r² û (vector, points inward), potential V = -GM/r (scalar, negative, zero at infinity). Practise one exercise where you compute both at the same point and state units (N/kg versus J/kg). When using energy conservation, write E = ½mv² - GMm/r and verify that bound orbits have E < 0.
In Coulomb-law superposition problems with three or more charges, computing each force magnitude correctly but then adding them algebraically instead of as vectors, ignoring direction, or misassigning the sign of the force from a negative charge.
The formula F = kq₁q₂/r² gives a number, and candidates plug numbers into a single line without sketching the geometry. The vector nature is invisible in the algebra, and negative charges make the sign convention confusing.
What to do instead
Adopt a mandatory sketch step: place charges on axes, draw each force arrow at the test charge, and resolve into components before any arithmetic. Use the convention that the force on the test charge points away from a positive source and toward a negative source, and encode direction in the arrow, not in the sign of the magnitude. Sum components separately and report the resultant with angle.
Applying Gauss's law by writing the flux as E·A with the full surface area of a sphere even when the charge distribution is a shell or a line, or claiming E = 0 inside a conductor but then still using the enclosed charge to compute a nonzero field there.
The law Φ = Q_enc/ε₀ is remembered as a formula for E rather than as a statement about flux through a chosen Gaussian surface. Candidates pick the wrong surface (sphere when cylindrical symmetry applies) and forget that Q_enc, not total Q, enters.
What to do instead
For every Gauss problem, first state the symmetry (spherical, cylindrical, planar), then choose the surface that matches it, then write Q_enc explicitly. For a conducting shell, do two separate cases: r < R gives Q_enc = 0 hence E = 0; r > R gives Q_enc = total charge. Verify continuity of E at the boundary as a self-check.
Using the right-hand rule for the magnetic force F = qv×B but assigning the force direction to a stationary charge or to a charge moving parallel to B, and forgetting that the magnetic force does no work so it cannot change the speed.
The cross product is mechanical and gets applied without checking the angle, and the v×B geometry is hard to visualise in three dimensions on paper. The 'no work' property is stated in class but rarely practised in problems.
What to do instead
Before computing, check sinθ: if v is parallel or antiparallel to B, state F = 0 immediately. Draw the three vectors with a consistent 3D sketch (v, B, F mutually perpendicular) and confirm with the right-hand rule twice. In circular-motion problems inside a field, write that the magnetic force provides the centripetal force and that kinetic energy is constant, which fixes the radius r = mv/(qB).
Applying Faraday's law as ε = -dΦ/dt but then reporting only the magnitude and ignoring the direction of the induced current, or failing to notice that flux changes because the area changes (moving rod) rather than because B changes.
Lenz's law requires reasoning about the change in flux, which is conceptually harder than the derivative, and the minus sign is often dismissed as a formality. Candidates also default to 'B is changing' because most worked examples vary B.
What to do instead
For every induction problem, write three lines before calculating: (1) what is Φ = B·A·cosθ now, (2) which factor changes with time, (3) which way the induced field must point to oppose that change. Then compute magnitude and state current direction explicitly. Practise at least one moving-rod and one rotating-coil example to cover area-change and angle-change cases.
In wave superposition and interference, adding amplitudes of two waves without regard to phase difference, or claiming two waves always interfere constructively because they have the same frequency.
Students treat amplitude as an additive scalar and forget that the resultant depends on the phase difference Δφ = 2πΔx/λ. The path-difference-to-phase conversion is a separate step that is often skipped.
What to do instead
Always convert a path difference to a phase difference first: Δφ = 2πΔx/λ, then use A_resultant² = A₁² + A₂² + 2A₁A₂cosΔφ. State the condition for constructive (Δx = nλ) and destructive (Δx = (n+½)λ) interference explicitly before substituting numbers, and check that the answer lies between |A₁ - A₂| and A₁ + A₂.
In Doppler-effect problems, using the same sign convention for a moving source and a moving observer, or applying the formula to light without noting that only relative motion matters.
The formula f' = f(v ± v_o)/(v ∓ v_s) has four sign combinations, and candidates memorise one version and reuse it. The physical meaning of each sign (approaching raises frequency) is not tied to the algebra.
What to do instead
Derive the sign from physics each time: approaching motion always increases observed frequency, receding decreases it. Write the general form and decide each sign by asking 'is the source moving toward or away from the observer?' Then check the limiting case: if v_s = v, the observed frequency should blow up for an approaching source.
Using the thin-lens or mirror equation 1/f = 1/s + 1/s' with the wrong sign for a virtual image or a diverging lens, and then reporting a real image where the geometry gives a virtual one.
The Cartesian sign convention (distances positive on the outgoing side) is easily inverted, and virtual images produce negative s' values that candidates 'correct' to positive because a negative distance seems unphysical.
What to do instead
Fix one sign convention at the start of the course and write it on every solution: for lenses, s positive on the incident side, s' positive on the outgoing side, f positive for converging. Interpret the sign of s' explicitly ('negative means virtual, same side as object') and cross-check with a ray diagram showing whether rays actually converge.
In the photoelectric effect, using the intensity of light to argue that electrons are emitted with greater kinetic energy, or writing hf = φ + E_k without checking whether f exceeds the threshold frequency.
Classical wave intuition says brighter light means more energetic electrons, and the photon model is learned as a formula rather than as a threshold condition. Candidates plug numbers into Einstein's equation even when no emission is possible.
What to do instead
Before using hf = φ + E_k, compute the threshold frequency f₀ = φ/h and compare with the incident frequency; if f < f₀, state that no emission occurs and E_k = 0. Separately state that intensity controls the number of photons (current), not the energy per electron. Solve one problem with f below threshold to internalise the check.
Reporting a laboratory result as a single number with no uncertainty, or adding absolute uncertainties of quantities that are multiplied rather than added, and drawing a best-fit line through the first and last data points instead of through the trend.
Uncertainty propagation rules (add absolute for sums, add relative for products) are confused because both involve 'adding errors', and graphing software encourages joining points rather than fitting. Candidates also treat the slope as a bare number without units.
What to do instead
Adopt a fixed procedure: for sums and differences add absolute uncertainties; for products and quotients add relative uncertainties; for powers multiply the relative uncertainty by the exponent. Report results as (value ± uncertainty) with consistent significant figures and units. For graphs, plot error bars, draw a line of best fit by eye or least squares (not point-to-point), and compute the slope from two widely separated points on the fitted line, stating its units.