PAU Physics (Castilla y León) common mistakes
PAU Physics (Castilla y León) · Understand the traps and how to avoid them.
When asked for gravitational field strength or potential at a point between or outside two masses, the student adds the magnitudes of g (or V) from each mass without regard to direction or sign, giving a scalar sum instead of the vector/signed sum.
In electrostatics courses the field between two charges of opposite sign is often computed as a magnitude difference, and students transfer a 'just add the numbers' habit; also g and V are introduced as scalars in early mechanics, so the vector character of g and the negative sign convention for V are not consolidated.
What to do instead
Before substituting numbers, draw the field vectors at the point for each source mass and label them with arrows toward each mass; then assign a coordinate axis and write g_total as an algebraic sum of components. For potential, state explicitly that V = -GM/r is always negative and that potentials add algebraically, so two masses give V = -GM1/r1 - GM2/r2. Practise one point on the line joining the masses, one off-axis, and one at the midpoint, checking that g can be zero where V is not.
For a satellite, the student sets the gravitational force equal to mv²/r but then uses the satellite's own radius or the altitude as r, or equates centripetal acceleration to g at the surface rather than at the orbit.
Students memorise 'F = mv²/r' and 'g = GM/r²' as separate formulas and do not internalise that r is measured from the centre of the central body and that the same r appears in both expressions; altitude is what the problem statement highlights, so it gets substituted directly.
What to do instead
Adopt a fixed routine: write r = R_body + h first, in the same line, before any formula. Then derive v = sqrt(GM/r), T = 2π sqrt(r³/GM) from the force balance rather than recalling them, and check the limiting case h = 0 against the known surface value. Redo one geostationary-orbit and one low-orbit problem insisting that every r in the working is written as (R + h).
In electric-field problems the student computes the potential at a point by adding magnitudes of kQ/r without signs, or confuses potential with field by using 1/r² for V or 1/r for E.
Both quantities are written as 'kQ over something r' and the inverse-square versus inverse-first distinction is learned by pattern-matching rather than by derivation; the sign of V for a negative charge is easily lost because only the magnitude of Q is substituted.
What to do instead
Derive V from E once (V = -∫E·dr) so the 1/r versus 1/r² relationship is owned, not memorised. Then build a two-column table for a dipole: at the midpoint E is large and V is zero; on the axis outside E and V both point/are signed consistently. Always carry the sign of the source charge into the expression and state the reference point (V = 0 at infinity).
When a charged particle enters a region with both electric and magnetic fields, or moves at an angle to B, the student adds the electric and magnetic forces as magnitudes or ignores that the magnetic force is perpendicular to v, treating the path as parabolic in all cases.
Projectile motion with a constant force is over-learned, so any 'charged particle in a field' is assumed to follow a parabola; the vector cross product and its velocity-dependent direction are not practised enough to be applied fluently.
What to do instead
Write F = qE + qv×B as a vector equation every time and evaluate the cross product explicitly with components or the right-hand rule before adding. Classify the motion first: if F is constant and parallel to v, straight-line acceleration; if F is constant and perpendicular to v, parabola; if F is always perpendicular to v (pure magnetic), circle with r = mv/(qB). Solve one velocity-selector problem (crossed E and B, net force zero) and one helical-motion problem to fix the distinction.
Applying Lenz's law, the student states the direction of the induced current by looking at the sign of the flux rather than its change, so the current is given as opposing the field instead of opposing the change in flux.
The phrase 'opposes the change' is memorised but the operational step - compare flux before and after, decide whether it is increasing or decreasing - is skipped, and the right-hand rule for the coil is applied to the external field rather than to the induced field.
What to do instead
Use a three-step written procedure: (1) define the area vector and compute Φ = B·A with a sign; (2) state whether Φ is increasing or decreasing; (3) choose the induced B that opposes that change, then get the current direction from the right-hand grip rule. Verify with the force-on-the-moving-wire approach: the induced current must produce a force opposing the motion that caused it.
In an induction problem the student differentiates the flux correctly but drops the number of turns N, or uses the peak emf when the question asks for the average, or forgets that a rotating coil gives a sinusoidal emf with peak NABω.
Faraday's law is often written as ε = -dΦ/dt with a single loop in textbook derivations, so N is treated as decoration; average versus instantaneous values are conflated because both appear in the same topic.
What to do instead
Always write ε = -N dΦ/dt with N visible in the first line. Distinguish explicitly: instantaneous emf for a rotating coil is ε = NABω sin(ωt) with peak NABω; average emf over a quarter turn from maximum flux to zero flux is NABω·(2/π) per the ΔΦ/Δt definition. Do one problem each for a rotating coil, a sliding rod, and a changing B, and state which quantity is being asked before calculating.
For a standing wave on a string or in a pipe, the student uses the wrong boundary condition - treating a closed pipe end as a displacement antinode, or forgetting that a free end is a displacement antinode but a pressure node - and so gets the wrong harmonic series.
The rule 'node at a fixed end, antinode at an open end' is learned for strings and then applied to pipes without distinguishing displacement from pressure, and open-open versus open-closed series (all harmonics versus odd only) are mixed up.
What to do instead
Write the boundary condition at each end before choosing a formula, and specify whether you are describing displacement or pressure. Then use L = nλ/2 for two fixed/closed ends, L = (2n-1)λ/4 for one closed and one open end, and check the fundamental by sketching the standing wave inside the given length. Test the result against the known frequency ratio 1:3:5 for a closed pipe.
In geometrical optics the student applies the thin-lens or mirror equation with a sign convention chosen ad hoc - mixing real-is-positive and Cartesian conventions within one problem - and then misinterprets a negative image distance as 'no image'.
Different textbooks and the regional syllabus use different sign conventions, and students switch between them mid-calculation; the physical meaning of a negative image distance (virtual image on the same side as the object for a lens) is not tied to a ray diagram.
What to do instead
Declare the convention at the top of every solution (e.g. Cartesian: distances measured from the optical centre, positive in the direction of incident light) and never change it. Draw the ray diagram first with two principal rays to predict whether the image is real or virtual and on which side, then let the algebra confirm it. Interpret the sign of the magnification to state orientation, and check the result against the diagram.
In relativity or quantum problems the student substitutes into E = mc² or E = hf without checking whether the regime is relativistic or whether photon momentum p = h/λ (not hf/c with the wrong λ) is required, and uses classical kinetic energy for electrons in the photoelectric effect.
The formulas are visually similar and the conditions of validity (v comparable to c; photon versus massive particle) are stated once and then forgotten; the photoelectric equation is often reduced to a single formula without the work function being identified from a graph.
What to do instead
Before calculating, write a one-line regime check: for a particle, compute v/c or the rest energy and compare with the kinetic energy; for a photon, note m = 0 so E = pc = hc/λ. For the photoelectric effect, always write hf = W + K_max and identify W from the threshold frequency or the intercept of the K_max versus f graph, with slope h. Do one Compton-style momentum problem and one de Broglie wavelength problem to separate p = h/λ from E = hf.
In the experimental question the student reports a result with more significant figures than the instrument allows, omits the uncertainty, or propagates uncertainty by simply averaging the absolute errors of the inputs instead of combining them in quadrature for independent random errors.
Numerical answers are copied straight from the calculator display, and the treatment of uncertainties is treated as a formality rather than a calculation; the distinction between resolution, reading uncertainty, and combined uncertainty is not practised.
What to do instead
Set a fixed reporting protocol: record the resolution of each instrument, quote the mean with its absolute uncertainty to the same decimal place, and give the relative uncertainty. For combined quantities use the standard rules - add absolute uncertainties for sums, add relative uncertainties for products and quotients, multiply the relative uncertainty by |n| for a power - and combine independent contributions in quadrature when the syllabus requires it. Finish by checking that the number of significant figures in the final answer matches the uncertainty.