Magnetic dipole moment — common mistake

“When you watch iron filings swirl around a bar magnet, the lines you see go north→south, but the magnet’s own moment still points S→N inside.”

The magnetic field lines you draw outside a magnet go from north to south, but the magnet’s dipole moment still points from its hidden south to north. Mistaking the external line direction for the moment flips the sign of τ = m × B and gives wrong energy. Keep the moment S→N inside, regardless of outside line flow.

Memory trick: Field lines N→S outside, moment S→N inside.

Rutherford scattering and nuclear atom — common mistake

“When a marble hits a tiny steel ball in a pinball machine, it scatters sharply—just like α-particles off a gold nucleus revealed the atom’s core.”

Rutherford’s scattering showed a tiny, massive nucleus surrounded by empty space, but a classical orbit would make electrons spiral inward, so the model cannot explain atomic stability or line spectra. Bohr introduced quantised circular orbits to fix this. In exams, avoid attributing spectral lines to Rutherford’s model; only Bohr’s postulates give discrete energies.

Memory trick: Rutherford → Nucleus; Bohr → Quantised lines

Nuclear size and density — common mistake

“If you double the marbles inside a ball, its size grows only a little, not twice.”

A common slip is to think radius ∝A. In reality R∝A^(1/3); doubling A increases R by only ∛2≈1.26. The trap is forgetting the exponent, which makes the radius error huge for large A.

Memory trick: Radius ∝ A^(1/3), not A.

Least count and instrument reading — common mistake

“When a bathroom scale shows +0.5 kg before you step on, you must subtract that 0.5 kg from the weight displayed.”

If the instrument has a positive zero error, the observed reading is higher than the true value; therefore corrected reading = observed – zero error. Many students mistakenly add the error, giving a larger result.

Memory trick: Positive zero error → subtract; negative → add.

Instantaneous velocity — common mistake

“When a runner pauses at a turn, the GPS shows zero average speed for that segment, but the instant speed is still defined.”

Average velocity uses total displacement over total time, while instantaneous velocity is the limit of Δx/Δt as Δt→0. Mistaking one for the other leads to wrong answers, especially when the motion is non-uniform. Remember: only the derivative gives the instant speed.

Memory trick: Avg ≠ instant; instant = derivative.

Work — common mistake

“Sliding a bag across a floor while holding it upright does no work, because the upward force is perpendicular to the horizontal displacement.”

Work = F·s = Fs cosθ. If θ = 90°, cosθ = 0, so the force does zero work. Students often forget the cosine factor and assume any force contributes. Only the component of force along the displacement does work; a normal or tension perpendicular to motion gives none.

Memory trick: Perp → No Work

Pressure in a fluid — common mistake

“A coin at 5 cm below water feels the same push in a bathtub as in a thin test tube.”

Pressure at a given depth depends only on ρ, g and h, not on the vessel’s width. Pascal’s law makes the force equal in all directions. The exam trap: assuming a wider container raises pressure – it does not.

Memory trick: Same h → same P, regardless of container width.

Path difference & fringes — common mistake

“A double-slit is like two synchronized flashlights; when their flashes line up (0 or 2π) the center spot shines bright, but a half-cycle lag makes it dark.”

For Young’s double-slit, constructive interference occurs when the path difference Δ = nλ (bright fringe) and destructive when Δ = (n+½)λ (dark fringe). The central fringe is bright only if the two sources are in phase; an extra π phase shift (e.g., from reflection) flips it dark. Forgetting this phase condition is a common exam trap.

Memory trick: Bright: n·λ, Dark: (n+½)·λ

Reactance — common mistake

“A microwave’s 2.45 GHz magnetron sees a tiny capacitor reactance, not the 50 Hz value used at home.”

Reactance depends on the operating angular frequency. Using the Xc value measured at mains (50 Hz) for the magnetron’s 2.45 GHz leads to huge error. Always recalculate Xc = 1/ωC for the specific ω.

Memory trick: Never copy Xc; recalc for each ω.

Forward & reverse bias — common mistake

“Opening a garden hose forward lets water gush; turning it opposite stops flow but a few drops still leak, and high pressure can burst it.”

A diode conducts large current when forward-biased; in reverse bias only a tiny leakage flows until the breakdown voltage, where a large reverse current appears. Exam trap: treating reverse current as zero in bias calculations or ignoring breakdown limits.

Memory trick: Forward = Flow, Reverse = Rest (tiny drip)

Combination of errors in a sum

“Weighing two almost equal apples together hides the tiny difference because the scale’s absolute error dominates.”

When quantities are added or subtracted, their absolute uncertainties (Δ) add linearly. The resulting relative error can become huge if the numbers nearly cancel, making the difference unreliable. Many miss this and treat subtraction as reducing error.

Memory trick: Add Δs for + or –

Elastic collision of equal masses

“Two identical billiard balls hitting head-on on a pool table simply trade their speeds.”

For m₁ = m₂ in a 1-D elastic collision, momentum and kinetic-energy conservation give v₁' = v₂ and v₂' = v₁. This swap holds only for motion along the line of impact; in oblique collisions only the normal components exchange. Applying the rule in 2-D gives wrong results.

Memory trick: Equal masses → swap normal components.

Couple

“Opening a door by pushing opposite ends makes it spin without sliding.”

A couple is two equal, opposite, parallel forces separated by distance d; net force zero, net torque = F·d, same about any point. The trap: collinear opposite forces cancel without producing torque.

Memory trick: Equal opposite, parallel, separated → pure torque

Weightlessness in orbit

“An astronaut feels weightless just like a passenger in a free-falling elevator that never reaches the floor.”

In orbit both astronaut and station are in continuous free fall, so the normal force is zero; only tidal forces give a tiny residual weight. The trap: assuming gravity vanishes at orbital altitude – g is still ~8.7 m/s².

Memory trick: Free fall together → no normal force

Average energy in SHM

“A child on a swing spends equal time climbing and descending, so average kinetic and potential energies balance.”

In one complete SHM cycle the time-average of kinetic energy equals that of potential energy, each being half the total mechanical energy (⟨KE⟩=⟨PE⟩=E/2). The equality holds only after averaging, not at every instant.

Memory trick: SHM average: KE̅ = PE̅ = E/2.

End correction in pipes

“A flute’s tone is slightly lower than its measured length predicts because the air vibrates a bit beyond the open holes.”

In an open pipe the antinode forms just outside the opening, so the effective acoustic length is L_eff = L + 0.6 r for each open end (r = pipe radius). Closed ends have a node at the wall, so no correction. A frequent mistake is adding 0.6 r to both ends of a pipe that is closed at one side.

Memory trick: Open end → +0.6 r; closed end → +0

Stefan-Boltzmann law

“A glowing charcoal grill radiates like a blackbody, while a polished aluminium pot at the same heat glows far less.”

Stefan-Boltzmann: P = εσAT⁴, with ε=1 for a perfect blackbody. Real surfaces have ε<1, so neglecting emissivity overestimates radiated power. The trap is to forget ε and treat every object as a blackbody.

P ~ T⁴

Memory trick: P=εσAT⁴ → check ε

Capacitance of an isolated sphere

“A lone metal ball on a kitchen counter stores charge like a tiny capacitor; its capacitance grows linearly with its radius.”

An isolated conducting sphere and infinity act as the two plates of a capacitor, giving C = 4π ε0 R. The result follows from V = Q/(4π ε0 R). A trap is mixing this with the parallel-plate formula or missing the 4π factor, which underestimates C.

Memory trick: C = 4π ε0 R → four-pi epsilon-R

Maximum power transfer

“A radio’s antenna draws the strongest signal when its impedance exactly matches the transmitter’s output impedance, just like a perfectly tuned earphone.”

Maximum power to a load occurs when RL equals the source’s internal resistance (or impedance for AC), giving Pmax = V²/4r and 50% efficiency. Matching maximizes delivered power, not overall efficiency; for complex sources impedance matching is required.

Memory trick: Max power when load = source resistance → each gets half the power

Hall effect

“When a river (current) flows across a magnetic field, the water (charge) is pushed to one bank, creating a measurable voltage like a water-level gauge.”

A magnetic field B deflects moving charge carriers, producing a transverse Hall voltage V_H = I B/(n e d). The sign of V_H tells whether the dominant carriers are positive or negative. Students often forget the sign dependence and assume V_H is always positive, leading to wrong carrier identification.

Memory trick: V_H = I·B/(n·e·d); sign = carrier type.

Energy stored in an inductor

“When a solenoid lights up, the magnetic field inside stores the same energy as a compressed spring.”

The magnetic field of an inductor stores energy U = ½ L I² at any instant, where I is the instantaneous current (use peak value for sinusoidal). It can also be written U = Φ²/(2L). Trap: substituting I_rms instead of peak I underestimates the stored energy by a factor of ½.

U = L I²/2

Memory trick: ½ L I² = ½ Φ²/L

Total internal reflection

“A fiber-optic cable guides internet signals by bouncing light inside like a marble in a glass tube.”

When light travels from a denser medium (n1) to a rarer one (n2) and incidence > θc = sin⁻¹(n2/n1), refraction ceases and all light reflects – total internal reflection. Applying it with n1<n2 gives no TIR, a classic mistake.

Memory trick: TIR: dense→rare, θ>arcsin(n₂/n₁)

Properties of nuclear force

“Nuclear force is like a magnet that only works when nucleons are within a few femtometers, ignoring charge.”

The strong nuclear force acts only over ~1–2 fm, is charge-independent (same for pp, nn, pn) and saturates—each nucleon feels the force from only a few nearest neighbours. Trap: treating binding energy as ∝A² instead of ∝A.

Memory trick: Short, charge-independent, saturates (few partners).

Order of the EM spectrum

“A rainbow shows red to violet; beyond violet lies ultraviolet, then X-rays and gamma rays, each with shorter wavelength.”

From longest to shortest wavelength the spectrum is: radio → microwave → infrared → visible → ultraviolet → X-ray → gamma. Frequency and photon energy rise in the same order. Trap: many mix up microwave and radio; remember radio waves have the longest λ, then microwaves.

Memory trick: R M I V U X G – radio to gamma