Field of standard distributions — common mistake

“Treating a long charged wire as a point charge is like using a needle to measure the depth of a swimming pool.”

Applying the point-charge 1/r² law to a long line or sheet gives wrong results; the correct dependences are 1/r for a line and constant for a sheet. The classic trap is mixing up these power laws, especially when the geometry is only ‘very long’ but not infinite.

Memory trick: Never use 1/r² for line or sheet; keep their rules

EMF and internal resistance

“A torch’s battery lights up, but as the bulb draws current the voltage at its terminals falls short of the cell’s EMF.”

A real cell has EMF ε and internal resistance r. When a current I flows, the terminal voltage V = ε – I r. Ignoring r gives a higher voltage than the circuit actually has, causing errors in power calculations.

Memory trick: V = ε – I·r.

Circular and helical motion

“A garden sprinkler spins water in circles while the hose pushes it forward, just as v⊥ makes circular motion and v∥ sets the helix pitch.”

A perpendicular velocity v⊥ in a uniform B makes circular motion with radius r = mv⊥/(qB) and period T = 2πm/(qB). The parallel component v∥ remains unchanged, producing a helix whose pitch = v∥·T. The classic error is using the total speed V in r; only v⊥ matters.

Memory trick: r ∝ v⊥, pitch ∝ v∥

Self and mutual inductance

“Two side-by-side speakers share a bass boost when one’s coil wiggles, like twins feeling each other's heartbeat.”

Self-induced emf ε = -L di/dt; mutual emf ε₂ = -M di₁/dt. The dot convention marks the polarity: dots together give the same induced polarity, dots apart give opposite. Ignoring dot polarity gives a sign error in coupled circuits.

Memory trick: Dots together → same polarity, dots apart → opposite.

Young's double-slit interference — common mistake

“Shining two unsynchronized flashlights through slits never paints clear stripes on the screen.”

Interference needs coherent sources; incoherent or single-slit illumination destroys stable fringes. The slit width also creates a diffraction envelope that modulates the double-slit pattern, reducing visibility if width ≈ separation. The exam trap: ignoring the envelope and assuming any light works.

Memory trick: Coherence required; ignore envelope → wrong

Logic gates

“When you press the power button, the microcontroller’s binary decisions run through NAND gates like a chef’s knife chopping ingredients.”

NAND (or NOR) alone is functionally complete: any Boolean function can be realised using only that gate. A NOT is a NAND with both inputs tied, AND = NAND followed by NOT, OR = NAND of two inverted inputs. The classic trap is assuming a single NAND gives OR directly, which adds hidden inversions and extra gate count.

Memory trick: NAND=NOT(AND); tie inputs→NOT; chain→AND, OR

Antenna height and range

“A TV tower’s horizon expands as its height climbs, like standing on a hill to see farther.”

The radio horizon distance d (km) ≈ 3.57√h (m) because Earth’s curvature limits line-of-sight. Thus doubling antenna height increases range by only √2, not double. A frequent mistake is using a linear h-relation, which over-predicts coverage.

Memory trick: Range ∝ √height (≈3.6√h km)

Stress and strain

“Pressing a thumbtack into cork: force per area is stress; the tiny indentation depth divided by cork thickness is strain.”

Stress is the internal restoring force per unit area (σ = F/A, unit Pa). Strain is the fractional change in dimension (ε = ΔL/L), dimensionless. A frequent trap is writing strain with metre units or mixing up cause (stress) with effect (strain).

Memory trick: σ = F/A (Pa); ε = ΔL/L (no unit).

Uniform circular motion acceleration — common mistake

“A car on a circular track at constant speed still pushes sideways toward the centre.”

Even with constant speed, a curved path requires a centripetal acceleration a = v²/r. The common error is writing a = 0 for uniform speed without checking the trajectory. Always examine the path shape.

Memory trick: Speed steady? Check curvature.

Conduction, convection and radiation — common mistake

“Sunlight entering a car through the window heats the interior – only radiation can cross the vacuum of space.”

The Sun’s energy reaches Earth through empty space, so only radiation can convey heat; convection and conduction need matter. Students often write “heat reaches Earth by convection,” which is impossible in vacuum. After radiation, the atmosphere redistributes energy by convection.

Memory trick: Vacuum ⇒ only radiation transfers heat.

Equipartition and heat capacities — common mistake

“A bike’s gears stay idle when the chain’s slack; similarly vibrational modes stay frozen if kT is too low.”

Equipartition applies only to degrees that are thermally excited. Vibrational modes require kT ≳ hν; below this they are frozen, so C_V is lower than the full-f prediction. The trap: adding vibrational contributions at room temperature for most gases.

Memory trick: Add vib modes only if kT ≫ hν

Capacitor energy

“Charging a capacitor is like filling a bathtub; the water level (voltage) climbs gradually, so you do only half the work of a full-force pump.”

Work done to charge a capacitor equals the area under the V-Q graph, a triangle with height V and base Q, giving U = ½ QV = ½ CV². The trap is to apply U = QV directly, which ignores the rising voltage during charging.

Memory trick: Energy = ½ Q V → half-pump rule.

Hysteresis — common mistake

“A fridge magnet made of high-coercivity alloy would overheat if used as a transformer core, showing the material mismatch.”

Transformer cores need high permeability and low coercivity so the B-H loop is narrow, minimizing energy loss. Permanent magnets require high coercivity and high remanence, giving a wide loop that holds magnetisation. Trap: choosing a material only for its high saturation magnetisation ignores the needed coercivity.

Memory trick: Core: low Hc, high μ; Magnet: high Hc, high Mr.

Excitation versus ionisation — common mistake

“Calling every climb a summit is like calling every upward jump ionisation.”

An upward transition does not always mean ionisation; only when the electron’s energy reaches zero (or positive) does it leave the atom. The trap is to label any excitation as ionisation, ignoring the sign of the final energy.

Memory trick: Only E≥0 = ionisation.

Activity — common mistake

“A kitchen oven’s 2000 W rating tells power, not how hot the food gets; similarly Bq tells decays, not dose.”

Becquerel measures how many nuclei decay each second, not how much energy is deposited in tissue. Absorbed dose (gray) and equivalent dose (sievert) depend on radiation type and energy. Mistaking Bq for dose overestimates risk.

Memory trick: Bq = decays/s, not dose (Gy or Sv)

Meter bridge balance condition — common mistake

“Measuring the bridge wire with a ruler, remember the two segments together must cover the whole wire, like two puzzle pieces forming the complete picture.”

A frequent error is using the lengths of the two segments without confirming they sum to the total wire length. The balance condition R1/R2 = L1/L2 is valid only when L1+L2 equals the full wire length; otherwise the ratio is distorted. Check the total length before applying the formula.

Memory trick: Verify L1+L2 = total wire length.

Relative velocity — common mistake

“A boat crossing a river can’t find its ground speed by just adding boat and river speeds unless they’re straight.”

Relative speed must be vectorial. For opposite directions add magnitudes, same direction subtract, and for perpendicular motions use √(a²+b²). Adding scalars is a classic error.

Memory trick: Opposite → add, same → subtract, perpendicular → √(a²+b²).

KE = ½mv²

“A bowling ball rolling at 4 m s⁻¹ carries four times the kinetic energy of the same ball at 2 m s⁻¹, showing the v² dependence.”

Kinetic energy is KE = ½ m v², valid in an inertial frame. Because of the v² term, doubling speed quadruples KE. A frequent mistake is writing KE = ½ m v or omitting the ½ factor, which halves the correct value.

KE = ½mv²

Memory trick: ½ m v² = half mass times speed squared

streamline flow vs turbulent flow

“Milk flows smoothly in a narrow straw but churns in a wide kitchen sink pipe, illustrating laminar vs turbulent flow.”

Flow regime is set by Reynolds number Re = ρ v D / μ; Re < ~2000 → laminar (smooth), Re > ~4000 → turbulent (chaotic). At bends or sudden expansions turbulence can appear even below the critical Re, a common exam pitfall.

Memory trick: Low Re smooth, high Re chaotic

step-up transformer vs step-down transformer

“A transformer is like a water pipe: a narrow outlet (step-up) gives high pressure (voltage) but low flow (current).”

For an ideal transformer Vₛ/Vₚ = Nₛ/Nₚ and Iₛ/Iₚ = Nₚ/Nₛ, so V·I ≈ constant. A step-up (Nₛ>Nₚ) raises voltage and lowers current; a step-down does the opposite. The trap: assuming current always rises with voltage— in a step-up the secondary current is reduced, and real devices have losses that break exact power constancy.

Memory trick: V ∝ N, I ∝ 1/N – power stays same.

Parallax error

“Reading the fuel gauge from the passenger seat gives a wrong level, just as viewing a scale from an angle creates parallax error.”

Parallax error occurs when the eye is not perpendicular to the scale, making the pointer appear displaced. Align the eye straight with the scale or use a mirror behind it. The trap: side-view reading adds a systematic error.

Memory trick: Eye straight → no shift

Elastic PE of a spring

“The spring inside a ball-point pen stores energy as you press the tip down.”

For an ideal Hooke’s law spring, U = ½ k x², where x is measured from the natural length. Beyond the elastic limit the formula breaks down; using it there overestimates stored energy – a frequent mistake.

U = k x²/2

Memory trick: U = ½ k x² – half the triangle area under F–x

Torque and angular momentum

“When a figure skater pulls in her arms, the spin speeds up, but about the rink’s fixed centre pole τ = dL/dt holds exactly.”

For an origin O fixed in an inertial frame τ_ext(O)=dL_O/dt. If O moves with velocity v_O, the correct relation is τ_ext= dL/dt + v_O×P (P=MV_CM). At the centre of mass v_O=V_CM, so the extra term vanishes. The exam trap is to apply τ=dL/dt without confirming the origin is inertial or the CM.

Memory trick: τ=dL/dt only for inertial or CM origin; otherwise add v_O×P.

Total energy of an orbit

“A satellite in a circular orbit carries half the magnitude of its potential energy as kinetic, giving total energy -GMm/2r.”

In a circular orbit kinetic energy K = +GMm/2r and potential U = -GMm/r, so total E = K+U = -GMm/2r. The trap: assuming a higher orbit has lower (more negative) energy, while it actually becomes less negative.

Memory trick: E = -½ U; higher r → E less negative.