Faraday's and Lenz's laws — common mistake

“A bicycle dynamo’s wheel cuts magnetic field lines, generating voltage, but a coil rotating about its own axis in a uniform field shows no emf because its linked flux stays constant.”

Faraday’s law (ε=−dΦ/dt) applies to a stationary loop; a changing magnetic flux induces emf. For moving conductors, emf arises only if the motion changes the flux linked with the closed circuit (Lorentz force). The exam trap: assuming any motion in a magnetic field creates emf—check flux change of the entire loop.

Memory trick: No flux change = no emf; motion ≠ emf unless flux varies.

Young's double-slit interference

“Two narrow slits act like twin speakers, creating alternating loud-soft spots on a distant wall.”

Bright fringes occur when path difference = mλ, giving fringe spacing β = λD/d under the small-angle approximation (sinθ≈y/D). The trap: using β = λD/d when D is not ≫ d, which requires the exact sinθ = mλ/d relation.

Memory trick: β = λD/d, y = mβ (small angle)

Zener diode voltage regulation

“A Zener diode in reverse is a pressure-release valve that snaps open at a set voltage, holding the circuit’s pressure steady.”

In reverse breakdown a Zener maintains a nearly constant voltage Vz. For Vz<5 V tunnelling dominates; >5 V avalanche dominates. A series resistor limits current. Trap: forgetting the resistor and exceeding power rating destroys the diode.

Memory trick: Zener = Zero-change voltage after breakdown

Amplitude versus frequency modulation

“AM is like a dimmer switch changing brightness; FM tweaks the pitch of a whistle.”

In AM the carrier’s amplitude follows the message, so any amplitude noise directly appears in the output. FM varies the carrier’s frequency; amplitude noise has little effect, giving better fidelity, but FM needs a bandwidth about twice the sum of the maximum deviation and the modulating frequency (Carson’s rule). Ignoring FM’s larger bandwidth leads to over-estimating channel capacity.

Memory trick: AM = amp, FM = freq, noise ↓

Viscosity temperature dependence

“Stirring a pot of hot soup is easier than stirring the same soup when it’s cold.”

For liquids η≈A·exp(E/RT); increasing T reduces the exponential term, so viscosity drops. For ideal gases kinetic theory gives η∝√T, so viscosity rises with temperature. A frequent exam trap is to treat gas viscosity like a liquid’s and write η∝1/T – it’s opposite.

Memory trick: Liquid = Less when hot; Gas = Grow (√T) when hot.

Uniform circular motion acceleration

“Whirling a stone on a string feels a pull toward the hand even though its speed feels unchanged.”

In uniform circular motion speed is constant but velocity changes direction, giving a centripetal acceleration a = v²/r toward the centre. Toppers note that a is non-zero even when ω is constant. The mistake is assuming zero acceleration because speed doesn’t vary.

Memory trick: v constant → a = v²/r inward.

Conduction, convection and radiation

“A metal spoon gets hot by conduction, a pot of soup by convection, and the Sun warms Earth by radiation.”

Conduction transfers heat through molecular collisions in solids, convection carries heat with bulk motion of fluids, and radiation transports energy as electromagnetic waves without any medium. Real problems often involve a combination, and the trap is to assume convection works in a vacuum where only radiation can occur.

Memory trick: Solid: collide; Fluid: flow; Space: glow.

Equipartition and heat capacities

“Adding extra blades to a kitchen blender lets it stir more ways, just as extra active modes raise a gas’s heat capacity.”

In the classical limit each active quadratic degree contributes k_BT/2 per molecule, giving U = f nRT/2, C_V = fR/2 and γ = (f+2)/f. Toppers note that γ drops when vibrational modes become active; using γ=5/3 for all gases is wrong.

Memory trick: γ = (f+2)/f → more f, smaller γ

Dielectric polarisation — common mistake

“A sealed balloon (isolated) heated expands, while a balloon tied to a pump (battery) keeps its volume constant.”

When a capacitor is isolated, the charge Q cannot change; inserting a dielectric therefore lowers the voltage and raises C by K. When the plates stay connected to a battery, the voltage is forced to stay constant, so the charge increases by K. Mixing these two situations leads to wrong answers.

Memory trick: Isolated? Q stays; Connected? V stays.

Hysteresis

“Cycling a transformer core draws a racetrack on the B-H screen; the loop’s area is the heat you feel.”

A hysteresis loop on a B-H plot shows that magnetisation lags the applied field; the enclosed area equals energy loss per unit volume per cycle (W = ∮ H dB). Narrow loops mean low coercivity and low core loss; wide loops indicate high coercivity for permanent magnets. Trap: confusing loop width with loss—area, not just width, matters.

Memory trick: Loop area = loss; narrow = low loss.

Excitation versus ionisation

“Heating water: below boiling molecules vibrate (excited bound), at boiling they escape as steam (ionised).”

Excitation moves an electron to a higher bound orbit, keeping its total energy negative. Ionisation supplies enough energy to reach n=∞, making the energy zero or positive, so the electron is free. Remember: negative E means bound, zero or positive means free.

Memory trick: E<0 bound, E≥0 free.

Activity

“A cloud chamber shows one visible track each second from a 1 Bq alpha source.”

Activity A = λN is the number of decays per second. As the number of undecayed nuclei N decreases exponentially, A follows the same law and halves each half-life. Measured counts also depend on detector efficiency, not on the definition of a becquerel.

Memory trick: A = λN → 'A' is amount of decays per second

Meter bridge balance condition

“Balancing a meter bridge is like a seesaw: when the galvanometer reads zero, the two wire lengths act as equal-weight arms.”

At balance no current flows through the galvanometer, so the ratio of the unknown resistance to the known one equals the ratio of the opposite wire lengths (R1/R2 = L1/L2). This holds only if the bridge wire is uniform and end effects are negligible. Forgetting uniformity leads to systematic error.

Memory trick: Balance → R1/R2 = L1/L2.

Relative velocity

“A cyclist overtaking a car sees the car moving backward relative to him.”

Relative velocity v_AB = v_A − v_B. If both move opposite, magnitudes add; if same direction, subtract. Swapping A and B flips the sign, a common slip.

Memory trick: A-B = A seen from B.

W = Fd cosθ

“Pushing a cart straight ahead uses full force, but pulling it at a 60° angle reduces the work to half because of the cos θ factor.”

For a constant force, work equals the dot product W = F·d = Fd cosθ. The angle must be between force and displacement; if the force varies along the path, integration is required. Traps: ignoring the angle or applying the formula to a variable force.

W = Fd cosθ

Memory trick: Work = F d cosθ

h = 2Tcosθ / (ρgr)

“Like a thin drinking straw pulling water up in a glass, the liquid climbs higher the narrower the straw.”

Capillary rise h = 2γ cosθ / (ρ g r) for a wetting liquid (θ<90°) in a tube of radius r. γ is surface tension, ρ density, g gravity. Toppers watch: use radius, not diameter, and keep θ as the liquid-solid contact angle—not the tube’s tilt. The relation holds only when r is much smaller than the capillary length, else gravity overwhelms.

h = 2Tcosθ / (ρgr)

Memory trick: γ cosθ ÷ r → taller rise; remember radius, not diameter.

resistance vs reactance

“A toaster glows from resistance, while a trampoline’s bounce mimics reactance that stores and returns energy without heating.”

Resistance R converts electrical energy to heat and does not vary with frequency. Reactance X (inductive or capacitive) stores energy temporarily and returns it each cycle, making X frequency-dependent and causing a 90° phase shift. Trap: assuming X dissipates power like R; average power in a pure reactance is zero.

Memory trick: R = heat, X = bounce – no net heat

Zero error of a screw gauge

“A jeweler’s screw gauge still shows a 0.02 mm gap even when the anvil touches the spindle, just like a tiny ruler that never quite reaches zero.”

Zero error is the reading when the anvil and spindle are in contact. If the gauge shows a positive error (+e) you must subtract e from the observed reading; if it shows a negative error (-e) you add |e|. The classic trap is to always subtract, ignoring the sign, which flips the result for a negative zero error.

Memory trick: ‘+ subtract, – add’ – plus goes out, minus comes in.

Power as force times velocity

“A cyclist pedalling uphill feels power only from the component of force along the road.”

Instantaneous power P = F·v = Fv cosθ. If force is perpendicular to velocity, P = 0 even though F ≠ 0. The trap is omitting cosθ and writing P = Fv for non-collinear cases.

P = F v cos(theta)

Memory trick: P = Fv cosθ – only parallel component works

Perpendicular axis theorem — common mistake

“A spinning pizza slice on a table shows that the vertical spin resistance equals the sum of resistances about two perpendicular lines drawn on the crust.”

For any planar lamina—mass confined to a single plane—the perpendicular-axis theorem holds: I_z = I_x + I_y, where all axes meet at the same point. The mass need not be uniform. The trap is to apply it to 3-D bodies or to axes that are not coplanar.

Memory trick: Flat plane → I_z = I_x + I_y (no uniformity needed)

Escape versus orbital velocity — common mistake

“Students often think a spacecraft can coast out of orbit at orbital speed, but it needs that extra √2 boost to break free.”

Confusing vₑ with v₀ is a frequent error; forgetting the √2 multiplier makes the required launch speed underestimate the true escape speed.

Memory trick: v_esc = 1.414 v_orb; don’t drop √2.

Springs in series and parallel — common mistake

“When stacking two springs like a mattress, many think the stiffness adds, but it actually halves.”

A frequent error is interchanging series and parallel formulas. In series the system is softer (for two identical springs k_eq = k/2); in parallel it is twice as stiff (k_eq = 2k). Remember the softness-stiffness flip.

Memory trick: Series = softer (k/2 for two equal), Parallel = stiffer (2k).

Standing waves

“A violin string fixed at both ends vibrates with nodes at the clamps and antinodes midway, forming a standing pattern.”

Two identical waves traveling opposite create a standing wave with fixed nodes (zero displacement) and antinodes (max displacement). Energy oscillates locally, no net transport. For both ends fixed, allowed λ satisfy L = nλ/2; node-node spacing = λ/2, node-antinode = λ/4. Mistaking spacing leads to wrong resonance condition.

Memory trick: Node-node λ/2, node-antinode λ/4

Mean free path

“In a packed subway, you collide every few steps, just like molecules in a high-pressure gas.”

Mean free path λ = kT/(√2 π d² P) shows λ shortens when pressure rises or molecular diameter grows. Assumes hard-sphere molecules and uniform speed. Trap: omitting the √2 factor or mixing radius with diameter.

Memory trick: λ ∝ 1/(P·d²)