The trap question field guide

A wire carries a current of $2.4\\,\\mathrm{A}$ and has diameter $0.40\\,\\mathrm{mm}$. Estimate the current density $J=I/A$.

The radius is half the diameter, expressed in metres:

Hence

so

Correct: the factor $10^{-3}$ was squared, and the diameter was halved before the area was found.

Trap: $1.9\times10^4$ treats square millimetres as though the conversion were linear. Using $0.40\,\mathrm{mm}$ as the radius creates a separate factor-of-four error.

For which real values of $m$ does

have two distinct positive roots? Factorise before reaching for the discriminant:

The roots are $1$ and $m$. Both are positive when $m>0$, but they are distinct only when $m\ne1$. Therefore

Correct: $m=0$ is excluded because zero is not positive; $m=1$ is excluded because the roots coincide.

Trap: $m\geq0$ checks neither the strict word “positive” nor the word “distinct”.

A particle's momentum increases by 10% while its mass stays constant. By what percentage does its kinetic energy increase?

Use $K=p^2/(2m)$. If $p'=1.10p$ and $m$ is fixed, then

The final kinetic energy is 121% of the original, so the increase is

Correct: translate the wording into a multiplier first, then convert the final multiplier back into a change.

Trap: 121% answers “what percentage of the original?”; 10% assumes kinetic energy is proportional to momentum.

An electron moves from a point at $120\,\mathrm{V}$ to one at $20\,\mathrm{V}$. Only the electric force does work. What happens to its kinetic energy?

For an electron $q=-e$, so

Conservation of energy gives $\Delta K=-\Delta U$, hence

Its kinetic energy decreases by $100\,\mathrm{eV}$.

Correct: the negative charge reverses the usual positive-charge intuition. The energy check confirms the direction.

Trap: saying “potential fell, so kinetic energy rose” forgets that electric potential and electric potential energy are different quantities.