Physics 9702 · Paper 4

The Velocity Selector

Cross an electric field with a magnetic field and only one speed survives in a straight line. This device appeared in some form in nearly every 2024–25 session — the hottest calculation in the topic.

Two forces, one speed

Crossed fields: the electric force EQ is fixed; the magnetic force BQv grows with speed. Only ions with v = E/B feel balanced forces and pass straight through — regardless of their charge or mass. Faster ions bend toward the magnetic force's side.

The two-mark logic, recycled verbatim (9702/41/M/J/24 Q5(c)(ii)) (9702/41/M/J/25 Q7(c)): the electric and magnetic forces act in opposite directions, and the particle is undeviated when their magnitudes are equal. Setting $EQ = BQv$ gives $v = \dfrac{E}{B}$ — and with plates, $E = V/d$ makes it $v = \dfrac{V}{Bd}$ (9702/42/F/M/25 Q6(a)).
$Q$ cancelled — the selected speed is independent of both charge and mass. A 2025 part asked exactly why an alpha particle at a proton's speed also passes straight through: the expression contains neither $m$ nor $q$ (9702/42/F/M/25 Q6(c)).
Too fast? The magnetic force $BQv$ grows with speed while the electric force stays fixed, so faster ions bend towards the magnetic force's side — drawn as a smooth curve starting at the entry point (9702/42/F/M/25 Q6(e)).

Worked example

The 2025 selector, fully chained

Ions of mass $3.2\times10^{-27}$ kg and kinetic energy $4.1\times10^{-17}$ J pass undeviated between plates 3.6 cm apart with 980 V across them. Find $B$ (9702/42/F/M/25 Q6(b)).

Speed from kinetic energy: $u = \sqrt{2E_K/m} = \sqrt{2 \times 4.1\times10^{-17} / 3.2\times10^{-27}} = 1.6\times10^{5}\ \text{m s}^{-1}$ .
$B = \dfrac{V}{ud} = \dfrac{980}{1.6\times10^{5} \times 3.6\times10^{-2}} = 0.17\ \text{T}$ .

Answer

B = 0.17\ \text{T}

Your turn— tap to reveal the worked answer (9702/42/F/M/25 Q6(d))

In that selector the top plate is positive and the ions are positive, moving left to right. Deduce the direction of the magnetic field.

Three marks, one per link: the electric force on the ions is downward (away from the + plate), so the magnetic force must be upward; positive ions moving right are a conventional current to the right; Fleming's left-hand rule then puts the field into the page.

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