IB Physics HL: Motion of Charges in Fields — Common Questions Answered

Most marks are lost on direction, not calculation. Students apply the right-hand rule inconsistently, forget that magnetic force does no work (so speed stays constant in a uniform B-field), or confuse the vector nature of $\vec{F}=q\vec{v}\times \vec{B}$ with the scalar electric force $F=qE$. Examiners see this every session.

An electric field exerts a force along the field line, $F=qE$, which can speed up, slow down or deflect a charge and does work on it. A magnetic field exerts a force perpendicular to both velocity and field, $F=qvB\sin \theta$, which changes direction only — it never changes speed or kinetic energy.

Because the magnetic force is always perpendicular to velocity, it acts as a centripetal force — it changes direction but never magnitude. Setting $qvB=\frac{m{v}^2}{r}$ gives the radius $r=\frac{mv}{qB}$. Since the force never has a component along the motion, speed and kinetic energy stay constant throughout the circular path.

Point your fingers along v, curl them towards B, and your thumb gives the direction of $\vec{v}\times \vec{B}$ — that's the force direction for a positive charge. For a negative charge, reverse it. Examiners specifically check this on velocity selector and mass spectrometer questions, so practise it until it's automatic.

Nail three things: vector direction (right-hand rule, every time), knowing which quantity stays constant (speed in B-fields, never in E-fields), and showing full working with units. In fifteen years of marking mocks, the students who lose the fewest marks are the ones who state the relevant equation before substituting numbers.

You need $F=qE$ and $E=\frac{V}{d}$ for uniform electric fields, $F=qvB\sin \theta$ and $r=\frac{mv}{qB}$ for magnetic fields, and the velocity selector condition $qE=qvB$ giving $v=\frac{E}{B}$. These sit in the IB Physics data booklet, so you don't need to memorise them — you need to know when to use each one.

These are multi-step questions, so IB mark schemes award marks in stages: one for the correct force-balance equation, one for correct rearrangement, one for correct substitution with units, and often one for a directional or qualitative explanation. Miss the direction reasoning and you can lose a mark even with the right numerical answer.

A helix appears when the charge's velocity has a component both parallel and perpendicular to B. The parallel component is unaffected by the magnetic force (since $\vec{v}\times \vec{B}=0$ along that direction), so the charge drifts at constant speed along B while circling perpendicular to it — combine the two and you get a helix.

It appears mainly on Paper 2 (extended-response, calculation-heavy) and Paper 3 (data-based/experimental questions, often tied to option or practical contexts), and can appear as multiple-choice on Paper 1. According to the IB, the current Physics guide (first exams 2025) places this content within Topic 5, Electricity and Magnetism, assessed at HL only for the field-combination applications.

Basic electric and magnetic force ideas are shared across SL and HL, but the combined field applications — velocity selectors, mass spectrometers, and full circular/helical motion analysis — sit in the HL-only extension of Topic 5. SL students see electric fields and simple magnetic force but not the full charge-in-combined-fields treatment.

The three most common mark-scheme deductions are: forgetting magnetic force does zero work (so wrongly changing speed in circular-motion answers), swapping the electric and magnetic force formulas, and giving direction as a word ("upwards") instead of relative to a diagram or named axis, which examiners often won't credit without a clear reference.

It connects directly to the Engineering physics option's treatment of particle accelerators and to Astrophysics via charged particle behaviour in magnetic fields (e.g. cosmic rays, solar wind deflection). For the Internal Assessment, students sometimes build simple velocity-selector or deflection-tube experiments, though apparatus access is often the limiting factor.

If your child is consistently losing marks on direction (not just calculation) across several mock papers, that's a sign the underlying vector reasoning needs targeted practice rather than more general revision. Topical worksheets that isolate force-direction questions from the numerical ones tend to fix this faster than redoing full past papers.