Fields: The IB DP Physics Guide to Flux, Induction & Charged Particle Motion

Q: Why can't a magnetic field change a charged particle's speed?

The magnetic force $q\vec v \times \vec B$ is always perpendicular to velocity, so it does zero work. Only an electric field (or another force with a component along velocity) can change kinetic energy.

Q: What's the difference between Faraday's law and Lenz's law?

Faraday's law gives the magnitude of induced emf ($\varepsilon = N\,d\Phi/dt$); Lenz's law gives its direction, ensuring the induced current always opposes the flux change that caused it.

Q: Why does the period of circular motion in a magnetic field not depend on speed?

Because $T = 2\pi m/(qB)$ has no $v$ term — a faster particle traces a proportionally larger circle, so it still takes the same time per revolution. This is the basis of the cyclotron.

Q: How do I know which side of a transformer has thicker wire?

Power is conserved ($V_pI_p = V_sI_s$), so the low-voltage side carries higher current and needs lower resistance, meaning thicker wire — regardless of which side has more turns.

Q: What is a velocity selector used for?

It uses balanced electric and magnetic forces ($qE = qvB$) so that only charged particles travelling at exactly $v = E/B$ pass through undeflected, regardless of their charge or mass.

Gravitational, electric and magnetic fields share more maths than you'd think — until magnetism breaks the rules.

Diagram comparing radial gravitational/electric field lines with a uniform magnetic field region containing a curving charged particle

Subject

Physics

Curriculum

IB Diploma Programme

Grade

Topic

Fields

Reading

7 min

Difficulty

Advanced

Quick facts

Difficulty

★★★★☆

Exam weight

~1/5 of HL Paper 1 & 2, plus regular Paper 3 data questions

Prerequisites

Circular motion, SL electric & gravitational fields

You'll learn

Flux, Faraday's & Lenz's laws, transformers, Lorentz force, circular motion

Revision time

45–60 min

Every IB Physics field question — gravitational, electric or magnetic — is really asking the same three things: what's the source, is the field radial or uniform, and does the force actually do work? Gravitational and electric fields obey identical inverse-square maths, differing only in the constant out front and whether attraction can flip to repulsion. Magnetism plays by different rules entirely: the force on a moving charge is always perpendicular to velocity, so it steers particles without ever speeding them up. At HL, this quirk unlocks two exam-heavy subtopics — motion in electromagnetic fields and electromagnetic induction — covering Faraday's law, Lenz's law, transformers, and circular motion in a magnetic field. This teaser walks through the five ideas examiners return to again and again, with the traps that catch out rushed answers. Full worked examples and derivations live in the complete RevisionPrep notes.

What you’ll be able to do

✓Compare radial and uniform fields across gravitational, electric and magnetic contexts

✓Explain why the magnetic force can never change a particle's speed

✓Calculate magnetic flux and identify what's changing (B, A or θ)

✓Apply Faraday's law and Lenz's law to find emf magnitude and direction

✓Use the ideal transformer equations to conserve power between coils

✓Derive the radius and period of circular motion in a uniform magnetic field

✓Apply the velocity selector condition v = E/B

✓Avoid the standard MCQ traps in induction and Lorentz force problems

Gravitational, Electric & Magnetic Fields: What's Shared, What's Different

Gravitational and electric fields are mathematical twins: both are inverse-square, $\propto 1/ r^{2}$ , both have a scalar potential, and both give a potential energy that depends only on separation. The only differences are the constant of proportionality and the fact that electric force can repel while gravity never does. Magnetism breaks the pattern completely — the force on a moving charge is always perpendicular to its velocity, so it can bend a path but never do work on it.

Comparison diagram of radial inverse-square field versus uniform field with perpendicular force on moving charge

Exam tip

Before reaching for any formula, decide: is this field radial (inverse-square) or uniform? That single decision tells you which equations are even relevant.

Mini summary

Gravity and electricity share inverse-square maths; magnetism is uniquely direction-only, never speed-changing.

Magnetic Flux and Faraday's Law (HL)

Everything in induction starts from $Φ = B A cos θ$ — the component of $B$ perpendicular to a coil's area, times that area. Flux changes because $B$ changes (transformers, MRI), $A$ changes (a rod sliding on rails), or $θ$ changes (a rotating coil, the generator case). Faraday's law then gives the size of the induced emf as $ε = N \frac{d Φ}{d t}$ — always check whether the coil has multiple turns before you finish the calculation.

Coil in a magnetic field showing flux through area with angle theta between B and the normal

Scenario	What's changing	Formula / approach
Field switched off or ramped	$B$	Use $Φ = B A cos θ$ , differentiate $B (t)$
Rod sliding on rails	$A$	Motional emf $ε = B v L$
Rotating coil (generator)	$θ$	$Φ = B A cos θ$ , differentiate $cos θ$

Exam tip

MCQ distractors love to drop the $N$ (number of turns) from Faraday's law — that gives the emf in one loop, not across the whole coil.

Common mistake

Forgetting to multiply by $N$ when a coil has multiple turns, giving an emf that's a factor of $N$ too small.

Mini summary

Identify whether B, A or θ is varying, then apply $ε = N d Φ/ d t$ — never skip the turns count.

Lenz's Law and Ideal Transformers (HL)

Lenz's law fixes the direction: induced current always opposes the change in flux that created it, guaranteeing energy conservation. A transformer is just two coils sharing one changing flux through an iron core — no wires connect primary to secondary, only magnetic coupling. Power is conserved in an ideal transformer: $V_{p} I_{p} = V_{s} I_{s}$ , alongside $\frac{V _{p}}{V _{s}} = \frac{N _{p}}{N _{s}} = \frac{I _{s}}{I _{p}}$ .

Ideal transformer diagram with primary and secondary coils on a shared iron core, turns and voltage labelled

Exam tip

Decide step-up or step-down from the given voltages first, then eliminate any turns-ratio option that inverts that direction — before you even plug in numbers.

Common mistake

Inverting the turns ratio, or forgetting to square $V_{s}$ when using $P = V^{2} / R$ to find power dissipated in the secondary.

Mini summary

Lenz's law = direction; transformers conserve power, not turns — low-voltage side always carries the higher current and thicker wire.

Motional EMF and Induced Electric Fields (HL)

A straight conductor of length $L$ sweeping through field $B$ at speed $v$ (all mutually perpendicular) generates $ε = B v L$ . Less obviously, a changing flux also induces a genuine electric field in the surrounding space, not just an emf in a wire: around a symmetric circular path enclosing that flux, $E \times 2 π r = \frac{d Φ}{d t}$ .

Circular loop with changing magnetic flux through it inducing an electric field around the circumference

Exam tip

In symmetric-loop problems (like an MRI field decreasing to zero), always divide by the full path length $2 π r$ , not just $r$ .

Common mistake

Dividing the flux rate by the radius $r$ instead of $2 π r$ , which inflates the induced electric field by a factor of $2 π$ .

Mini summary

A changing B-field creates a real E-field in space — use the full circumference $2 π r$ when solving for it.

Lorentz Force, Circular Motion & Velocity Selectors (HL)

The total force on a moving charge is $F = q E + q v \times B$ . A charge entering a uniform $B$ field perpendicular to $v$ moves in a circle with $r = \frac{m v}{q B}$ , and the period $T = \frac{2 π m}{q B}$ contains no $v$ at all — every particle of the same charge-to-mass ratio takes the same time per revolution, the whole basis of a cyclotron. A velocity selector balances the two forces so only particles at $v = E / B$ pass through undeflected.

Charged particle moving in a circular path inside a uniform magnetic field, with radius and velocity vectors labelled

Exam tip

'Derive' questions want the algebra from a named principle (force balance, $F_{n e t} = F_{ce n t r i p e t a l}$ ) shown line by line — jumping straight to the final formula loses marks even with the right answer.

Common mistake

Assuming the magnetic force changes a charged particle's speed — it's always perpendicular to $v$ , so it does zero work; only an electric (or other non-magnetic) force can change kinetic energy.

Mini summary

$r$ scales with speed but $T$ does not — that independence is the entire principle behind the cyclotron.

Quick formula sheet

Φ = B A cos θ

Magnetic flux through a coil, in webers — B times the area facing it — cosθ handles the tilt

ε = - N \frac{d Φ}{d t}

Faraday's law: magnitude of induced emf from changing flux linkage — Don't forget the N!

ε = B v L

Motional emf for a conductor sweeping through a field, all perpendicular

E \times 2 π r = \frac{d Φ}{d t}

Induced electric field around a symmetric circular path enclosing changing flux

\frac{V _{p}}{V _{s}} = \frac{N _{p}}{N _{s}} = \frac{I _{s}}{I _{p}}

Ideal transformer turns-voltage-current relationship

V_{p} I_{p} = V_{s} I_{s}

Power conservation in an ideal (100% efficient) transformer

F = q E + q v \times B

Lorentz force: total electromagnetic force on a moving charge

r = \frac{m v}{q B}

Radius of circular path for a charge moving perpendicular to B

T = \frac{2 π m}{q B}

Period of circular motion in a magnetic field — independent of speed

v = \frac{E}{B}

Speed selected by a velocity selector (crossed E and B fields)

Practice questions

Easy

State Lenz's law and explain what it guarantees about energy conservation.
Write down the equation for magnetic flux and identify each symbol.
A charge moves through a region of uniform magnetic field perpendicular to its velocity. Describe the shape of its path and explain why its speed stays constant.

Medium

A coil of 150 turns experiences a flux change of $2.0 \times 1 0^{- 3}$ Wb over 0.50 s. Calculate the average induced emf.
An ideal transformer has 400 primary turns and 100 secondary turns, connected to a 230 V rms supply. Find the secondary voltage and state whether this is a step-up or step-down transformer.
A proton moves at $1.5 \times 1 0^{6} m s^{- 1}$ perpendicular to a 0.30 T magnetic field. Calculate the radius of its circular path.

Challenge

Derive the expression $T = 2 π m / (q B)$ for the period of a charged particle's circular motion, starting from the force balance between magnetic force and centripetal force.
A circular loop of radius 0.10 m sits perpendicular to a magnetic field that decreases uniformly from 2.0 T to 0 T in 0.40 s. Determine the magnitude of the induced electric field at the loop's edge.
Explain, using the transformer power conservation equation, why the low-voltage side of a step-down transformer must be wound with thicker wire than the high-voltage side.

Frequently asked questions

Is induction on the SL or HL IB Physics syllabus?+

Induction (flux, Faraday's law, Lenz's law, transformers, generators) is entirely HL-only — SL students are never examined on it.

Why can't a magnetic field change a charged particle's speed?+

The magnetic force $q v \times B$ is always perpendicular to velocity, so it does zero work. Only an electric field (or another force with a component along velocity) can change kinetic energy.

What's the difference between Faraday's law and Lenz's law?+

Faraday's law gives the magnitude of induced emf ( $ε = N d Φ/ d t$ ); Lenz's law gives its direction, ensuring the induced current always opposes the flux change that caused it.

Why does the period of circular motion in a magnetic field not depend on speed?+

Because $T = 2 π m / (q B)$ has no $v$ term — a faster particle traces a proportionally larger circle, so it still takes the same time per revolution. This is the basis of the cyclotron.

How do I know which side of a transformer has thicker wire?+

Power is conserved ( $V_{p} I_{p} = V_{s} I_{s}$ ), so the low-voltage side carries higher current and needs lower resistance, meaning thicker wire — regardless of which side has more turns.

What is a velocity selector used for?+

It uses balanced electric and magnetic forces ( $q E = q v B$ ) so that only charged particles travelling at exactly $v = E / B$ pass through undeflected, regardless of their charge or mass.

Get the Full IB DP Physics Fields Revision Notes

Complete worked examples for flux, transformers, and Lorentz force problems Step-by-step derivations examiners expect to see for full marks All common mistakes and MCQ traps flagged with fixes Formula sheet and practice questions with full solutions

Get the Fields notes on RevisionPrep →

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