Where can I learn Motion in electromagnetic fields for IB Physics?

This free lesson on MarkScheme covers syllabus point D.3 (Motion in electromagnetic fields) for IB Diploma Physics (Higher Level). It includes visual revision, key points, and links to criterion-based practice marking at markscheme.app/ib/courses/physics-hl/d-3-motion-in-electromagnetic-fields.

Motion in electromagnetic fields — IB…

Motion in electromagnetic fields

A magnetic field grips anything that carries a current or moves as a charge, and it always pushes sideways — at right angles to the motion. That one idea runs through this whole topic: it lifts current-carrying wires, spins electric motors, and bends beams of charged particles into circles inside everything from old television tubes to particle accelerators. This lesson develops the two force laws you need, shows how they connect, and applies them to circular motion and to crossed fields. As in every calculation topic, the worked examples are laid out exactly the way our engine marks your own practice: the method is on the page, mark by mark.

BY THE END, YOU CAN…

exam checklist — tick these off

1Calculate the magnetic force on a current-carrying conductor using $F = BIL\sin\theta$ and find its direction with Fleming's left-hand rule.
2Calculate the magnetic force on a moving charge using $F = qvB\sin\theta$ and give its direction, remembering to reverse it for a negative charge.
3Explain why a charge moving perpendicular to a uniform magnetic field follows a circular path and derive and apply the radius $r = \frac{mv}{qB}$ .
4Describe the motor effect and explain qualitatively the force between two parallel current-carrying wires and the operation of a velocity selector.
5Present working so that method marks and error-carried-forward (ECF) protect the final answer.

In simple terms

A friendly intro before the formal notes — no formulas yet.

The Invisible Sideways Shove

A magnetic field never pushes a charge along its direction of travel — it always shoves it sideways, at right angles to the motion. That single fact explains everything here: wires that jump in a field, electric motors that spin, and charges that curl into perfect circles.

THINK OF IT LIKE…

Think of holding your hand flat out of a moving car window. The air is the magnetic field and your forward speed is the charge's velocity. Tilt your palm and the air shoves your hand up or down — sideways to the car's motion, never forwards or backwards. A magnetic force behaves the same way: it acts perpendicular to the velocity, so it can steer a charge but can never speed it up or slow it down. Keep steering something at a constant speed and always at right angles, and it goes in a circle.

1
Decide what is moving: a whole current in a wire (use $F = BIL\sin\theta$ ) or a single charge (use $F = qvB\sin\theta$ ).
2
Read off the angle $\theta$ between the current/velocity and the field $B$ . The force is largest at $90^\circ$ and zero when they are parallel.
3
Find the direction. For conventional current use Fleming's left-hand rule; for a positive charge treat its velocity as the current direction; for a negative charge reverse the answer.
4
If the charge moves perpendicular to a uniform field, set the magnetic force equal to the centripetal force $\frac{mv^2}{r}$ and solve for the radius $r = \frac{mv}{qB}$ .

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure Live interactive1 / 4

Loading simulation…

Fetching from 3JCN Physics Simulation by Thomas Nguyen…

Charge in Magnetic Field

r = mv / (qB): faster charges make bigger circles and stronger fields make smaller ones.

If the embed does not load, use Open simulation.

3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Step 1

Decide what is moving: a whole current in a wire (use $F = BIL\sin\theta$ ) or a single charge (use $F = qvB\sin\theta$ ).

29 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

29 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

The Physics ClassroomStart here · 19702 20.2 · IB D.3
Magnetic Field Sim (Kirby)
Adjust the current, conductor length, field strength and orientation and see the force on the wire
Why this one: Rotate the wire from perpendicular to parallel and watch the force fall with sin(theta).
Try this
1. Double the current and read the force.
2. Rotate the wire parallel to the field.
3. Double the conductor length.
Look for The force equals BIL sin θ.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
SimuPhysicsStart here · 29702 20.2 · IB D.3
3D Fleming's Left Hand Rule
Rotate a hand model in 3D together with the field, current and force vectors until the rule makes sense
Why this one: Turn the hand model until thumb, first and second finger line up with force, field and current.
Try this
1. Rotate the hand so the first finger lies along the field.
2. Line the second finger up with the current.
3. Read the force direction from the thumb.
Look for Field, current and force are mutually perpendicular.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
The Physics ClassroomStart here · 39702 20.3 · IB D.3
The Mass Spectrometer
Fire ions down the chamber through the charge accelerator, velocity selector and detector; analyse each section
Why this one: In the velocity selector only ions with v = E/B go straight; the rest curve away.
Try this
1. Fire an ion and find where it lands in the detector.
2. Double the mass and fire again.
3. Change the charge and compare.
Look for The radius in the detector is proportional to mass divided by charge.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN PhysicsStart here · 49702 20.2 · IB D.3
DC Motor
Run a DC motor; see the force couple and commutator reversal
Why this one: Watch the force couple on the coil and the commutator flip the current every half turn.
Try this
1. Run the motor and watch the forces on the two sides of the coil.
2. Watch the commutator reverse the current each half turn.
Look for Opposite forces on the two sides make a couple, and the commutator keeps the torque in one direction.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 59702 18.2 · IB D.3
Charged Particle in an Electric Field
Shoot a charged particle into a uniform electric field; adjust charge, mass, speed and field; see parabolic path
Why this one: Fire a charge across a uniform E field: constant force gives a parabola; a negative charge curves the other way.
Try this
1. Fire the particle in and watch the parabolic path.
2. Double the field strength.
3. Reverse the sign of the charge.
Look for The path is a parabola because the force is constant and perpendicular to the entry velocity; a negative charge curves the other way.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)

More simulations24 more on this topic — core ones first

oPhysicsCore9702 18.2 · 9702 11.1 · IB D.3
The Millikan Oil-Drop Experiment
Simplified Millikan oil-drop: adjust plate voltage to balance a charged droplet and deduce its charge
Try this
1. Raise the plate voltage until the droplet hangs still.
2. Deduce the charge from the balancing voltage.
3. Repeat with a new droplet and compare the charges.
Look for Balancing voltages give charges that are whole-number multiples of e.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 20.2 · IB D.3 · IB D.2
DC Motor
DC motor: adjust voltage, field strength and number of turns; see force on the coil and rotation
Try this
1. Increase the voltage and watch the rotation.
2. Reverse the field.
3. Add turns to the coil.
Look for The force on each side of the coil grows with current, field and turns, and reversing the field reverses the rotation.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 20.3 · IB D.3 · IB E.1
Electron Charge to Mass Ratio Lab
Thomson e/m experiment: balance electric and magnetic deflection of an electron beam and compute e/m
Try this
1. Apply the electric field and note the beam deflection.
2. Add the magnetic field and adjust until the beam is straight.
3. Compute e/m from the balanced fields.
Look for When eE = evB the beam is undeflected, and e/m follows from the field values and beam speed.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 20.3 · IB D.3
Charged particle in a Magnetic Field
Shoot a charged particle into a uniform magnetic field; vary q, m, v and B; see the circular path and radius
Try this
1. Double v and read the radius.
2. Double B instead.
3. Reverse the sign of q.
Look for Radius r = mv/qB grows with speed and shrinks with field; reversing the charge reverses the sense of rotation.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 20.3 · IB D.3
Charged Particle in a Magnetic Field 3D
3D charged particle in a magnetic field with velocity components along and across B; see helical motion
Try this
1. Set the velocity purely across B and watch the circle.
2. Add a component along B.
3. Increase the along-B component.
Look for The across-B component makes the circle and the along-B component stretches it into a helix.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsCore9702 18.2 · 9702 20.3 · IB D.3
Cathode Ray Tube
An electron gun, accelerating anode and deflecting plates; drive the glowing spot around the screen
Try this
1. Raise the anode voltage and watch the spot.
2. Change the plate voltage and move the spot.
3. Reverse the plate voltage.
Look for The spot deflects towards the positive plate by an amount proportional to the plate voltage.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$F = BIL\sin\theta$

KEY RELATION

$F = qvB\sin\theta$

KEY RELATION

$qvB = \frac{mv^2}{r} \quad\Longrightarrow\quad r = \frac{mv}{qB}$

Full topic notes

Formal explanation with the rigour you need for the exam.

Force on a current-carrying conductor

A wire carrying a current is a stream of moving charges, so when it lies in a magnetic field it feels a force. This is the motor effect. The size of the force depends on the field strength $B$ , the current $I$ , the length $L$ of wire that lies in the field, and the angle $\theta$ between the current and the field. The force is a maximum when the wire is perpendicular to the field and drops to zero when the wire runs along the field lines.

$F = BIL\sin\theta$

Here $B$ is in tesla (T), $I$ in amperes (A), $L$ in metres (m) and the force $F$ in newtons (N). The direction of the force is perpendicular to BOTH the current and the field, and you find it with Fleming's left-hand rule.

Magnitude: $F = BIL\sin\theta$ — largest when the wire is perpendicular to $B$ ( $\theta = 90^\circ$ ), zero when parallel ( $\theta = 0^\circ$ ).
Fleming's left-hand rule (for conventional current): thumb = thruST (Force), First finger = Field, seCond finger = Current.
Direction: the force is always perpendicular to both the current and the field — it points out of the plane containing them.
The motor effect is the name for this force on a current-carrying conductor; it is what makes electric motors turn.

Not clear?

Force on a moving charge

The force on a wire is really the combined force on all the individual charges drifting through it. Zoom in on a single charge $q$ moving with speed $v$ through a field $B$ and the force on it is $F = qvB\sin\theta$ , where $\theta$ is the angle between the velocity and the field. Just like the wire, a stationary charge feels no magnetic force, and a charge moving along the field lines feels none either — only the component of velocity perpendicular to the field matters.

$F = qvB\sin\theta$

Only moving charges feel a magnetic force; a charge at rest feels none.
Only the perpendicular component of velocity counts — the force is $qvB\sin\theta$ , zero when $v$ is parallel to $B$ .
Direction: treat a positive charge's velocity as the current direction and apply Fleming's left-hand rule; for a negative charge, reverse the result.
No work is done: the force is perpendicular to $v$ , so the speed and kinetic energy stay constant — the field only changes direction.

Not clear?

Circular motion in a uniform magnetic field

Fire a charge into a uniform magnetic field so that its velocity is perpendicular to the field, and something elegant happens. The magnetic force has a constant magnitude $qvB$ (the speed cannot change, because the force does no work) and it always points at right angles to the velocity. A constant-magnitude force that is always perpendicular to the motion is exactly the definition of a centripetal force, so the charge is pushed round a circle at constant speed. Equating the magnetic force to the centripetal force gives the radius of that circle.

$qvB = \frac{mv^2}{r} \quad\Longrightarrow\quad r = \frac{mv}{qB}$

The radius grows with the particle's momentum ( $mv$ ) and shrinks as the charge or field increases. This is why a mass spectrometer can separate ions: with the same speed, charge and field, heavier ions swing round on wider arcs. Notice the speed $v$ cancels from neither side by accident — it stays in the formula, so faster particles do trace larger circles even though the field does no work on them.

Not clear?

The motor effect and forces between parallel wires

Because every current-carrying wire in a field feels a force, a coil of wire in a field feels a turning effect. In a simple d.c. motor the current runs up one side of a coil and down the other, so by Fleming's left-hand rule the two sides are pushed in opposite directions. That pair of opposite forces on either side of the axle is a couple, and it spins the coil — the motor effect turned into rotation. A commutator flips the current direction every half turn so the coil keeps rotating the same way.

Two parallel wires interact through the same effect. Each wire produces a magnetic field in the space around it, and the other wire, carrying current through that field, feels a force $F = BIL$ . Working through the directions with Fleming's left-hand rule gives a clean qualitative rule: currents in the same direction attract, and currents in opposite directions repel. This mutual magnetic force is how the ampere was historically defined.

Motor effect: a current-carrying conductor in a magnetic field feels a force $F = BIL\sin\theta$ .
Electric motor: opposite sides of a current-carrying coil are pushed in opposite directions, creating a torque that spins the coil.
Parallel wires, same-direction currents: attract.
Parallel wires, opposite-direction currents: repel.

Not clear?

A charge in combined fields: the velocity selector

When a charge moves through a region containing both an electric field and a magnetic field, it feels an electric force $F_E = qE$ (which acts on the charge whether or not it is moving) and a magnetic force $F_B = qvB$ (which acts only because it is moving). A velocity selector arranges the two fields at right angles so that these forces point in opposite directions. The electric force $qE$ is independent of speed, but the magnetic force $qvB$ grows with speed, so the two can balance for only one particular speed.

A velocity selector uses perpendicular (crossed) electric and magnetic fields.
The electric and magnetic forces on the charge are set to point in opposite directions.
They balance when $qE = qvB$ ; the charge cancels, giving the selected speed $v = \dfrac{E}{B}$ .
Only charges with that exact speed pass straight through undeflected. Faster charges feel a larger magnetic force and are deflected one way; slower charges feel a larger relative electric force and are deflected the other way — regardless of their charge or mass.

Not clear?

Common mistakes examiners penalise

Claiming the magnetic force changes a charge's speed — it never does. The force is perpendicular to the velocity, so it does no work; speed and kinetic energy stay constant and the motion is a circle at constant speed, not a spiral.
Forgetting the $\sin\theta$ factor — both $F = BIL\sin\theta$ and $F = qvB\sin\theta$ use the angle between the current/velocity and the field. Only the perpendicular component contributes; a charge moving parallel to $B$ feels zero force.
Using the wrong hand or forgetting to reverse for a negative charge — Fleming's LEFT hand gives the force on conventional current or a positive charge. For an electron or other negative charge, reverse the direction.
Mixing up the two force laws — use $F = BIL\sin\theta$ for a current in a length of wire and $F = qvB\sin\theta$ for a single moving charge. Do not put a single charge into the wire formula or vice versa.
Getting the attract/repel rule for parallel wires backwards — same-direction currents attract, opposite-direction currents repel.
Thinking the velocity selector's speed depends on the charge or mass — it does not. Because $q$ cancels, $v = E/B$ selects by speed alone.
Dropping units or over-rounding mid-calculation — carry extra figures through the working and round only the final answer; always attach the correct unit (N, m, T, V m⁻¹).

Not clear?

Where this leads

The magnetic force on a moving charge is the engine behind an enormous amount of physics and technology. The circular-motion result $r = mv/qB$ is the working principle of mass spectrometers and cyclotrons, and the same force that spins a motor, run in reverse, is what generates electricity in the induction topic that follows. Master the habit here — decide whether you have a current or a single charge, pick the matching force law, watch the angle, use the left hand and reverse for negatives, and set magnetic force equal to centripetal force for circular paths — and the field topics that follow become variations on a method you already own.

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A straight wire of length 0.25 m carries a current of 4.0 A. It lies perpendicular to a uniform magnetic field of flux density 0.30 T. Calculate the magnetic force on the wire. [3]

1
List the quantities. $B = 0.30$ T, $I = 4.0$ A, $L = 0.25$ m, $\theta = 90^\circ$ so $\sin\theta = 1$ .

EXAMPLE 2

An electron (charge magnitude $1.6 \times 10^{-19}$ C) moves at $3.0 \times 10^{7}$ m s⁻¹ perpendicular to a uniform magnetic field of flux density $0.20$ T. Calculate the magnitude of the magnetic force on the electron. [3]

1
List the quantities. $q = 1.6 \times 10^{-19}$ C, $v = 3.0 \times 10^{7}$ m s⁻¹, $B = 0.20$ T, $\theta = 90^\circ$ so $\sin\theta = 1$ .

EXAMPLE 3

A proton ( $q = 1.6 \times 10^{-19}$ C, $m = 1.67 \times 10^{-27}$ kg) enters a $0.50$ T magnetic field at $2.0 \times 10^{6}$ m s⁻¹ perpendicular to the field. Calculate the radius of its circular path. [3]

1
Model answer — full working.

EXAMPLE 4

A velocity selector has crossed fields with magnetic flux density $0.15$ T. It is designed to let through only particles travelling at $2.0 \times 10^{5}$ m s⁻¹. Calculate the electric field strength required. [3]

1
State the principle. A particle passes straight through only when the electric force balances the magnetic force: $F_E = F_B \Rightarrow qE = qvB$ . [M1: correct condition]

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAMotion in electromagnetic fields

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

Force on a current-carrying conductor: $F = BIL\sin\theta$ , where $B$ is the field, $I$ the current, $L$ the length of conductor in the field and $\theta$ the angle between the current and the field. Maximum when the wire is perpendicular to $B$ ; zero when parallel.
Fleming's left-hand rule: For conventional (positive) current: thumb = thruST (force), First finger = Field, seCond finger = Current. It gives the direction of the force on a current-carrying wire, always perpendicular to both $I$ and $B$ .
Force on a moving charge: $F = qvB\sin\theta$ , where $q$ is the charge, $v$ its speed, $B$ the field and $\theta$ the angle between $v$ and $B$ . A magnetic field exerts no force on a stationary charge or on motion parallel to the field.
Circular motion in a uniform field: A charge moving perpendicular to a uniform $B$ feels a constant-magnitude force always at right angles to $v$ — the definition of centripetal force — so it travels in a circle at constant speed.
Radius of the circular path: Set magnetic force = centripetal force: $qvB = \dfrac{mv^2}{r}$ , so $r = \dfrac{mv}{qB}$ . Faster or heavier particles curve in larger circles; stronger fields or larger charges tighten the circle.
The motor effect: A current-carrying wire placed in a magnetic field experiences a force ( $F = BIL\sin\theta$ ). In a motor a coil carries current in a field, and the forces on its opposite sides act in opposite directions, producing a turning effect (torque) that spins the coil.
Parallel current-carrying wires: Each wire sits in the magnetic field of the other and feels a force. Currents in the SAME direction attract; currents in OPPOSITE directions repel.
Velocity selector: Crossed (perpendicular) electric and magnetic fields exert opposing forces on a moving charge. Only particles with speed $v = E/B$ have $qE = qvB$ and pass straight through undeflected; all other speeds are deflected.

09Remember

Name it

Read the meaning, then pick which of this lesson’s terms it describes. Miss one and you see what your choice really means.

1 of 6 · set 1 of 2

Which of these is being described?

$F = qvB\sin\theta$ , where $q$ is the charge, $v$ its speed, $B$ the field and $\theta$ the angle between $v$ and $B$ . A magnetic field exerts no force on a stationary charge or on motion parallel to the field.

Choose the term this describes.

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 5 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 11 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

Magnitude: $F = BIL\sin\theta$ — largest when the wire is perpendicular to $B$ ( $\theta = 90^\circ$ ), zero when parallel ( $\theta = 0^\circ$ ).
Fleming's left-hand rule (for conventional current): thumb = thruST (Force), First finger = Field, seCond finger = Current.
Direction: the force is always perpendicular to both the current and the field — it points out of the plane containing them.
The motor effect is the name for this force on a current-carrying conductor; it is what makes electric motors turn.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Real past paper[0]

Get a Paper 2 calculation marked: solve a magnetic-force problem with full working

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

IB Physics Data Booklet↗

Frequently asked

Why doesn't a magnetic field ever change a charge's speed?

What's the difference between

F = BIL\sin\theta

and

F = qvB\sin\theta

How do I get the direction of the force on a negative charge?

Why do parallel wires carrying current in the same direction attract?

What actually makes an electric motor turn?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do Get a Paper 2 calculation marked: solve a magnetic-force problem with full working on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUSD.2 Electric and magnetic fields NEXT →D.4 Induction

⚛

Discuss Motion in electromagnetic fields

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Motion in electromagnetic fields

BY THE END, YOU CAN…

exam checklist — tick these off

1Calculate the magnetic force on a current-carrying conductor using $F = BIL\sin\theta$ and find its direction with Fleming's left-hand rule.
2Calculate the magnetic force on a moving charge using $F = qvB\sin\theta$ and give its direction, remembering to reverse it for a negative charge.
3Explain why a charge moving perpendicular to a uniform magnetic field follows a circular path and derive and apply the radius $r = \frac{mv}{qB}$ .
4Describe the motor effect and explain qualitatively the force between two parallel current-carrying wires and the operation of a velocity selector.
5Present working so that method marks and error-carried-forward (ECF) protect the final answer.

In simple terms

A friendly intro before the formal notes — no formulas yet.

The Invisible Sideways Shove

THINK OF IT LIKE…

1
Decide what is moving: a whole current in a wire (use $F = BIL\sin\theta$ ) or a single charge (use $F = qvB\sin\theta$ ).
2
Read off the angle $\theta$ between the current/velocity and the field $B$ . The force is largest at $90^\circ$ and zero when they are parallel.
3
Find the direction. For conventional current use Fleming's left-hand rule; for a positive charge treat its velocity as the current direction; for a negative charge reverse the answer.
4
If the charge moves perpendicular to a uniform field, set the magnetic force equal to the centripetal force $\frac{mv^2}{r}$ and solve for the radius $r = \frac{mv}{qB}$ .

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure Live interactive1 / 4

Loading simulation…

Fetching from 3JCN Physics Simulation by Thomas Nguyen…

Charge in Magnetic Field

r = mv / (qB): faster charges make bigger circles and stronger fields make smaller ones.

If the embed does not load, use Open simulation.

3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Step 1

Decide what is moving: a whole current in a wire (use $F = BIL\sin\theta$ ) or a single charge (use $F = qvB\sin\theta$ ).

29 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

29 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

The Physics ClassroomStart here · 19702 20.2 · IB D.3
Magnetic Field Sim (Kirby)
Adjust the current, conductor length, field strength and orientation and see the force on the wire
Why this one: Rotate the wire from perpendicular to parallel and watch the force fall with sin(theta).
Try this
1. Double the current and read the force.
2. Rotate the wire parallel to the field.
3. Double the conductor length.
Look for The force equals BIL sin θ.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
SimuPhysicsStart here · 29702 20.2 · IB D.3
3D Fleming's Left Hand Rule
Rotate a hand model in 3D together with the field, current and force vectors until the rule makes sense
Why this one: Turn the hand model until thumb, first and second finger line up with force, field and current.
Try this
1. Rotate the hand so the first finger lies along the field.
2. Line the second finger up with the current.
3. Read the force direction from the thumb.
Look for Field, current and force are mutually perpendicular.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
The Physics ClassroomStart here · 39702 20.3 · IB D.3
The Mass Spectrometer
Fire ions down the chamber through the charge accelerator, velocity selector and detector; analyse each section
Why this one: In the velocity selector only ions with v = E/B go straight; the rest curve away.
Try this
1. Fire an ion and find where it lands in the detector.
2. Double the mass and fire again.
3. Change the charge and compare.
Look for The radius in the detector is proportional to mass divided by charge.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN PhysicsStart here · 49702 20.2 · IB D.3
DC Motor
Run a DC motor; see the force couple and commutator reversal
Why this one: Watch the force couple on the coil and the commutator flip the current every half turn.
Try this
1. Run the motor and watch the forces on the two sides of the coil.
2. Watch the commutator reverse the current each half turn.
Look for Opposite forces on the two sides make a couple, and the commutator keeps the torque in one direction.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 59702 18.2 · IB D.3
Charged Particle in an Electric Field
Shoot a charged particle into a uniform electric field; adjust charge, mass, speed and field; see parabolic path
Why this one: Fire a charge across a uniform E field: constant force gives a parabola; a negative charge curves the other way.
Try this
1. Fire the particle in and watch the parabolic path.
2. Double the field strength.
3. Reverse the sign of the charge.
Look for The path is a parabola because the force is constant and perpendicular to the entry velocity; a negative charge curves the other way.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)

More simulations24 more on this topic — core ones first

oPhysicsCore9702 18.2 · 9702 11.1 · IB D.3
The Millikan Oil-Drop Experiment
Simplified Millikan oil-drop: adjust plate voltage to balance a charged droplet and deduce its charge
Try this
1. Raise the plate voltage until the droplet hangs still.
2. Deduce the charge from the balancing voltage.
3. Repeat with a new droplet and compare the charges.
Look for Balancing voltages give charges that are whole-number multiples of e.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 20.2 · IB D.3 · IB D.2
DC Motor
DC motor: adjust voltage, field strength and number of turns; see force on the coil and rotation
Try this
1. Increase the voltage and watch the rotation.
2. Reverse the field.
3. Add turns to the coil.
Look for The force on each side of the coil grows with current, field and turns, and reversing the field reverses the rotation.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 20.3 · IB D.3 · IB E.1
Electron Charge to Mass Ratio Lab
Thomson e/m experiment: balance electric and magnetic deflection of an electron beam and compute e/m
Try this
1. Apply the electric field and note the beam deflection.
2. Add the magnetic field and adjust until the beam is straight.
3. Compute e/m from the balanced fields.
Look for When eE = evB the beam is undeflected, and e/m follows from the field values and beam speed.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 20.3 · IB D.3
Charged particle in a Magnetic Field
Shoot a charged particle into a uniform magnetic field; vary q, m, v and B; see the circular path and radius
Try this
1. Double v and read the radius.
2. Double B instead.
3. Reverse the sign of q.
Look for Radius r = mv/qB grows with speed and shrinks with field; reversing the charge reverses the sense of rotation.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 20.3 · IB D.3
Charged Particle in a Magnetic Field 3D
3D charged particle in a magnetic field with velocity components along and across B; see helical motion
Try this
1. Set the velocity purely across B and watch the circle.
2. Add a component along B.
3. Increase the along-B component.
Look for The across-B component makes the circle and the along-B component stretches it into a helix.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsCore9702 18.2 · 9702 20.3 · IB D.3
Cathode Ray Tube
An electron gun, accelerating anode and deflecting plates; drive the glowing spot around the screen
Try this
1. Raise the anode voltage and watch the spot.
2. Change the plate voltage and move the spot.
3. Reverse the plate voltage.
Look for The spot deflects towards the positive plate by an amount proportional to the plate voltage.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$F = BIL\sin\theta$

KEY RELATION

$F = qvB\sin\theta$

KEY RELATION

$qvB = \frac{mv^2}{r} \quad\Longrightarrow\quad r = \frac{mv}{qB}$

Full topic notes

Formal explanation with the rigour you need for the exam.

Force on a current-carrying conductor

$F = BIL\sin\theta$

Magnitude: $F = BIL\sin\theta$ — largest when the wire is perpendicular to $B$ ( $\theta = 90^\circ$ ), zero when parallel ( $\theta = 0^\circ$ ).
Fleming's left-hand rule (for conventional current): thumb = thruST (Force), First finger = Field, seCond finger = Current.
Direction: the force is always perpendicular to both the current and the field — it points out of the plane containing them.
The motor effect is the name for this force on a current-carrying conductor; it is what makes electric motors turn.

Not clear?

Force on a moving charge

$F = qvB\sin\theta$

Only moving charges feel a magnetic force; a charge at rest feels none.
Only the perpendicular component of velocity counts — the force is $qvB\sin\theta$ , zero when $v$ is parallel to $B$ .
Direction: treat a positive charge's velocity as the current direction and apply Fleming's left-hand rule; for a negative charge, reverse the result.
No work is done: the force is perpendicular to $v$ , so the speed and kinetic energy stay constant — the field only changes direction.

Not clear?

Circular motion in a uniform magnetic field

$qvB = \frac{mv^2}{r} \quad\Longrightarrow\quad r = \frac{mv}{qB}$

Not clear?

The motor effect and forces between parallel wires

Motor effect: a current-carrying conductor in a magnetic field feels a force $F = BIL\sin\theta$ .
Electric motor: opposite sides of a current-carrying coil are pushed in opposite directions, creating a torque that spins the coil.
Parallel wires, same-direction currents: attract.
Parallel wires, opposite-direction currents: repel.

Not clear?

A charge in combined fields: the velocity selector

A velocity selector uses perpendicular (crossed) electric and magnetic fields.
The electric and magnetic forces on the charge are set to point in opposite directions.
They balance when $qE = qvB$ ; the charge cancels, giving the selected speed $v = \dfrac{E}{B}$ .
Only charges with that exact speed pass straight through undeflected. Faster charges feel a larger magnetic force and are deflected one way; slower charges feel a larger relative electric force and are deflected the other way — regardless of their charge or mass.

Not clear?

Common mistakes examiners penalise

Claiming the magnetic force changes a charge's speed — it never does. The force is perpendicular to the velocity, so it does no work; speed and kinetic energy stay constant and the motion is a circle at constant speed, not a spiral.
Forgetting the $\sin\theta$ factor — both $F = BIL\sin\theta$ and $F = qvB\sin\theta$ use the angle between the current/velocity and the field. Only the perpendicular component contributes; a charge moving parallel to $B$ feels zero force.
Using the wrong hand or forgetting to reverse for a negative charge — Fleming's LEFT hand gives the force on conventional current or a positive charge. For an electron or other negative charge, reverse the direction.
Mixing up the two force laws — use $F = BIL\sin\theta$ for a current in a length of wire and $F = qvB\sin\theta$ for a single moving charge. Do not put a single charge into the wire formula or vice versa.
Getting the attract/repel rule for parallel wires backwards — same-direction currents attract, opposite-direction currents repel.
Thinking the velocity selector's speed depends on the charge or mass — it does not. Because $q$ cancels, $v = E/B$ selects by speed alone.
Dropping units or over-rounding mid-calculation — carry extra figures through the working and round only the final answer; always attach the correct unit (N, m, T, V m⁻¹).

Not clear?

Where this leads

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A straight wire of length 0.25 m carries a current of 4.0 A. It lies perpendicular to a uniform magnetic field of flux density 0.30 T. Calculate the magnetic force on the wire. [3]

1
List the quantities. $B = 0.30$ T, $I = 4.0$ A, $L = 0.25$ m, $\theta = 90^\circ$ so $\sin\theta = 1$ .

EXAMPLE 2

1
List the quantities. $q = 1.6 \times 10^{-19}$ C, $v = 3.0 \times 10^{7}$ m s⁻¹, $B = 0.20$ T, $\theta = 90^\circ$ so $\sin\theta = 1$ .

EXAMPLE 3

1
Model answer — full working.

EXAMPLE 4

1
State the principle. A particle passes straight through only when the electric force balances the magnetic force: $F_E = F_B \Rightarrow qE = qvB$ . [M1: correct condition]

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAMotion in electromagnetic fields

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

Force on a current-carrying conductor: $F = BIL\sin\theta$ , where $B$ is the field, $I$ the current, $L$ the length of conductor in the field and $\theta$ the angle between the current and the field. Maximum when the wire is perpendicular to $B$ ; zero when parallel.
Fleming's left-hand rule: For conventional (positive) current: thumb = thruST (force), First finger = Field, seCond finger = Current. It gives the direction of the force on a current-carrying wire, always perpendicular to both $I$ and $B$ .
Force on a moving charge: $F = qvB\sin\theta$ , where $q$ is the charge, $v$ its speed, $B$ the field and $\theta$ the angle between $v$ and $B$ . A magnetic field exerts no force on a stationary charge or on motion parallel to the field.
Circular motion in a uniform field: A charge moving perpendicular to a uniform $B$ feels a constant-magnitude force always at right angles to $v$ — the definition of centripetal force — so it travels in a circle at constant speed.
Radius of the circular path: Set magnetic force = centripetal force: $qvB = \dfrac{mv^2}{r}$ , so $r = \dfrac{mv}{qB}$ . Faster or heavier particles curve in larger circles; stronger fields or larger charges tighten the circle.
The motor effect: A current-carrying wire placed in a magnetic field experiences a force ( $F = BIL\sin\theta$ ). In a motor a coil carries current in a field, and the forces on its opposite sides act in opposite directions, producing a turning effect (torque) that spins the coil.
Parallel current-carrying wires: Each wire sits in the magnetic field of the other and feels a force. Currents in the SAME direction attract; currents in OPPOSITE directions repel.
Velocity selector: Crossed (perpendicular) electric and magnetic fields exert opposing forces on a moving charge. Only particles with speed $v = E/B$ have $qE = qvB$ and pass straight through undeflected; all other speeds are deflected.

09Remember

Name it

Read the meaning, then pick which of this lesson’s terms it describes. Miss one and you see what your choice really means.

1 of 6 · set 1 of 2

Which of these is being described?

Choose the term this describes.

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 5 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 11 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

Magnitude: $F = BIL\sin\theta$ — largest when the wire is perpendicular to $B$ ( $\theta = 90^\circ$ ), zero when parallel ( $\theta = 0^\circ$ ).
Fleming's left-hand rule (for conventional current): thumb = thruST (Force), First finger = Field, seCond finger = Current.
Direction: the force is always perpendicular to both the current and the field — it points out of the plane containing them.
The motor effect is the name for this force on a current-carrying conductor; it is what makes electric motors turn.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Real past paper[0]

Get a Paper 2 calculation marked: solve a magnetic-force problem with full working

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

IB Physics Data Booklet↗

Frequently asked

Why doesn't a magnetic field ever change a charge's speed?

What's the difference between

F = BIL\sin\theta

and

F = qvB\sin\theta

How do I get the direction of the force on a negative charge?

Why do parallel wires carrying current in the same direction attract?

What actually makes an electric motor turn?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUSD.2 Electric and magnetic fields NEXT →D.4 Induction

⚛

Discuss Motion in electromagnetic fields

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In simple terms

Explore the concept

Simulations

Magnetic Field Sim (Kirby)

3D Fleming's Left Hand Rule

The Mass Spectrometer

DC Motor

Charged Particle in an Electric Field

The Millikan Oil-Drop Experiment

DC Motor

Electron Charge to Mass Ratio Lab

Charged particle in a Magnetic Field

Charged Particle in a Magnetic Field 3D

Cathode Ray Tube

Key formulas

Full topic notes

Force on a current-carrying conductor

Force on a moving charge

Circular motion in a uniform magnetic field

The motor effect and forces between parallel wires

A charge in combined fields: the velocity selector

Common mistakes examiners penalise

Where this leads

Worked examples

How it all connects

Glossary

Name it

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Get a Paper 2 calculation marked: solve a magnetic-force problem with full working

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Motion in electromagnetic fields

Revise Motion in electromagnetic fields for IB Physics (D.3)

In simple terms

Explore the concept

Simulations

Magnetic Field Sim (Kirby)

3D Fleming's Left Hand Rule

The Mass Spectrometer

DC Motor

Charged Particle in an Electric Field

The Millikan Oil-Drop Experiment

DC Motor

Electron Charge to Mass Ratio Lab

Charged particle in a Magnetic Field

Charged Particle in a Magnetic Field 3D

Cathode Ray Tube

Key formulas

Full topic notes

Force on a current-carrying conductor

Force on a moving charge

Circular motion in a uniform magnetic field

The motor effect and forces between parallel wires

A charge in combined fields: the velocity selector

Common mistakes examiners penalise

Where this leads

Worked examples

How it all connects

Glossary

Name it

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Get a Paper 2 calculation marked: solve a magnetic-force problem with full working

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Motion in electromagnetic fields