How does the magnetic force differ from the electric force on a charged particle?

The magnetic force only acts if the charge is *moving* and has a velocity component perpendicular to the magnetic field. An electric force acts on *any* charge (moving or stationary) in an electric field.

Why does a charged particle move in a circle in a uniform magnetic field?

When a charged particle moves perpendicularly to a uniform magnetic field, the magnetic force acts perpendicular to its velocity at all times. This continuously changing force direction provides the centripetal force required for circular motion.

Can the Hall effect be used to determine the type of charge carriers in a material?

Yes, the polarity of the Hall voltage (which side becomes positive or negative) directly indicates whether the charge carriers are positive (holes) or negative (electrons).

Where can I learn Force on a moving charge for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 20.3 (Force on a moving charge) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/20-3-force-on-a-moving-charge.

Is Force on a moving charge (20.3) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Force on a moving charge.

How do I revise Force on a moving charge for 9702 exams?

Start with the visual steps on this page, note the key exam points, then attempt a 9702 past-paper question on Force on a moving charge using MarkScheme's /mark tool. Mark strictly against the official scheme and re-read any marks you lost.

Force on a moving charge 9702 — Free A-Level…

Force on a moving charge

Imagine tiny charged particles speeding through space, only to be suddenly pushed sideways by an invisible force! This is the magnetic force on a moving charge, a fundamental concept in electromagnetism. We'll explore how this force arises, how to predict its direction using Fleming's Left-Hand Rule, and its fascinating applications in velocity selectors and the Hall effect. This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 20.3.

BY THE END, YOU CAN…

1Describe the magnetic force on a moving charge and apply F = BQvsinθ.
2Explain the function of a velocity selector and how it utilises electric and magnetic fields.
3Outline the principles of the Hall effect and its application in Hall probes.

In simple terms

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

Force on a moving charge

Cambridge 9702 Paper 4 — Force on a moving charge (20.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
The force $F = BQv\sin\theta$ is maximum when the charge moves perpendicular to the field ( $\theta=90^\circ$ ).
2
The force is zero when the charge moves parallel to the field ( $\theta=0^\circ$ ).
3
Fleming's Left-Hand Rule determines the force direction for a positive charge. For a negative charge, the force is in the opposite direction.
4
The magnetic force is always perpendicular to both the velocity of the charge and the magnetic field.

What this topic covers

The official Cambridge syllabus points this lesson works through.

20.3.1
Determine the direction of the force on a charge moving in a magnetic field
20.3.2
Recall and use $F = BQv \sin θ$
20.3.3
Understand the origin of the Hall voltage and derive and use the expression $V_H = BI/(ntq)$, where t = thickness
20.3.4
Understand the use of a Hall probe to measure magnetic flux density
20.3.5
Describe the motion of a charged particle moving in a uniform magnetic field perpendicular to the direction of motion of the particle
20.3.6
Explain how electric and magnetic fields can be used in velocity selection

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Key formulas

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

$F = BQv\sin\theta$

Tap a symbol — great for exam definitions

$F_B = F_E$

Tap a symbol — great for exam definitions

$V_H = \frac{BI}{nQt}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

Magnetic Force on Individual Charges

When a charged particle travels through a magnetic field, it can experience a force that's completely different from an electric force. Crucially, this magnetic force only appears if the particle's velocity has a component perpendicular to the magnetic field lines. If it moves perfectly parallel or anti-parallel to the field, no magnetic force acts on it.

$F = BQv\sin\theta$ Where:

$F$ = magnetic force (N)
$B$ = magnetic flux density (T)
$Q$ = magnitude of the charge (C)
$v$ = speed of the particle (m s⁻¹)
$\theta$ = angle between the velocity vector ( $\vec{v}$ ) and the magnetic field vector ( $\vec{B}$ )

The force $F = BQv\sin\theta$ is maximum when the charge moves perpendicular to the field ( $\theta=90^\circ$ ).
The force is zero when the charge moves parallel to the field ( $\theta=0^\circ$ ).
Fleming's Left-Hand Rule determines the force direction for a positive charge. For a negative charge, the force is in the opposite direction.
The magnetic force is always perpendicular to both the velocity of the charge and the magnetic field.
Since the force is perpendicular to the direction of motion, the magnetic force does no work on the charge, and its kinetic energy does not change.

Circular Motion and Velocity Selectors

If a charged particle enters a uniform magnetic field perpendicularly, the magnetic force always acts at right angles to its velocity. This constant perpendicular force acts as a centripetal force, compelling the particle to move in a circular path. An important consequence is that the magnetic force does no work on the particle, so its speed and kinetic energy remain constant. This principle is key to devices like mass spectrometers.

A velocity selector is a clever arrangement of perpendicular electric and magnetic fields. Only particles moving at a specific velocity will pass through undeflected, because the magnetic force ( $F_B$ ) will exactly cancel out the electric force ( $F_E$ ). Particles too fast or too slow will be deflected.

For undeflected particles: $F_B = F_E$ $BQv = EQ$ $v = \frac{E}{B}$ Where:

$v$ = selected velocity (m s⁻¹)
$E$ = electric field strength (V m⁻¹ or N C⁻¹)
$B$ = magnetic flux density (T)

A uniform magnetic force acting perpendicular to velocity provides the centripetal force ( $F = \frac{mv^2}{r}$ ), leading to circular motion.
Velocity selectors filter particles based on speed, useful in experimental physics.
The balance $BQv = EQ$ means the charge $Q$ cancels out, so the selection is independent of the particle's charge magnitude.

The Hall Effect: Measuring Magnetic Fields

The Hall effect is a fascinating phenomenon observed when a current-carrying conductor is placed in a magnetic field perpendicular to the current. The magnetic force pushes the charge carriers (e.g., electrons) to one side of the conductor, creating a build-up of charge. This charge separation generates an electric field and, consequently, a measurable potential difference across the conductor, known as the Hall voltage ( $V_H$ ).

$V_H = \frac{BI}{nQt}$ Where:

$V_H$ = Hall voltage (V)
$B$ = magnetic flux density (T)
$I$ = current (A)
$n$ = charge carrier number density (m⁻³)
$Q$ = charge of one carrier (C)
$t$ = thickness of the conductor perpendicular to B and I (m)

The Hall voltage is directly proportional to the magnetic flux density ( $B$ ).
Hall probes are compact devices that use the Hall effect to precisely measure magnetic field strengths.
The sign of the Hall voltage can reveal the sign of the charge carriers (e.g., electrons or holes).
The thickness 't' is perpendicular to both current and magnetic field, affecting the path for charge accumulation.

Worked examples

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

EXAMPLE 1

A proton enters a velocity selector with an electric field strength of $2.0 \times 10^4 \, \text{V m}^{-1}$ and a magnetic flux density of $0.50 \, \text{T}$ . Calculate the speed at which the proton will pass through undeflected.

1
Identify the given values: $E = 2.0 \times 10^4 \, \text{V m}^{-1}$ , $B = 0.50 \, \text{T}$ .

EXAMPLE 2

An electron travels at a speed of 5.0 x 10^6 m/s and enters a region of uniform magnetic field of flux density 0.020 T. The electron's path is perpendicular to the magnetic field. Calculate the radius of the circular path it follows. (Charge of an electron = 1.60 x 10^-19 C, mass of an electron = 9.11 x 10^-31 kg)

1
Identify the forces acting on the electron. The magnetic force provides the centripetal force for the circular motion.

How it all connects

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

MAIN IDEAForce on a moving charge

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

Glossary

Try to recall each definition before you reveal it.

Quick check

Answer in your head first — then tap to check. No pressure.

Revision flashcards

Flip the card. Test yourself before the exam.

QUESTION · 1 / 15

What causes a charged particle to experience a magnetic force?

TAP OR SPACE TO FLIP

ANSWER

It experiences a magnetic force when it moves through a magnetic field, provided its velocity has a component perpendicular to the field.

TAP OR SPACE TO FLIP BACK

1 / 15 · ← → space

Key takeaways

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

✓
The force $F = BQv\sin\theta$ is maximum when the charge moves perpendicular to the field ( $\theta=90^\circ$ ).
✓
The force is zero when the charge moves parallel to the field ( $\theta=0^\circ$ ).
✓
Fleming's Left-Hand Rule determines the force direction for a positive charge. For a negative charge, the force is in the opposite direction.
✓
The magnetic force is always perpendicular to both the velocity of the charge and the magnetic field.
✓
Since the force is perpendicular to the direction of motion, the magnetic force does no work on the charge, and its kinetic energy does not change.

Practice — then mark it

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

Real past paper[2]

9702/41 · Q5(c)(ii)

Explain, with reference to the forces exerted by the two fields on the electron, why the path of the electron is undeviated.

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.

Frequently asked

✓

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 9702/41 · Q5(c)(ii) 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

← PREVIOUS20.2 Force on a current-carrying conductor NEXT →20.4 Magnetic fields due to currents

Force on a moving charge

BY THE END, YOU CAN…

1Describe the magnetic force on a moving charge and apply F = BQvsinθ.
2Explain the function of a velocity selector and how it utilises electric and magnetic fields.
3Outline the principles of the Hall effect and its application in Hall probes.

In simple terms

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

Force on a moving charge

Cambridge 9702 Paper 4 — Force on a moving charge (20.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
The force $F = BQv\sin\theta$ is maximum when the charge moves perpendicular to the field ( $\theta=90^\circ$ ).
2
The force is zero when the charge moves parallel to the field ( $\theta=0^\circ$ ).
3
Fleming's Left-Hand Rule determines the force direction for a positive charge. For a negative charge, the force is in the opposite direction.
4
The magnetic force is always perpendicular to both the velocity of the charge and the magnetic field.

What this topic covers

The official Cambridge syllabus points this lesson works through.

20.3.1
Determine the direction of the force on a charge moving in a magnetic field
20.3.2
Recall and use $F = BQv \sin θ$
20.3.3
Understand the origin of the Hall voltage and derive and use the expression $V_H = BI/(ntq)$, where t = thickness
20.3.4
Understand the use of a Hall probe to measure magnetic flux density
20.3.5
Describe the motion of a charged particle moving in a uniform magnetic field perpendicular to the direction of motion of the particle
20.3.6
Explain how electric and magnetic fields can be used in velocity selection

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Key formulas

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

$F = BQv\sin\theta$

Tap a symbol — great for exam definitions

$F_B = F_E$

Tap a symbol — great for exam definitions

$V_H = \frac{BI}{nQt}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

Magnetic Force on Individual Charges

$F = BQv\sin\theta$ Where:

$F$ = magnetic force (N)
$B$ = magnetic flux density (T)
$Q$ = magnitude of the charge (C)
$v$ = speed of the particle (m s⁻¹)
$\theta$ = angle between the velocity vector ( $\vec{v}$ ) and the magnetic field vector ( $\vec{B}$ )

The force $F = BQv\sin\theta$ is maximum when the charge moves perpendicular to the field ( $\theta=90^\circ$ ).
The force is zero when the charge moves parallel to the field ( $\theta=0^\circ$ ).
Fleming's Left-Hand Rule determines the force direction for a positive charge. For a negative charge, the force is in the opposite direction.
The magnetic force is always perpendicular to both the velocity of the charge and the magnetic field.
Since the force is perpendicular to the direction of motion, the magnetic force does no work on the charge, and its kinetic energy does not change.

Circular Motion and Velocity Selectors

For undeflected particles: $F_B = F_E$ $BQv = EQ$ $v = \frac{E}{B}$ Where:

$v$ = selected velocity (m s⁻¹)
$E$ = electric field strength (V m⁻¹ or N C⁻¹)
$B$ = magnetic flux density (T)

A uniform magnetic force acting perpendicular to velocity provides the centripetal force ( $F = \frac{mv^2}{r}$ ), leading to circular motion.
Velocity selectors filter particles based on speed, useful in experimental physics.
The balance $BQv = EQ$ means the charge $Q$ cancels out, so the selection is independent of the particle's charge magnitude.

The Hall Effect: Measuring Magnetic Fields

$V_H = \frac{BI}{nQt}$ Where:

$V_H$ = Hall voltage (V)
$B$ = magnetic flux density (T)
$I$ = current (A)
$n$ = charge carrier number density (m⁻³)
$Q$ = charge of one carrier (C)
$t$ = thickness of the conductor perpendicular to B and I (m)

The Hall voltage is directly proportional to the magnetic flux density ( $B$ ).
Hall probes are compact devices that use the Hall effect to precisely measure magnetic field strengths.
The sign of the Hall voltage can reveal the sign of the charge carriers (e.g., electrons or holes).
The thickness 't' is perpendicular to both current and magnetic field, affecting the path for charge accumulation.

Worked examples

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

EXAMPLE 1

1
Identify the given values: $E = 2.0 \times 10^4 \, \text{V m}^{-1}$ , $B = 0.50 \, \text{T}$ .

EXAMPLE 2

1
Identify the forces acting on the electron. The magnetic force provides the centripetal force for the circular motion.

How it all connects

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

MAIN IDEAForce on a moving charge

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

Glossary

Try to recall each definition before you reveal it.

Quick check

Answer in your head first — then tap to check. No pressure.

Revision flashcards

Flip the card. Test yourself before the exam.

QUESTION · 1 / 15

What causes a charged particle to experience a magnetic force?

TAP OR SPACE TO FLIP

ANSWER

It experiences a magnetic force when it moves through a magnetic field, provided its velocity has a component perpendicular to the field.

TAP OR SPACE TO FLIP BACK

1 / 15 · ← → space

Key takeaways

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

✓
The force $F = BQv\sin\theta$ is maximum when the charge moves perpendicular to the field ( $\theta=90^\circ$ ).
✓
The force is zero when the charge moves parallel to the field ( $\theta=0^\circ$ ).
✓
Fleming's Left-Hand Rule determines the force direction for a positive charge. For a negative charge, the force is in the opposite direction.
✓
The magnetic force is always perpendicular to both the velocity of the charge and the magnetic field.
✓
Since the force is perpendicular to the direction of motion, the magnetic force does no work on the charge, and its kinetic energy does not change.

Practice — then mark it

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

Real past paper[2]

9702/41 · Q5(c)(ii)

Explain, with reference to the forces exerted by the two fields on the electron, why the path of the electron is undeviated.

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.

Frequently asked

✓

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 9702/41 · Q5(c)(ii) 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

← PREVIOUS20.2 Force on a current-carrying conductor NEXT →20.4 Magnetic fields due to currents

Revise Force on a moving charge for Cambridge 9702 (20.3)

In simple terms

What this topic covers

Explore the concept

Key formulas

Full topic notes

Magnetic Force on Individual Charges

Circular Motion and Velocity Selectors

The Hall Effect: Measuring Magnetic Fields

Worked examples

How it all connects

Glossary

Quick check

Revision flashcards

Key takeaways

Practice — then mark it

9702/41 · Q5(c)(ii)

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

In simple terms

What this topic covers

Explore the concept

Key formulas

Full topic notes

Magnetic Force on Individual Charges

Circular Motion and Velocity Selectors

The Hall Effect: Measuring Magnetic Fields

Worked examples

How it all connects

Glossary

Quick check

Revision flashcards

Key takeaways

Practice — then mark it

9702/41 · Q5(c)(ii)

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Force on a moving charge