Physics • Year 12 • Module 6 • Lesson 4
Magnetic Fields and the Lorentz Force
Lock in the core vocabulary, the Lorentz force law, and the right-hand rule before tackling harder problems.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: Lorentz force, magnetic field, right-hand rule, tesla, cross product, magnetic force, velocity, perpendicular, work, kinetic energy. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The force exerted on a moving charged particle by a magnetic field, given by F = qvB sin θ. | |
| 1.2 | A vector field that exerts a force on moving charges but does no work on them. Measured in teslas. | |
| 1.3 | A method for finding the direction of the magnetic force on a positive charge: thumb points in the direction of velocity, fingers point along the field, and the palm pushes in the direction of force. | |
| 1.4 | The SI unit of magnetic field strength. Equal to 1 N/(A m). | |
| 1.5 | The mathematical vector operation whose result gives the direction of the magnetic force: v × B. | |
| 1.6 | At 90° to another quantity; describes the relationship between the magnetic force and the velocity of the charged particle at every instant. | |
| 1.7 | The speed and direction of motion of a charged particle. The symbol for its magnitude appears in the Lorentz force formula. | |
| 1.8 | The energy associated with a particle’s motion. The magnetic force cannot change this quantity. | |
| 1.9 | The product of force and displacement in the direction of the force. Equal to zero for a magnetic force because F is always perpendicular to displacement. | |
| 1.10 | The push or pull exerted by a magnetic field on a moving charged particle; always perpendicular to both v and B. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 The magnetic force on a stationary charged particle is equal to qB. T / F
2.2 When a charged particle moves perpendicular to a uniform magnetic field, the magnitude of the magnetic force is at its maximum value of qvB. T / F
2.3 A magnetic field can speed up a charged particle because the force acts in the direction of motion. T / F
2.4 For an electron (negative charge) the magnetic force direction is opposite to that predicted by the right-hand rule. T / F
2.5 When a charged particle moves parallel to a magnetic field (θ = 0°), the magnetic force is at its maximum. T / F
2.6 A cross symbol (×) on a physics diagram represents a magnetic field pointing out of the page, like the tip of an arrow flying toward you. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
charge · direction · kinetic energy · magnetic field · opposite · perpendicular · sin θ · work
The Lorentz force law states that the force on a moving charged particle in a ___________ is given by F = qvB ___________, where q is the ___________ of the particle, v is its speed, and B is the field strength. The direction of the force is always ___________ to both the velocity and the field. For a negative charge such as an electron, the force direction is ___________ to that predicted by the right-hand rule for a positive charge. Because the force is always perpendicular to the velocity, the magnetic force does no ___________ on the particle. As a result, the particle’s ___________ and speed remain constant; only the ___________ of motion changes.
4. Short recall questions
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 State the condition under which the magnetic force on a moving charged particle is equal to zero. Use the Lorentz force equation to justify your answer.
4.2 Explain why the magnetic force can change the direction of a particle’s velocity but cannot change the magnitude of its velocity (i.e. its speed).
4.3 Describe, in words, how to use the right-hand rule to determine the direction of the magnetic force on a positively charged particle.
4.4 On a physics diagram, what symbol indicates a magnetic field pointing into the page, and what symbol indicates a field pointing out of the page? Explain the visual mnemonic behind each symbol.
5. Label the Lorentz force equation
The equation below has five components labelled A–E. In the table, write the name, SI unit, and a brief description of what each symbol represents. 10 marks (2 per row)
F = q × v × B × sin θ
A B C D E
| Label | Symbol | Name | SI unit | Brief description |
|---|---|---|---|---|
| A | F | |||
| B | q | |||
| C | v | |||
| D | B | |||
| E | sin θ |
Q1 — Term–definition match
1.1 Lorentz force • 1.2 magnetic field • 1.3 right-hand rule • 1.4 tesla • 1.5 cross product • 1.6 perpendicular • 1.7 velocity • 1.8 kinetic energy • 1.9 work • 1.10 magnetic force.
Q2 — True / false with correction
2.1 False. The magnetic force on a stationary particle is zero, because the Lorentz force equation is F = qvB sin θ; if v = 0, then F = 0 regardless of q or B.
2.2 True. When θ = 90°, sin 90° = 1, so F = qvB (the maximum value).
2.3 False. The magnetic force is always perpendicular to the velocity, so it can never act in the direction of motion. It therefore does no work and cannot change the particle’s speed. Only an electric field can accelerate (speed up) a charged particle.
2.4 True. The right-hand rule applies to positive charges. For negative charges the force is reversed.
2.5 False. When θ = 0°, sin 0° = 0, so F = 0. The force is zero, not maximum, when the velocity is parallel to the field.
2.6 False. A cross symbol (×) represents a field pointing into the page (like the tail feathers of an arrow flying away). A dot (·) represents a field pointing out of the page (like the tip of an arrow flying toward you).
Q3 — Cloze paragraph
In order: magnetic field / sin θ / charge / perpendicular / opposite / work / kinetic energy / direction.
Q4.1 — Zero magnetic force
The magnetic force is zero when the particle moves parallel to the field (θ = 0° or 180°). In the equation F = qvB sin θ, sin 0° = 0, so F = 0. The force is also zero if the particle is stationary (v = 0).
Q4.2 — Direction changes, speed does not
The magnetic force is always perpendicular to the velocity vector. Because the force has no component along the direction of motion, the work done (W = F·d = Fd cos 90° = 0) is zero. By the work-energy theorem, zero net work means zero change in kinetic energy, so the speed (magnitude of velocity) is constant. The force continuously redirects the velocity without changing its magnitude.
Q4.3 — Right-hand rule description
Point your thumb in the direction of the particle’s velocity (v). Curl your fingers so they point in the direction of the magnetic field (B). Your palm then faces in the direction of the magnetic force (F) on a positive charge. For a negative charge, the force is in the opposite direction.
Q4.4 — Field symbols
A cross (×) represents a field pointing into the page — it looks like the tail feathers of an arrow flying away from you. A dot (·) represents a field pointing out of the page — it looks like the tip of an arrow flying toward you.
Q5 — Lorentz force equation labels
A — F: Magnetic force; unit = newton (N); the magnitude of the force exerted on the moving charge by the field.
B — q: Electric charge; unit = coulomb (C); the charge carried by the particle (positive for proton, negative for electron).
C — v: Speed of the particle; unit = m/s; the magnitude of the velocity vector of the charged particle.
D — B: Magnetic field strength (magnetic flux density); unit = tesla (T); the strength of the external magnetic field.
E — sin θ: Dimensionless (no unit); the sine of the angle between the velocity vector and the magnetic field vector. Accounts for the fact that only the component of velocity perpendicular to B contributes to the force.