The shape of the lesson
By the end of the lesson, learners can
- A circle, then a selector: In the magnetic field, the force points to the centre and the charge loops round; change the speed or the field and watch the radius follow r = mv / BQ.
- The Hall voltage: A current in a slab sits in a field pointing into the page.
- From wire to charge: The force on a wire and the force on a charge are the same physics seen two ways.
- On a conductor: F = BIL sinθ; the tesla is defined from B = F/(IL) (N A⁻¹ m⁻¹).
- On a charge: F = BQv sinθ, always perpendicular to v, so the path is a circle with r = mv/BQ.
- Induction: Φ = BA, flux linkage = NΦ, induced e.m.f. = rate of change of flux linkage (Faraday); direction opposes the change (Lenz).
One picture every idea returns to
A charge moving through a magnetic field feels a force F = BQv sinθ, always perpendicular to its velocity. A perpendicular force does no work, so the speed is constant and the path is a circle with r = mv / BQ. Cross the magnetic field with an electric one and only the speed v = E / B passes straight through, a velocity selector.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Bending a beam of charge.. The motor effect is really a force on each moving charge. | Whole class, then pairs |
| 5 to 13 min | Teach and check: A circle, then a selector | In the magnetic field, the force points to the centre and the charge loops round; change the speed or the field and watch the radius follow r = mv / BQ. Project tab 4 of the lab (Force on a moving charge) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: The Hall voltage | A current in a slab sits in a field pointing into the page. Project the simulation and let a student drive it while the class predicts. | Pairs |
| 21 to 30 min | Teach and check: From wire to charge | The force on a wire and the force on a charge are the same physics seen two ways. | Anticipation / Reaction Guide |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (4 questions, 46 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in From wire to charge, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Anticipation / Reaction Guide
Before the lesson, students mark five statements true or false. After the teaching they mark them again and justify any change of mind in one sentence each. The statements come from the examiner traps below.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| The magnetic force does no work: it changes direction, not speed, so the path is a circle, not a spiral that speeds up. | In r = mv / BQ the radius is proportional to speed and inversely proportional to B. A velocity selector passes v = E / B regardless of charge or mass. Keep the Hall voltage (across the slab) separate from the driving p.d. (along it). |
Force on a moving charge: topic worksheet
4 questions, 46 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
An electron travelling at 3.0 × 10⁶ m s⁻¹ enters a uniform magnetic field of flux density 2.0 mT at right angles to the field. (electron mass 9.11 × 10⁻³¹ kg, charge 1.6 × 10⁻¹⁹ C)
(a) Explain why the electron follows a circular path at constant speed. [2]
(b) Calculate the magnitude of the magnetic force on the electron. [2]
(c) Show that the radius of the path is given by r = mv/BQ, and calculate r. [3]
(d) Calculate the period of the circular motion. [2]
(e) State and explain the effect on the radius of doubling the speed. [2]
(f) State the effect on the period of doubling the speed. [1]
A slice of a current-carrying semiconductor is placed in a magnetic field perpendicular to its largest face. A steady Hall voltage appears across the slice.
(a) Explain how the Hall voltage is set up. [3]
(b) The Hall voltage is Vₐ = BI / (ntq). A slice has charge-carrier density n = 1.0 × 10²² m⁻³, thickness t = 0.50 mm, and carries a current of 20 mA. The Hall voltage is 2.4 mV. Calculate the flux density. [3]
(c) Explain why a semiconductor, rather than a metal, is used for a Hall probe. [2]
(d) State what a Hall probe is used to measure. [1]
(e) State the effect on the Hall voltage of doubling the flux density. [1]
Fig. 5.1 shows a velocity selector. Positive ions pass through a region of crossed electric and magnetic fields. The electric field is produced by parallel plates 2.0 cm apart with a potential difference of 600 V across them, and the magnetic field has flux density 0.050 T.
(a) Show that an ion travels straight through only if its speed is v = E/B. [2]
(b) Calculate the electric field strength between the plates, and hence the selected speed. [3]
(c) Explain what happens to ions that are travelling faster than the selected speed. [2]
(d) The selected ions, each of charge +1.6 × 10⁻¹⁹ C, then enter a magnetic field of flux density 0.20 T and move in a circle of radius 8.0 cm. Calculate the mass of an ion. [3]
(e) State the name of an instrument that uses this arrangement. [1]
This question links three lessons of the topic. A long solenoid carries a current and a coil of 500 turns is wound around its middle.
(a) Describe the magnetic field inside the solenoid, and state the effect of placing a soft iron core inside it. [2]
(b) The current is switched off, and the flux linkage of the 500-turn coil falls from 0.080 Wb to zero in 0.040 s. Calculate the average e.m.f. induced. [3]
(c) State the direction of the induced current relative to the change, and the law used. [2]
(d) An electron now enters the solenoid's field of flux density 0.015 T at 2.0 × 10⁶ m s⁻¹, at right angles to the field. Calculate the radius of its circular path. [3]
(e) State and explain the effect on this radius of doubling the flux density. [2]
(f) State why the magnetic force on the electron does not change its speed. [1]
Answer key and marking notes
- (a)The magnetic force is always perpendicular to the velocity ✓, so it does no work and the speed is constant, while the constant-magnitude perpendicular force gives circular motion ✓
- (b)F = BQv = 2.0 × 10⁻³ × 1.6 × 10⁻¹⁹ × 3.0 × 10⁶ ✓ = 9.6 × 10⁻¹⁶ N ✓
- (c)The magnetic force provides the centripetal force: BQv = mv²/r ✓, so r = mv/BQ ✓. r = (9.11 × 10⁻³¹ × 3.0 × 10⁶)/(2.0 × 10⁻³ × 1.6 × 10⁻¹⁹) = 8.5 × 10⁻³ m (8.5 mm) ✓
- (d)T = 2πm/BQ = 2π × 9.11 × 10⁻³¹ / (2.0 × 10⁻³ × 1.6 × 10⁻¹⁹) ✓ = 1.8 × 10⁻⁸ s ✓
- (e)The radius doubles ✓, since r = mv/BQ is proportional to v ✓
- (f)No change: the period is independent of speed ✓
- (a)The moving charge carriers feel a magnetic force BQv and are pushed to one side ✓; charge builds up there, creating a transverse electric field (p.d.) ✓; this grows until its electric force balances the magnetic force, giving a steady Hall voltage ✓
- (b)B = Vₐ n t q / I = (2.4 × 10⁻³ × 1.0 × 10²² × 0.50 × 10⁻³ × 1.6 × 10⁻¹⁹) / 0.020 ✓✓ = 0.096 T ✓
- (c)A semiconductor has a much smaller carrier density n ✓, so for the same B and I the Hall voltage is much larger and easier to measure ✓
- (d)Magnetic flux density ✓
- (e)It doubles ✓
- (a)For a straight path the electric and magnetic forces balance: qE = qvB ✓, so v = E/B ✓
- (b)E = V/d = 600 / 0.020 = 3.0 × 10⁴ V m⁻¹ ✓; v = E/B = 3.0 × 10⁴ / 0.050 ✓ = 6.0 × 10⁵ m s⁻¹ ✓
- (c)A faster ion has a larger magnetic force (BQv) than electric force ✓, so it is deflected toward the magnetic-force side and does not pass straight through ✓
- (d)r = mv/BQ, so m = BQr/v = (0.20 × 1.6 × 10⁻¹⁹ × 0.080) / (6.0 × 10⁵) ✓✓ = 4.3 × 10⁻²⁷ kg ✓
- (e)A mass spectrometer ✓
- (a)Strong and almost uniform inside (parallel, equally spaced lines) ✓; a soft iron core greatly increases the flux density ✓
- (b)ε = Δ(NΦ)/Δt. Here the quoted flux linkage falls from 0.080 to 0 Wb ✓; ε = 0.080 / 0.040 ✓ = 2.0 V ✓
- (c)The induced current acts to oppose the fall in flux (it tries to maintain it) ✓; this is Lenz's law ✓
- (d)r = mv/BQ = (9.11 × 10⁻³¹ × 2.0 × 10⁶)/(0.015 × 1.6 × 10⁻¹⁹) ✓✓ = 7.6 × 10⁻⁴ m (0.76 mm) ✓
- (e)The radius halves ✓, since r = mv/BQ is inversely proportional to B ✓
- (f)The force is always perpendicular to the velocity, so it does no work ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
The magnetic force on a charge moving through a field does no work on it because the force is always:
- Aperpendicular to the velocity
- Bparallel to the velocity
- Cequal to the electric force
- Ddirected along the field
A charged particle moves in a circle in a uniform magnetic field. If its speed is doubled while B, charge and mass are unchanged, the radius:
- Adoubles
- Bhalves
- Cstays the same
- Dquadruples
In a velocity selector with crossed electric and magnetic fields, a charged particle travels straight through only when its speed equals:
- AE / B
- BB / E
- CE × B
- DE + B
A Hall probe is an instrument used to measure:
- Amagnetic flux density
- Belectric current
- Celectrical resistance
- Dthe charge of an electron
Quiz key
Work needs a force component along the motion. The magnetic force is at right angles to v, so it does no work and the speed is constant.
r = mv / BQ, so r is proportional to v: doubling the speed doubles the radius. The period T = 2πm/BQ is unchanged.
The fields balance when the electric force equals the magnetic force: QE = BQv, giving v = E / B, independent of charge and mass.
The Hall voltage V_H = BI/(ntq) is proportional to B for a fixed current, so a calibrated Hall probe reads the magnetic flux density.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.