A Level Physics: Magnetic Fields — Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Magnetic Fields revision notes

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Questions

1. Define magnetic flux density. [2]

2. State Fleming’s left-hand rule, saying what it applies to, and state Lenz’s law, saying what it is used for. [4]

3. A wire of length 0.18 m carrying 4.5 A lies at 40° to a magnetic field of 0.32 T.

(a) Calculate the force on the wire. [3] (b) State the angle at which the force would be maximum, and its value. [2]

4. A proton enters a uniform magnetic field of 0.85 T perpendicular to the field lines at 3.2 × 10⁶ m s⁻¹. (m_p = 1.67 × 10⁻²⁷ kg; e = 1.60 × 10⁻¹⁹ C)

(a) Calculate the magnetic force on it. [2] (b) Explain why the path is circular. [2] (c) Calculate the radius of the path. [3] (d) State and explain what happens to the radius if the speed is doubled. [2]

5. A coil of 400 turns and area 2.5 × 10⁻³ m² is perpendicular to a field of 0.60 T. The coil is removed from the field in 0.20 s.

(a) Calculate the initial flux linkage. [2] (b) Calculate the average induced e.m.f. [2]

6. State Lenz’s law and explain how it follows from conservation of energy. [3]

7. Describe the pattern of the magnetic field produced by (a) a long straight current-carrying wire, and (b) a long current-carrying solenoid. [4]

8. (Part (b) is an extension beyond the 9702 electromagnetic induction syllabus — the rotating-coil generator formula ε₀ = BANω is not a 9702 recall requirement or data-booklet equation; it is included for context only, not examinable.) A coil of 200 turns and area 0.010 m² rotates at 50 revolutions per second in a magnetic field of flux density 0.050 T.

(a) Calculate the angular frequency of rotation. [2] (b) (Extension, not examinable.) Calculate the peak e.m.f. induced. (c) State how the e.m.f. varies with time. [1]

9. A coil of insulated wire is connected to a sensitive centre-zero galvanometer. The north pole of a bar magnet is pushed into one end of the coil, held at rest inside it, and then pulled out.

(a) Describe what the galvanometer shows during each of the three stages. [3] (b) State two changes to the apparatus or the method that would give a larger maximum deflection, and explain why each works. [4] (c) State the magnetic polarity of the end of the coil nearest the magnet while the magnet is being pushed in, and explain why work must be done to push the magnet in. [3]

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Answers

1. The force per unit length per unit current on a conductor at right angles to the field [1]; B = F ÷ (IL), measured in tesla [1].

2. Fleming’s left-hand rule — First finger Field, seCond finger Current, thuMb Motion [1]; applies to the motor effect, i.e. the direction of the force on a current-carrying conductor in a magnetic field [1]. Lenz’s law — the induced e.m.f. (and hence induced current) acts in a direction that opposes the change producing it [1]; it is used to determine the direction of an induced e.m.f. in electromagnetic induction [1].

3. (a) F = BIL sin θ = 0.32 × 4.5 × 0.18 × sin 40° [1] [1] = 0.167 N [1]. (b) At 90° [1]; F = 0.32 × 4.5 × 0.18 = 0.259 N [1].

4. (a) F = BQv = 0.85 × 1.60 × 10⁻¹⁹ × 3.2 × 10⁶ [1] = 4.35 × 10⁻¹³ N [1]. (b) The force is always perpendicular to the velocity [1], so it changes the direction but not the magnitude of the velocity — the definition of a centripetal force [1]. (c) BQv = mv² ÷ r, so r = mv ÷ BQ [1] = (1.67 × 10⁻²⁷ × 3.2 × 10⁶) ÷ (0.85 × 1.60 × 10⁻¹⁹) [1] = 3.93 × 10⁻² m [1]. (d) The radius doubles [1], since r is directly proportional to v [1].

5. (a) NΦ = NBA = 400 × 0.60 × 2.5 × 10⁻³ [1] = 0.60 Wb turns [1]. (b) e.m.f. = Δ(NΦ) ÷ Δt = 0.60 ÷ 0.20 [1] = 3.0 V [1].

6. The induced current acts in the direction that opposes the change producing it [1]. If it assisted the change instead, the induced current would increase the flux, inducing a larger current still, and energy would be created from nothing [1]. Opposing the change means work must be done against the induced effect, and that work supplies the electrical energy [1].

7. (a) Concentric circles around the wire, centred on it [1]; the flux density increases with current and decreases with distance from the wire [1]. (b) A strong, uniform field inside the solenoid, similar to a bar magnet’s field but concentrated and controllable via the current [1]; the field is weaker and spreads out outside the solenoid’s ends [1]. Reversing the current direction reverses the polarity of the field, exactly as it would for a bar magnet.

8. (a) ω = 2πf, converting the rotation rate from rev/s to rad/s first [1] = 2π × 50 = 314 rad s⁻¹ [1]. (b) (Extension, not part of the 9702 mark scheme.) peak e.m.f. = NBAω = 200 × 0.050 × 0.010 × 314 = 31.4 V. (c) It varies sinusoidally with time, oscillating between +31.4 V and −31.4 V [1].

9. (a) Pushed in: a brief deflection in one direction [1]. At rest: no deflection (zero reading), because the flux linkage is not changing [1]. Pulled out: a brief deflection in the opposite direction [1]. (b) Any two, each with its reason [1] + [1]: move the magnet faster — the flux linkage changes in less time; use a stronger magnet — a larger change of flux; use a coil with more turns — a larger change of flux linkage NΦ; wind the coil on an iron core and move the magnet towards its end — the iron concentrates more of the magnet’s flux through the turns. (A larger coil area is not credited: a wider loop around a bar magnet also encloses the magnet’s return field, so the net flux linked does not increase.) Each increases the rate of change of flux linkage, and by Faraday’s law the induced e.m.f. (and so the current) is proportional to it. (c) A north pole [1]. By Lenz’s law, the induced current opposes the change producing it, so the coil repels the approaching magnet [1]; work must be done against this repulsive force, and this work is transferred to electrical energy in the circuit (conservation of energy) [1].

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Where marks are usually lost

• Omitting sin θ when the conductor is not perpendicular to the field.
• Using the left hand for induction.
• Saying the magnetic force does work on a charged particle — it does not.
• Stating Lenz’s law without linking it to conservation of energy.
• Describing the field of a solenoid as circular, like a straight wire, rather than as a strong uniform field resembling a bar magnet’s.
• Forgetting to convert frequency in rev/s (or Hz) to angular frequency ω = 2πf (this conversion is examinable even though the generator e.m.f. formula ε₀ = BANω it feeds into, in Q8(b), is an extension beyond the 9702 syllabus).

Work through the Magnetic Fields revision notes alongside these questions: the notes summarise the three ways to induce an e.m.f. and the flux/flux-linkage definitions in condensed form, while these questions test whether you can apply the generator e.m.f. formula and describe field patterns for a specific current-carrying conductor, rather than just recall the equations.