A Level Physics: Magnetic Fields — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — 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]

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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].

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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.