A-LevelPhysicsMagnetic fields9702/42 · Oct/Nov 2020 · Q98 Marks

A small coil is placed close to one end of a solenoid connected to a power supply. The plane of the small coil is normal to the axis of the solenoid, as illustrated in [Figure 9.1]. The power supply causes the current I in the solenoid to vary with time t as shown in [Figure 9.2].

(a)(i)State Faraday's law of electromagnetic induction.[2]
(a)(ii)On the axes of [Figure 9.3], sketch a graph to show the variation with time t of the electromotive force (e.m.f.) induced in the small coil.[4]
(b)The small coil in (a) is now replaced by a Hall probe. The Hall probe is positioned so that the reading for the probe is a maximum. The current I in the solenoid varies again as shown in [Figure 9.2]. On the axes of [Figure 9.4], sketch a graph to show the variation with time t of the reading V_H of the probe.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[M1] (induced) e.m.f. (directly) proportional to rate
[A1] of change of magnetic flux (linkage)
[B1] e.m.f. = 0 apart from thin pulses at t₁ and t₂
[B1] rectangular pulses centred on t₁ and t₂, of widths 2 small squares and 1 small square respectively
[B1] e.m.fs. at t₁ and t₂ have opposite polarities
[B1] magnitude of e.m.f. at t₂ double the magnitude of e.m.f. at t₁
[M1] VH shown as zero before (t₁ – 2 squares) and after (t₂ + 2 squares) and rises to a constant non-zero value between t₁ and t₂
[A1] change at t₁ shown as 2 small squares wide and change at t₂ shown as 1 small square wide

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