A-LevelPhysicsMagnetic fields9702/41 · Oct/Nov 2020 · Q88 Marks

A slice of a conducting material has its face QRLK normal to a uniform magnetic field of flux density B, as illustrated in Fig. 8.1. [Figure 8.1]. Electrons enter the slice travelling perpendicular to face PQKJ.

(a)(i)For the free electrons moving in the slice: state the direction of the force on an electron due to movement of the electron in the magnetic field[1]
(a)(ii)identify the faces, using the letters on Fig. 8.1, between which a potential difference is developed.[1]
(b)Explain why the potential difference in (a)(ii) reaches a maximum value.[2]
(c)The number of free electrons per unit volume in the slice of material is 1.3 × 10²⁹m⁻³. The thickness PQ of the slice is 0.10 mm. The magnetic flux density B is 4.6 × 10⁻³T. Calculate the potential difference across the slice for a current of 6.3 × 10⁻⁴A.[2]
(d)The slice in (c) is a metal. By reference to your answer in (c), suggest why Hall probes are usually made using semiconductors rather than metals.[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.

[B1] downwards
[B1] PQRS and JKLM
[B1] (as charge separates) an electric field is created (between opposite faces)
[B1] (maximum value is reached when) electric force (on electron) is equal and opposite to magnetic force (on electron)
[C1] V_H = BI / ntq
[C1] = (4.6 × 10⁻³ × 6.3 × 10⁻⁴) / (1.3 × 10²⁹ × 0.10 × 10⁻³ × 1.60 × 10⁻¹⁹)
[A1] = 1.4 x 10⁻¹² V
[B1] semiconductors have a (much) smaller value for n
[B1] V_H for semiconductors is (much) larger so more easily measured

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