A-LevelPhysicsMagnetic fields9702/42 · Feb/Mar 2017 · Q89 Marks

(b) A particle of charge +q and mass m is travelling in a vacuum with speed v. The particle enters, at a right angle, a uniform magnetic field of flux density B, as shown in Fig. 8.1. particle charge +q mass m speed v d uniform magnetic field flux density B Fig. 8.1 The particle leaves the field after following a semi-circular path of diameter d.

(a)State what is meant by a magnetic field.[2]
(b)(i)State the direction of the magnetic field.[1]
(b)(ii)Explain why the speed of the particle is not affected by the magnetic field.[2]
(b)(iii)Show that the diameter d of the semi-circular path is given by the expression d = 2mv / Bq[2]
(b)(iv)Use the expression in (b)(iii) to show that the time T_F spent in the field by the particle is independent of its speed v.[2]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

[M1] region (of space) where there is a force
[A1] produced by/on a magnet/magnetic pole/moving charge/current-carrying conductor
[B1] out of (the plane of) the paper/page
[B1] the force on the particle is (always) perpendicular to the velocity/perpendicular to the direction of travel/towards the centre of path
[B1] no work is done by the force on the particle/there is no acceleration in the direction of the velocity/the acceleration is (always) perpendicular to the velocity
[C1] F = Bqv or F = mv² /r
[A1] mv²/(d/2) = Bqv so d = 2mv / Bq
[C1] time = distance / speed T_F = πd/2v
[A1] T_F = (π/2v) × (2mv/Bq)
[A1] T_F = πm/Bq and so T_F independent of v

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