A-LevelPhysicsMagnetic fields9702/42 · May/June 2021 · Q810 Marks

Define magnetic flux density.

(a)Define magnetic flux density.[2]
(b)Electrons, each of mass m and charge q, are accelerated from rest in a vacuum through a potential difference V. Derive an expression, in terms of m, q and V, for the final speed v of the electrons. Explain your working.[2]
(c)(i)Show that the specific charge q/m of the electrons is given by the expression q/m = 2V / B²r². Explain your working.[2]
(c)(ii)Electrons are accelerated through a potential difference V of 230 V. The electrons are injected normally into the magnetic field of flux density 0.38 mT. The radius r of the circular orbit of the electrons is 14 cm. Use this information to calculate a value for the specific charge of an electron.[2]
(c)(iii)Suggest why the arrangement outlined in (ii), using the same values of B and V, is not practical for the determination of the specific charge of α-particles.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[2] • force per unit length • force per unit current • length/current perpendicular to field
[1] change in potential energy = change in kinetic energy OR qV = ½mv²
[1] v = √(2qV/m)
[1] magnetic force = centripetal force OR Bqv = mv² / r
[1] clear substitution of expression for v and correct algebra leading to q / m = 2V / B²r²
[1] q/m = (2 × 230) / [(0.38 × 10⁻³)² × 0.14²]
[1] = 1.6 × 10¹¹ C kg⁻¹
[1] (for α-particle,) q / m is (much) smaller
[1] r would be much larger

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