CBSE Class 12 · 2014 · Delhi · Magnetic Effects of CurrentLong Answer

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(a) Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of the velocity or energy of the particle.
(b) Draw a schematic sketch of a cyclotron. Explain, giving the essential details of its construction, how it is used to accelerate charged particles.

Answer: $f = \frac{q B}{2 π m}$ , independent of $v$ .

Solution

(a) For circular motion,

q v B = \frac{m v ^{2}}{r} \Rightarrow r = \frac{m v}{q B}

. The frequency

f = \frac{v}{2 π r} = \frac{v}{2 π} \cdot \frac{q B}{m v} = \frac{q B}{2 π m},

which contains no

v

— it is independent of the particle's speed or energy. (b) A cyclotron has two hollow D-shaped electrodes (dees) in a perpendicular magnetic field, with a high-frequency alternating voltage across the gap. The field curves the ion into semicircles; every gap-crossing the voltage (tuned to

f

) accelerates it, so it spirals outward gaining energy until it leaves at the rim.

CBSE Class 12 Board · 2014 · Delhi · Subjective

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CBSE Class 12 · 2014 · Delhi · Magnetic Effects of CurrentLong Answer

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