CBSE Class 12 · 2016 · All India · Magnetic Effects of CurrentShort Answer

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State the principle of a cyclotron. Show that the time period of revolution of particles in a cyclotron is independent of their speeds. Why is this property necessary for the operation of a cyclotron?

Answer: $T = \frac{2 π m}{q B}$ , independent of speed; this lets a fixed-frequency electric field stay in step with the particle.

Solution

\textbf{Principle:} a charged particle is accelerated repeatedly across the gap by an alternating field while a perpendicular magnetic field keeps it circling. For circular motion the magnetic force supplies the centripetal force:

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

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

which contains no

v

— the period is independent of speed (and radius). This is essential so that a single fixed-frequency oscillator stays synchronised with the particle on every revolution, no matter how fast it has become.

CBSE Class 12 Board · 2016 · All India · Subjective

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CBSE Class 12 · 2016 · All India · Magnetic Effects of CurrentShort Answer

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