Question
Draw a schematic diagram of a cyclotron. Explain its underlying principle and working, stating clearly the function of the electric and magnetic fields applied on a charged particle. Deduce an expression for the period of revolution and show that it does not depend on the speed of the charged particle.

Answer

  1.  
  1. Principle and working.
  2. The magnetic field make the charged particles go round in circular path inside the dees and electric field accelerates them every time the particles move from one dee to other.
$\frac{\text{mv}^{2}}{\text{r}} = \text{qvB}$
$\therefore \text{v} = \frac{\text{qBr}}{\text{m}}$
$\therefore$ Period of revolution, $\text{T} = \frac{2\pi\text{r}}{\text{v}}$
$=\frac{2\pi\text{rm}}{\text{qBr}} = \frac{2\pi\text{m}}{\text{qB}}$
$\therefore$ 'T' is independent of 'v'.

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