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?
CBSE OUTSIDE DELHI - SET 2 NORTH 2016
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The cyclotron uses both electric and magnetic fields, in combination, to increase the energy of the charged particles.
Alternate Answer
Cyclotron uses:
$\frac{\text{mv}^{2}}{\text{r}} = \text{qvB}$
$\therefore\text{r} = \frac{\text{mv}}{\text{qB}}$
Also $\text{T} = \frac{2\pi\text{r}}{\text{v}}$
$\therefore\text{T} = \frac{2\pi\text{m}}{\text{qB}}$
$\therefore$ T is ondependent of v, the speed of the charged particles.
This property ensures that if the frequency of the applied alternating electric field matches the cyclotron frequency, the particle whould keep on getting accelerated every time it crosses the gap between the dees.
Alternate Answer
Because of the property, the applied alternating electric field can be made to accelerate the charged particles continuously. This property ensures that the resonance condition can be satisfied and the particle gets accelerated continously.
This property ensures that we can have $\vartheta = \vartheta_{c} , $ the resonance condition.
Alternate Answer
Cyclotron uses:
- A magnetic field to make the charged particles move in a circular path.
- An alternating electric field which accelerates the charged particles as they repeatedly cross it in a way that makes them gain energy continuously.
$\frac{\text{mv}^{2}}{\text{r}} = \text{qvB}$
$\therefore\text{r} = \frac{\text{mv}}{\text{qB}}$
Also $\text{T} = \frac{2\pi\text{r}}{\text{v}}$
$\therefore\text{T} = \frac{2\pi\text{m}}{\text{qB}}$
$\therefore$ T is ondependent of v, the speed of the charged particles.
This property ensures that if the frequency of the applied alternating electric field matches the cyclotron frequency, the particle whould keep on getting accelerated every time it crosses the gap between the dees.
Alternate Answer
Because of the property, the applied alternating electric field can be made to accelerate the charged particles continuously. This property ensures that the resonance condition can be satisfied and the particle gets accelerated continously.
This property ensures that we can have $\vartheta = \vartheta_{c} , $ the resonance condition.
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