Question

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 1

Cyclotron is a device used to accelerate charged particles to high energies. It was devised by Lawrence. Cyclotron works on the principle that a charged particle moving normal to a magnetic field experiences magnetic lorentz force due to which the particle moves in a circular path.

The particle follows a circular path inside the cyclotron, and the necessary centripetal force is provided by the magnetic field. ... The time period should be independent of speed so that the frequency of revolution of the particle remains equal to the frequency of the ac source applied to the cyclotron.

Cyclotron uses the fact that the frequency of revolution of the charged particle in a magnetic field is independent of its energy. ... In this way the charged particles keeps moving in the two Dees each time increasing in velocity and radius of path.

Answer 2

Cyclotron accelerates charged particles upto very high energies. Its working principle is: A charged particle like electron and proton when moves normal to a magnetic field, it experiences a magnetic force and moves in a circular path.

Magnetic force is equal to the centripetal force

$qvB=\frac{mv^2}{r}\\\frac{v}{r}=\frac{qB}{m}\\T=\frac{2\pi r}{v}\\T=\frac{2\pi m}{qB}$

So, time period of revolution of particles in a cyclotron is independent of speed.

This is important so that the frequency remains equivalent to frequency of the ac source connected to the cyclotron.

Learn more about: Cyclotron

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