Question

State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies.

Answer 1

Cyclotron is based on the principle of Lorentz force on a charged particle moving in a magnetic and electric field.

Charged particles (usually protons) are injected into cyclotron at low speeds. Inside cyclotron, perpendicular electric and magnetic fields exists. It gains speed along the direction of electric field and feels a centripetal force perpendicular to the magnetic field. Force on the particle is given by:

$\overrightarrow{F}=q(\overrightarrow{E}+\overrightarrow{v}\times \overrightarrow{B})$

Since centripetal force is provided by magnetic force,

$\frac{m{v}^2}{r}=qvB$

$r=\frac{mv}{qB}$

Hence, radius of a proton is decided by its speed.

In the presence of electric field, speed keeps increasing and hence, radius also keeps increasing. This concept is hence used to accelerate the charged particle to high energies.

Particles at selected speeds can also be extracted by extracting the particles at the corresponding radius.