Question

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

Answer 1

Hint: A type of circular particle accelerator is a cyclotron. In a cyclotron, under the action of a static magnetic field and an alternate electric field, a charged particle is accelerated along a spiral path. In a cyclotron, the charged particle is inserted so that its direction of motion is perpendicular to the magnetic static field. The magnetic field causes the particle to rotate and after each rotation, the electric field accelerates the particle. A high-frequency electric field is generated.

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

At low speeds, charged particles (generally protons) are injected into the cyclotron.

Perpendicular electrical and magnetic fields exist inside the cyclotron. It gains velocity and feels a centripetal force perpendicular to the magnetic field in the direction of the electric field. The force on the particle is provided by:
$\overrightarrow{\mathrm{F}}=\mathrm{q}(\overrightarrow{\mathrm{E}}+\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}})$

Since centripetal force is provided by magnetic force,
$\dfrac{\mathrm{mv}^{2}}{\mathrm{r}}=\mathrm{qvB}$
$\mathrm{r}=\dfrac{\mathrm{mv}}{\mathrm{qB}}$

Therefore, a proton's radius is decided by its velocity. Speed continues to increase in the presence of the electric field, and therefore the radius also continues to increase. In order to accelerate the charged particle to high energies, this idea is therefore used. It is also possible to extract particles at selected speeds by extracting the particles at the corresponding radius.

Note:
Just at the moment when the charged particle completes its half circle, the accelerating electric field reverses so that it gets accelerated across the gap between the dees. Again and again the particle gets accelerated, and its speed increases. It therefore achieves elevated kinetic energy,