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# The period of revolution of a charged particle inside a cyclotron does not depend on:A. The magnetic inductionB. The charge of the particleC. The velocity of the particleD. The mass of the particle

Last updated date: 18th Jun 2024
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Hint: Cyclotron hastens up charged particles to very large scales energies. Its working principle is: When a charged particle such as electron and proton moves normally to a magnetic field, it experiences magnetic force and moves in a circular path.

Complete step by step solution:
Cyclotron: A cyclotron is an accelerator of particles. It is a powered electrical machine producing a beam of charged parts which is used for medical purpose, industrial and investigational applications. Cyclotron was invented by Ernest O. Lawrence in $1929 - 1930$ at the University of California. In an outward path from the center of a flat, cylindrical vacuum chamber, a cyclotron accelerates charged particles. The particles are tracked by a static magnetic field on a spiral trajectory and accelerated through a quickly varying electric field (radio frequency). For this invention, Lawrence received the $1939$ Nobel Prize for Physics.

Velocity: The velocity of an object is the rate of change of position relative to a reference framework and depends on time. Velocity is equivalent to the specified speed and direction of motion of an object (e.g. northward $60\,{\text{km/h}}$). Velocity, the branch of classical mechanics which describes the motion of bodies, is a fundamental concept in kinematics.

The particle moves in a plane perpendicular to B when the velocity of a charged particle is perpendicular to a uniform B magnetic field. This motion is referred to as a cyclotron. Here is the necessary magnetic force to keep the particle in a circle motion.

Here,
${F_B} = qvB \\ = \dfrac{{m{v^2}}}{r} \\$
Or,
$r = mv/qB$
So, the period of revolution,
$T = \dfrac{{2\pi r}}{v} = \dfrac{{2\pi m}}{{qB}}$
The revolution period does not therefore depend on velocity, $v$.

Hence, the required answer is C.

Note: When the velocity of a charged particle is perpendicular to a uniform B magnetic field, the particle moves in a plane perpendicular to B. This motion is termed a cyclotron. Here's the magnetic force needed to keep the particle in motion in a circle.