Question

What is the principle of cyclotron?

Answer 1

Hint:Cyclotron is an accelerator used for accelerating charged particles, so that they can acquire energy large enough to carry out the nuclear reactions. Cyclotron works on the principle of creating electric fields to accelerate the charged particles across the gap between the magnetic field region. Now the question is how these fields are being created, to know the answer stepping to the complete solution.

Complete answer:
Cyclotron was designed by Lawrence and Livingstone in $1931$ to overcome the drawbacks of linear accelerators. Cyclotron is based on the principle that a positive ion acquires sufficiently large energy with small potential difference by making it to cross the same electric field time and making the use of a strong magnetic field.

It consists of two D-shaped hollow semicircular metal chambers called Dees. These Dees are connected to high electric fields and the Dees are enclosed in metal boxes containing low pressure. The magnetic field is acting perpendicular to the plane of Dees. If $B$ is the strength of the magnetic field and $m$, $v$ and $q$ are mass, velocity and charge of the positive ion. $Bqv = \dfrac{{m{v^2}}}{r}$

The positive ion spends the same time inside the Dee irrespective of its velocity or the radius of the circular path.
$t = \dfrac{{length}}{{velocity}}$
$\Rightarrow t = \dfrac{{\pi r}}{v}$
$\therefore t = \dfrac{{\pi m}}{{Bq}}$
This is the time which positive ions spend inside the Dee and we come to know that it is independent of velocity and its radius.

Note:Time period of revolution of a charged particle is independent of the velocity and radius of the circular path but depends on the value of its charge, mass and magnetic strength of the field. The charged particle gets accelerated only due to the electric field.There is no effect of the magnetic field on the velocity of the charged particle. The magnetic field is just to make the electric field cross again and again along the circular path.