Question

Before entering the cyclotron, the particles are accelerated by a potential difference V. Find the speed v with which the particles enter the cyclotron. Express your answer in terms of V, m, and q.

Answer 1

Answer:

Speed, $v=\sqrt{\dfrac{2qV}{m}}$

Explanation:

The device which is used to accelerate charged particles to higher energies is called a cyclotron. It is based on the principle that the particle when placed in a magnetic field will possess a magnetic force. Just because of this Lorentz force it moves in a circular path.  

Let m, q and V are the mass, charge and potential difference at which the particle is accelerated.

The work done by the particles is equal to the kinetic energy stored in it such that,

$qV=\dfrac{1}{2}mv^2$

v is the speed with which the particles enter the cyclotron

So,

$v=\sqrt{\dfrac{2qV}{m}}$

So, the speed with which the particles enter the cyclotron is $v=\sqrt{\dfrac{2qV}{m}}$. Hence, this is the required solution.