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.

Speed,

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,

v is the speed with which the particles enter the cyclotron

So,

So, the speed with which the particles enter the cyclotron is . Hence, this is the required solution.

a gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm2/s, flows through a pipe 0.25 m internal diameter and 5 km long at the rate of 0.4 m3/s and is delivered at atmospheric pressure.