The cyclotron is a particle accelerator. It is mainly used to accelerate positively charged ions.
Charged particle is allowed to pass through electric and magnetic fields acting right angles to each other continuously.
kinetic energy of the particle increases in the electric field and direction of the particle changes in the magnetic field.
It consists of 2 D-shaped chambers connected to high voltage radio frequency oscillator. The whole arrangement is placed in a uniform magnetic field acting in right angles to the chambers.
Source of ions which are to be accelerated is placed between the 2 D-shaped chambers.
When the power supply is on the ion experiences a force in the electric field which is set up between the 2 chambers. It accelerates and enters into the chamber which is at low potential (-ve). Inside the chamber electric field is 0 but the magnetic field changes the direction of the particle into semi-circular path. By the time it completes the semi circular path, polarity of the chambers change. Hence, charged particle enter into other chamber with grater velocity.it performs greater semicircular path in the chamber. This process continues till the particle is ejected out with a strong deflection.
Moving charge experiences force in the magnetic field for its circular motion.
Therefore centripetal force mv ² /r = qvBsin θ mv/r = qBsin90 v= qBr/m ……………….(1)
T/2 = πr/v
T = 2πr/v
T = 2πrm/qbr [from (1)]
T = 2πm/Bq
Form the eqns for time period we cay say that it is independent of velocity and radius of the orbit.
Frequency = I/t = Bq/2πm
K.E = ½ mv ²
= ½ mq ² B ² r ² [from(1)]
K.E = q²B²r²/2m
This particle accelerator cannot be used to accelerate electrons or negatively charged ions to high energy particles.
As the electrons are small, soon these electrons reach the speed of light, hence the mass changes.
As the mass changes the frequency will not match with the frequency of the supply.
Finally, this leads to an explosion.