Derivation of cyclotron

• Cyclotron is a device used to accelerate charged bodies to very high velocities (or high kinetic energies) using crossed (or mutually perpendicular) electric and magnetic fields
• Cyclotron is based on the independency of frequency (of rotation of charged particle) on the energy (velocity) and radius (of revolution) of charged particle. The motion of charge , electric field, and the magnetic field are mutually perpendicular(θ= 90°), so:

f_c = 1/T = qB(sinθ)/(2πm) = qB/(2πm)

• Cyclotron is made up of 2 hollow metallic discs D₁ and D₂, semi-circular in shape and an oscillator.
• The discs(D) perform mainly 2 functions: a) to block(shield) electric field inside it (known as electrostatic shielding) b) act as a capacitor outside the region between the 2 discs to provide some electric field
• The oscillator’s job is to reverse the direction of electric field at the time interval of eachrevolution of charge, meaning frequency of oscillator f_o should be same as the frequency of cyclotron f_o.It is because when the charge moves from one D to another, the direction of electric field should always be such that the charge always accelerates(and never decelerates)