Discuss the working of cyclotron in detail.

Explanation

Cyclotron :
It is a device used to accelerate the charged particles to gain large K.E.
Principle :
When a charged particle moves normal to the magnetic field it experiences magnetic Lorentz force..
Construction :
(i) `D_1`, and `D_2`, (Dees) - hollow metal cylinder enclosed in an evacuated chamber.
(ii) The dees are kept separated.
(iii) A source of ions is placed at the centre (S).
(iv) Dees are placed in a uniform magnetic field controlled by an electromagnet.
(v) The direction of magnetic field is normal to the plane of the Dees.
(vi) The does are connected to a high frequency oscillator.
Working : (i) q- charge of positive ion, m - mass of the positive ion.
(ii) Positive ion is accelerated towards the Dees having negative potential.
(iii) Since the megmetic field is normal to the plane of the Dees, the ion undergoes i circular path.
(iv) When the ion auives at the gap, the polarity of the Dees gets reversed.
(v) Hence the ion is once again accelerated and moves into the other Dee with a greater velocity and greater radius.
(vi) Thus the particle moves in a spiral path of increasing radius. (vii) For this circular motion, the centripetal force is provided by Lorentz force.
`(mv^2)/r = q v B`
` r =m/(qB)v`
` r alphav`
(viii) When it comes near the edge it is taken out with the help of deflector plate and allowed to hit the target (T). The time period of oscillation is
`T = (2 pi m)/(qB)`
The kinetic energy the charged particle is kinetic energy `1/2 mv^2 = (q^2 B^2 r^2)/(2m)`
In resonance condition :
Frequency f which the positive ion circulates in the magnetic field is equal to constant frequency of electrical osculation force.
`F_("osc") = (qB)/(2 pim)`