Question

State the underlying principle of a cyclotron. Explain its working with the help of a schematic diagram. Obtain the expression for cyclotron frequency.

Answer 1

Answer:

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Answer 2

                  Cyclotron is a device which is used to accelerate the positively charged particles such as protons,deutrons etc. .

PRINCIPLE

• Cyclotron works on the principle that a positively charged particle can be accelerated by making it to cross the same electric field repeatedly with the help of a magnetic field.

WORKING OF CYCLOTRON:

•    The positive ions produced from a source S at the centre are accelerated by a dee which is at negative potential at that moment.
• Due to the presence of perpendicular magnetic field the ion will move in a circular path inside the Dees.
• The magnetic field and the frequency of the applied voltages are so chosen that as the ion comes out of a dee, the Dees change their polarity (positive becoming negative and vice-versa) and the ion is further accelerated and moves with higher velocity along a circular path of greater radius.
• The phenomenon is continued till the ion reaches at the periphery of the Dees where an auxiliary negative electrode (deflecting plate) deflects the accelerated ion on the target to be bombarded.
• The function of electric field is to accelerate the charged particle and so to impart energy to the charged particle.
• The function of magnetic field is to provide circular path to charged particle and so to provide the location where charged particle is capable of gaining energy from electric field.

EXPRESSION FOR CYCLOTRON FREQUENCY:

•       Suppose the positive ion with a charge q moves in a dee  with a velocity v then       $qvB=\frac{mv^{2} }{r}$

• this implies             $r=\frac{mv}{qB}$

where m is mass , r is the radius of the path of the ion in the dee ,B is the strength of the magnetic field

• the angular velocity of the ion is     ω=$\frac{v}{r}$

                                          $=\frac{vqB}{mv} = \frac{qB}{m}$

• The time taken by the ion to describe a semi circle is

                     t=π/ω

                     T/2=t

•    The period of revolution T =2t

                                                    T=2πm/qB

•     The frequency of the revolution F=1/T

                                                         F = qB/2πm