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a cyclotron is a device which is used to accelerate charged particles to higher energies.
PRINCIPLE: when a charge q moves normal to a magentic field it experiences magnetic lorentz force due to which it moves in circular path .
when a charged particle of mass ' m' and charge q is accelerated towards the Dee having -ve polarity at that instant and normal magnetic field produces magnetic lorentz force which provides centripetal force for the electron to move in a circular path of radius 'r' .By the time the particle reaches the gap the polarity changes thus the particle is again accelerated towards the Dee having -ve polarity at that instant. thus the particle moves in spiral path increasing the radius and velocity.we it reaches the edge the particle is taken out with the help of a deflector plate
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