Advertisements
Advertisements
प्रश्न
Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic field in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles.
उत्तर
Schematic sketch of cyclotron:
The combination of crossed electric and magnetic fields is used to increase the energy of the charged particle. Cyclotron uses the fact that the frequency of revolution of the charged particle in a magnetic field is independent of its energy. Inside the dees the particle is shielded from the electric field and magnetic field acts on the particle and makes it to go round in a circular path inside a dee. Every time the particle moves from one dee to the other it comes under the influence of electric field which ensures to increase the energy of the particle as the sign of the electric field changed alternately. The increased energy increases the radius of the circular path so the accelerated particle moves in a spiral path.
Since radius of trajectory,
`r =(vm)/(qB)`
`therefore v = (rqB)/m`
Hence, the kinetic energy of ions,
`1/2 mv^2`
`1/2 m (r^2 q^2 B^2)/m^2`
`= 1/2 (r^2q^2B^2)/m`
APPEARS IN
संबंधित प्रश्न
State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies
Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.
A deuteron and a proton are accelerated by the cyclotron. Can both be accelerated with the same oscillator frequency? Give reason to justify your answer.
Two metal strips, each of length l, are clamped parallel to each other on a horizontal floor with a separation b between them. A wire of mass m lies on them perpendicularly, as shown in the figure. A vertically-upward magnetic field of strength B exists in the space. The metal strips are smooth but the coefficient of friction between the wire and the floor is µ. A current i is established when the switch S is closed at the instant t = 0. Discuss the motion of the wire after the switch is closed. How far away from the strips will the wire reach?
A conducting wire of length l, lying normal to a magnetic field B, moves with a velocity v,as shown in the figure. (a) Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons concentrate at one end, resulting in an electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when the redistribution stops. (c) What potential difference is developed between the ends of the wire?
A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the ratio frequency field is doubled?
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Its centripetal acceleration is ______.
A particle of mass m is moving in a circular path of constant radius r such that, its centripetal acceleration ac is varying with time t as ac = k2rt2, where k is a constant. The power delivered to the particle by the forces acting on it is ______.
In a cyclotron, a charged particle ______.
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
