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प्रश्न
Obtain the expression for the cyclotron frequency.
उत्तर
When a charged particle having charge q moves inside a magnetic field `vecB`with velocity v, it experiences a force `vecF=q(vecvxxvecB)`.
When `vecv` is perpendicular to`vecB`, the force `vecF` on the charged particle acts as the centripetal force and makes it move along a circular path.
Let m be the mass of charged particle and r be the radius of the circular path.
Then `q(vecv xx vecB )=(mv^2)/r`
∵ v and B are at right angles
`∴ qvB=(mv^2)/r`
`⇒r=(mv)/(Bq)`
Time period of the circular motion of a charged particle is given by
`T=(2pir)/v`
`T=(2pi)/v (mv)/(Bq)`
`therefore T=(2pim)/(Bq)`
Angular frequency,`omega=(2pi)/T`
`therefore omega=(Bq)/m`
This is often called cyclotron frequency.
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संबंधित प्रश्न
Which one of the following particles cannot be accelerated by a cyclotron?
(A) Electrons
(B) Protons
(C) Deuterons
(D) α- particles
Show that the time period of revolution of particles in a cyclotron is independent of their speeds. Why is this property necessary for the operation of a cyclotron?
If a watch-glass containing a small quantity of water is placed on two dissimilar magnetic poles, then water ______.
An α-particle and a proton are released from the centre of the cyclotron and made to accelerate.
(i) Can both be accelerated at the same cyclotron frequency?
Give reason to justify your answer.
(ii) When they are accelerated in turn, which of the two will have higher velocity at the exit slit of the does?
Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.
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) An electron moves along a circle of radius 1 m in a perpendicular magnetic field of strength 0.50 T. What would be its speed? Is it reasonable? (b) If a proton moves along a circle of the same radius in the same magnetic field, what would be its speed?
A cyclotron's oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its 'dees' is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator.
A cyclotron can accelerate ______.
Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.
