Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Frequency of oscillators (v) = 10 MHz = 107 Hz
Mass of proton, `"m" = 1.67 xx 10^-27 "kg"`
Charge of proton = 1.6 x 10-19 C
Operating magnetic field is given by the relation
`"B" = (2pi"mv")/q = (2 xx 3.14 xx 1.67 xx 10^-27 xx 10^7)/(1.6 xx 10^-19)`
= 0.65 T
Radius of dees= 60 cm = 0.6 m
`"KE" = ("q"^2"B"^2"r"^2)/(2"m") = ((1.6 xx 10^-19)^2(0.65)^2(0.6)^2)/(2 xx 1.67 xx 10^-27 xx 1.6 xx 10^-13) "Mev"`.
APPEARS IN
संबंधित प्रश्न
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?
Obtain the expression for the cyclotron frequency.
A proton and an electron travelling along parallel paths enter a region of uniform magnetic field, acting perpendicular to their paths. Which of them will move in a circular path with higher frequency?
Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.
A cyclotron is used to accelerate protons to a kinetic energy of 5 MeV. If the strength of magnetic field in the cyclotron is 2T, find the radius and the frequency needed for the applied alternating voltage of the cyclotron. (Given : Velocity of proton= `3xx10^7 m//s`)
An electron is projected horizontally with a kinetic energy of 10 keV. A magnetic field of strength 1.0 × 10−7 T exists in the vertically upward direction.
(a) Will the electron deflect towards the right or left of its motion?
(b) Calculate the sideways deflection of the electron while travelling through 1 m. Make appropriate approximations.
Cyclotron frequency of a charged particle having charge q and mass m in a cyclotron producing magnetic field B is ______.
Which of the following is not correct about cyclotron?
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 ______.
