Advertisements
Advertisements
प्रश्न
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
Advertisements
उत्तर
In cyclotron, charge particle describes the circular path where the magnetic force acts as centripetal force.
`(mv^2)/R = ev B`
On simplifying the terms, we have
∴ `(eB)/m = v/R = ω`
We know that `B = F/(ev) = ([MLT^-2])/([AT][LT^-1]) = [MA^-1T^-2]`
And then dimensional formula of angular frequency
∴ [ω] = `[(eB)/m] = [v/R]`
[ω] = `([AT][MA^-1T^-2])/([M]) - [T^-1]`
APPEARS IN
संबंधित प्रश्न
In a cyclotron, magnetic field of 3·5Wb/m2 is used to accelerate protons. What should be the time interval in which the electric field between the Dees be reversed?
(Mass of proton = 1· 67 x 10-27Kg, Charge on proton =1·6x10-19c).
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.
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?
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.
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`)
Verify that the units weber and volt second are the same.
If a charged particle kept at rest experiences an electromagnetic force,
(a) there must be an electric field
(b) there must be a magnetic field
(c) both fields cannot be zero
(d) both fields can be non-zero
(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?
Cyclotron is used to ______.
Assertion: The frequency of circular motion of a charged particle in cyclotron is independent of the mass of the particle.
Reason: Greater the mass of the particle less will be the frequency of the particle.
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Its centripetal acceleration is ______.
The life time of muon in the rest frame is 2 × 10-6 sec. A beam of muons emerges from a cyclotron with velocity where c is the velocity of light The mean life of muons observed in the laboratory frame will be ______.
The cyclotron was designed by ______
In a cyclotron, a charged particle ______.
Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.
