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प्रश्न
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
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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]`
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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
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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?
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(a) there must be an electric field
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(c) both fields cannot be zero
(d) both fields can be non-zero
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(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.
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Answer the following question.
State the underlying principle of a cyclotron. Explain its working with the help of a schematic diagram. Obtain the expression for cyclotron frequency.
Cyclotron is used to ______.
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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 ______.
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