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प्रश्न
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
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
State the principle of a cyclotron.
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If a charged particle kept at rest experiences an electromagnetic force,
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(d) both fields can be non-zero
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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.
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.
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