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  4. The proton of energy 1 MeV describes a circular path in plane at right angles to a uniform magnetic field of 6.28 × 10-4 T. The mass of the proton is 1.7 × 10-27 kg. The cyclotron frequency of the proton is very nearly equal to :

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Q. The proton of energy $1 MeV$ describes a circular path in plane at right angles to a uniform magnetic field of $6.28 \times 10^{-4} T$. The mass of the proton is $1.7 \times 10^{-27} kg$. The cyclotron frequency of the proton is very nearly equal to :

VITEEEVITEEE 2007

Solution:

Cyclotron frequency is given by
$v=\frac{q B}{2 \pi m} $
$\therefore v =\frac{1.6 \times 10^{-19} \times 6.28 \times 10^{-4}}{2 \times 3.14 \times 1.7 \times 10^{-27}}$
$= 0.94 \times 10^{4} $
$\approx 10^{4} Hz$