A beam of 30 MeV α-particles is to be obtained from a cyclotron of radius 50cm. The strength of magnetic field required to be applied will be

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15.82 T

0.01582 T

1.582 T

0.1582 T

answer is A.

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Detailed Solution

$\begin{array}{l} r = \frac{\sqrt{2 mkE}}{Bq}; B = \frac{\sqrt{2 m \times kE}}{q (r)} \\ B = \frac{\sqrt{2 \times 1 .6 \times 10^{- 27} \times 4 \times 30 \times 1 .6 \times 10^{- 13}}}{1 .6 \times 10^{- 19} \times 50 \times 10^{- 2}} \end{array}$
B = 1.58T

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