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A particle having a charge of 100µC and mass of 10mg is projected in a uniform magnetic field of 25 Tesla, with a speed of 10ms^–1. The velocity is perpendicular to the field. The radius of path and period of revolution are

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a

4cm, 25sec

b

4m, 25 millisec

c

$4 cm, 25 \times 10^{- 3} \sec$

d

4m, 25sec

answer is C.

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Detailed Solution

$\begin{array}{l} r = \frac{mv}{qB}, T = \frac{2 πr}{v} \\ r = \frac{10 \times 10^{- 6} \times 10}{100 \times 10^{- 6} \times 25} = \frac{1}{25} m = \frac{100}{25} = 4 cm \\ T = \frac{2 π \times 1}{25 \times 10} = 25 \times 10^{- 3} \sec \end{array}$

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