A particle of charge q moves with a-velocity $v = a \hat{i}$ in a magnetic field $B = b \hat{j} + c \hat{k}$ where a, b and c are constants. The magnitude of the force experienced by the particle is

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zero

$qa (b + c)$

$qa {(b^{2} - c^{2})}^{1 / 2}$

$qa {(b^{2} + c^{2})}^{1 / 2}$

answer is D.

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Detailed Solution

$F = q (v \times B)$

. $= q {a \hat{i} \times (b \hat{j} + c \hat{k})}$

$= q (ab \hat{i} \times \hat{j} + ac \hat{i} \times \hat{k})$

$= q (ab \hat{k} - ac \hat{j})$

$= qa (b \hat{k} - c \hat{j})$

magnitude of $F = qa {(b^{2} + c^{2})}^{1 / 2}$

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