A charge $2 .0 μC$ moves with a speed of $2 .0 \times 10^{6} {ms}^{- 1}$ along the positive x- axis. A magnetic field $\vec{B}$ of strength $(0 .20 \hat{j} + 0 .40 \hat{k}) T$ exists in space. Find the magnetic force acting on the charge.

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$(0 .5 \hat{k} - 1 .6 \hat{j}) N$

$(0 .5 \hat{k} - 2 .6 \hat{j}) N$

$(0 .5 \hat{j} - 2 .1 \hat{k}) N$

$(0 .8 \hat{k} - 1 .6 \hat{j}) N$

answer is A.

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Detailed Solution

The force on the charge $= q \vec{v} \times \vec{B}$
$\begin{array}{l} = (2 .0 \times 10^{- 6} C) (2 .0 \times 10^{6} {ms}^{- 1} \hat{i}) \times (0 .20 \hat{j} + 0 .40 \hat{k}) T \\ = 4 .0 (0 .20 \hat{i} \times \hat{j} + 0 .40 \hat{i} \times \hat{k}) N \\ = (0 .8 \hat{k} - 1 .6 \hat{j}) N \end{array}$