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The magnetic force acting on a charged particle of charge $-2 \mu \mathrm{c}$ in a magnetic field of $2 \mathrm{~T}$ acting in $\mathrm{y}$ direction, when the particle velocity is $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \times 10^6 \mathrm{~ms}^{-1}$, is :
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Verified Answer
The correct answer is:
$8 \mathrm{~N}$ in $\mathrm{z}-$ direction
$$
\begin{aligned}
\overrightarrow{\mathrm{F}} & =\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}) \\
& =-2 \times 10^{-6}\left[(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \times 10^6 \times 2 \hat{\mathrm{j}}\right] \\
& =-(8 \mathrm{~N}) \hat{\mathrm{k}}
\end{aligned}
$$
\begin{aligned}
\overrightarrow{\mathrm{F}} & =\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}) \\
& =-2 \times 10^{-6}\left[(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \times 10^6 \times 2 \hat{\mathrm{j}}\right] \\
& =-(8 \mathrm{~N}) \hat{\mathrm{k}}
\end{aligned}
$$
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