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A current of 1 A is flowing along positive $x$ -axis through a straight wire of length $0.5 \mathrm{m}$ placed in a region of a magnetic field given by $\mathbf{B}=(2 \mathbf{i}+4 \mathbf{j}) \mathrm{T} .$ The magnitude and the direction of the force experienced by the wire respectively are
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The correct answer is:
$2 \mathrm{N}$, along positive $z$ -axis
The force experienced by the wire placed in magnetic field, $F=B il$
$$
\begin{array}{l}
=(2 \hat{i}+4 \hat{j})\left(1 \hat{i} \times \frac{1}{2}\right) \\
=\hat{i} \times \hat{i}+4 \times \frac{1}{2}(\hat{i} \times \hat{j})=2 \hat{k} N
\end{array}
$$
Direction of this force can be find out by Fleming's left hand rule which is along pasitive z-axis
$$
\begin{array}{l}
=(2 \hat{i}+4 \hat{j})\left(1 \hat{i} \times \frac{1}{2}\right) \\
=\hat{i} \times \hat{i}+4 \times \frac{1}{2}(\hat{i} \times \hat{j})=2 \hat{k} N
\end{array}
$$
Direction of this force can be find out by Fleming's left hand rule which is along pasitive z-axis
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