Question: A wire carrying a current $I$ along the positive $x$-axis has length $L$. It is kept in a magnetic field $\vec{B}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}) \mathrm{T}$. The magnitude of the magnetic force acting on the wire is :
A) $\sqrt{5} \mathrm{IL}$
B) 5 IL
C) $\sqrt{3} \mathrm{IL}$
D) $3 \mathrm{IL}$
Answer: (B) 5 IL
Sol:
$$ \begin{aligned} & \vec{F}=I(\vec{\ell} \times \vec{B}) \ & =I[(L \hat{i}) \times(2 \hat{i}+3 \hat{j}-4 \hat{k})] \ & =I(4 L \hat{j}+3 L \hat{k}) \ & |\vec{F}|=5 \mathrm{IL} \end{aligned} $$
