A wire carrying a current $I$ along the positive x-axis has length $L$. It is kept in a magnetic field $\overrightarrow{B}=\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-4\hat{\mathrm{k}} \right) \mathrm{T}$. The magnitude of the magnetic force acting on the wire is:

The formula to calculate the magnetic force acting on the wire is given by

$\overrightarrow{F}=I\overrightarrow{L}\times \overrightarrow{B} ...\left(1\right)$

As the length of the wire is along positive x-axis, it can be written that

$\overrightarrow{L}=L\hat{i} ...\left(2\right)$

Substitute the expressions of the required parameters into equation (2) to obtain the force.

$\begin{array}{rcl}\overrightarrow{F}& =& IL\hat{i}\times \left(2\hat{i}+3\hat{j}-4\hat{k}\right)\\ & =& 3IL\hat{k}+4IL\hat{j} ...\left(3\right)\end{array}$

Hence, the magnitude of the force can be written as

$\begin{array}{rcl}F& =& \sqrt{{\left(3IL\right)}^2+{\left(4IL\right)}^2}\\ & =& 5IL\end{array}$