Question

If an electron moves with a velocity, $\overrightarrow{v}=(2\hat{i}-3\hat{j}+\hat{k})m/s$ in a magnetic field, $\overrightarrow{B}=(2\hat{i}+\hat{j}-\hat{k})T.$ then, calculate the Lorentz force.

Answer 1

The value of lorentz force

$\overrightarrow{F_L}=q(\overrightarrow{v}\times \overrightarrow{B})$

Here, $q=-1.6\times {10}^{-19}C;\overrightarrow{v}=(2\hat{i}-3\hat{j}+\hat{k});$

$\overrightarrow{B}=(2\hat{i}+\hat{j}-\hat{k})$

Now, $(\overrightarrow{v}\times \overrightarrow{B})=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& -3& 1\\ 2& 1& -1\end{array}\right|$

$=\hat{i}(3-1)+\hat{j}(2+2)+\hat{k}(2+6)$

$=(2\hat{i}+4\hat{j}+8\hat{k})$

$\therefore$ Lorentz force

$\overrightarrow{F_L}=-1.6\times {10}^{-19}(2\hat{i}+4\hat{j}+8\hat{k})N$