Question

An electron is moving with velocity $(2\hat{i}+2\hat{j})m/s$ in an electric field of intensity $\overrightarrow{E}=\hat{i}+2\hat{j}-8\hat{k}volt/m$ and a magnetic field of $\overrightarrow{B}=(2\hat{j}+3\hat{k})$ tesla. Find the magnitude of force on the electron.

Answer 1

Force acting on electron
$\overrightarrow{F}=q(\overrightarrow{E}+\overrightarrow{v}\times \overrightarrow{B})\overrightarrow{v}\times \overrightarrow{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 2& 0\\ 0& 2& 3\end{array}\right|=\hat{i}(6-0)-\hat{j}(6-0)+\hat{k}(4-0)=(6\hat{i}-6\hat{j}+4\hat{k})\therefore \overrightarrow{F}=1.6\times {10}^{-19}\left[\right(\hat{i}+2\hat{j}-8\hat{k})+(6\hat{i}-6\hat{j}+4\hat{k}\left)\right]=1.6\times {10}^{-19}(7\hat{i}-4\hat{j}-4\hat{k})|\overrightarrow{F}|=1.6\times {10}^{-19}\times \sqrt{(7{)}^2+(-4{)}^2+(-4{)}^2}=1.6\times {10}^{-19}\times 9=14.4\times {10}^{-19}N$