Question

23.An electron is moving with speed 2x10^{​5 m/s} along the positive x-direction in the presence of magnetic induction
B=i+4j-3k. The magnitude of the force experienced by the electron in N (e=1.6x19^-19 C)

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{magnitude}\mathrm{of}\mathrm{the}\mathrm{force}\mathrm{experienced}\mathrm{by}\mathrm{the}\mathrm{electron}\mathrm{is}\mathrm{given}\mathrm{by}, \\ \overrightarrow{\mathrm{F}}=\mathrm{q}[\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}}] \\ =1.6\times {10}^{-19}\left[\right(2\times {10}^5\hat{\mathrm{i}})\times (\hat{\mathrm{i}}+4\hat{\mathrm{j}}-3\hat{\mathrm{k}})] \\ =1.6\times {10}^{-19}[8\times {10}^5\hat{\mathrm{k}}+6\times {10}^5\hat{\mathrm{j}}] \\ \mathrm{Thus}, \\ |\overrightarrow{\mathrm{F}}|=1.6\times {10}^{-19}\times {10}^6 \\ =1.6\times {10}^{-13}\mathrm{N} \end{gathered}$$