Answer
${\bf{F}} = - 1.6 \times {10^{ - 18}}{\bf{k}}$ N
Work Step by Step
We have
The charge of the electron: $q = - 1.6 \times {10^{ - 19}}$ C. Velocity of the electron: ${\bf{v}} = {10^5}{\bf{i}}$.
Uniform magnetic field: ${\bf{B}} = 0.0004{\bf{i}} + 0.0001{\bf{j}}$.
The force ${\bf{F}}$ on the electron is given by ${\bf{F}} = q\left( {{\bf{v}} \times {\bf{B}}} \right)$. So,
${\bf{F}} = q\cdot{10^5}{\bf{i}} \times \left( {0.0004{\bf{i}} + 0.0001{\bf{j}}} \right)$
${\bf{F}} = q\cdot{10^5}\left( {0.0004{\bf{i}} \times {\bf{i}} + 0.0001{\bf{i}} \times {\bf{j}}} \right)$
Since ${\bf{i}} \times {\bf{i}} = 0$ and ${\bf{i}} \times {\bf{j}} = {\bf{k}}$, we get
${\bf{F}} = q\cdot{10^5}\left( {0.0001{\bf{k}}} \right)$
Substituting $q = - 1.6 \times {10^{ - 19}}$ in ${\bf{F}}$ gives
${\bf{F}} = - 1.6 \times {10^{ - 19}} \times {10^5} \times {10^{ - 4}}{\bf{k}} = - 1.6 \times {10^{ - 18}}{\bf{k}}$ N
