Question

If M is the magnitude of the magnetic field, find $x$ such that $x=100\times M$.

Answer 1

From the second condition:
$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$
$\overrightarrow{F}$ is acting in y-direction.q is positive $\overrightarrow{v}$ is along z-axis.Therefore, $\overrightarrow{B}$ should be along x-direction.
Let, $\overrightarrow{B}=B_o\hat{i}$
$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$
$\therefore (5\sqrt{2}\times {10}^{-3})(-\hat{k})={10}^{-6}\left[\right(\frac{{10}^6}{\sqrt{2}}\hat{i}+\frac{{10}^6}{\sqrt{2}})\hat{j}\times (B_o\hat{i}\left)\right]$
Solving this equation, we get:
$B_o={10}^{-2}T$