Question

Each of the lettered points at the corners of the cube in figure represents a positive charge q moving with a velocity of magnitude v in the direction indicated.The region in the figure is in a uniform magnetic field $\overrightarrow{B}$,parallel to the x-axis and directed toward the right .Find the magnitude and direction of the force on each charge.

Answer 1

Apply $\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$
For example, let us apply for charged particle at e.

$\overrightarrow{F_e}=q\left[\right(\frac{v}{\sqrt{2}}\hat{j}-\frac{v}{\sqrt{2}}\hat{k})\times (B\hat{i}\left)\right]$

$=\frac{qvB}{\sqrt{2}}(-\hat{j}-\hat{k})$