Question

A particle initially moving towards the south in a vertically downward magnetic field is deflected towards the east. What is the sign of the charge on the particle?

Answer 1

Let the particle be moving in the south,i.e.along$-y$ axis.
so, $\overrightarrow{v}=v\left(\overrightarrow{j}\right)$
The magnetic field is downward, i.e along $-z$ axis
so, $\overrightarrow{B}=B\left(\overrightarrow{k}\right)$
Now, if $q$ be the change then magnetic force
$\begin{array}{c}{\overrightarrow{F}}_m=q\left(\overrightarrow{v}\times \overrightarrow{B}\right)\\ {\overrightarrow{F}}_m=q\left(v\left(-\overrightarrow{j}\right)\times B\left(-\overrightarrow{k}\right)\right)\\ {\overrightarrow{F}}_m=qvB\overrightarrow{i}\end{array}$
That means if $q$ has positive sign then force will act along the $+x$ axis that is along east
so,sign of change is positive.