Question

A charged particle moves with velocity $\overrightarrow{v}=a\hat{i}+d\hat{j}$ in a magnetic field $\overrightarrow{B}=A\hat{i}+D\hat{j}$. The force acting on the particle has magnitude $F$. Then,

• A. $F=0$, if $aD=dA$
• B. $F=0$, if $aD=-dA$
• C. $F=0$, if $aA=-dD$
• D. $F\propto (a^2+b^2{)}^{1/2}\times (A^2+D^2{)}^{1/2}$

Answer 1

The correct option is A $F=0$, if $aD=dA$

$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$
$=q\left(\right(a\hat{i}+d\hat{j})\times (A\hat{i}+D\hat{j}\left)\right)$

$=q(aD-dA)\hat{k}$

If $aD-dA=0$

$\overrightarrow{F}=0$