Solve the following :


The force on a charged particle due to electric and magnetic fields is given by $\vec{F}=q \vec{E}+q \vec{v} \times \vec{B}$. $v$ should a positively charged particle be sent so that the net force on it is zero?


$F=q(E+v \times B)$

Now, for net force to be 0 , we must have $E=-(v \times B)$

So, the direction of $E$ must be opposite to that of $(v \times B)$, so $v$ must be in $Z$ axis and its magnitude is $\mathrm{E} /(\mathrm{B} \sin \theta)$. For $v$ to be minimum. $\theta=90^{\circ}$, so $v=E / B$.

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