Question:
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?
Solution:
$F=q(E+v \times B)$
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 $v=E / B$.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.