Q. A uniform magnetic field $\overrightarrow{B} = B_{0}\widehat{j}$ exists in space. A particle of mass m and charge q is projected towards $x$-axis with speed $v$ from a point ($a,0,0).$ The maximum value of $v$ for which the particle does not hit the y-z plane is
A) $\frac{B\ q\ a}{m}$
B) $\frac{B\ q\ a}{2\ m}$
C) $\frac{B\ q}{a\ m}$
D) $\frac{B\ q\ }{2\ a\ m}$
Explanation
(a) Here, the particle is projected in a direction perpendicular to the uniform magnetic field, hence it will describe a circular path. The particle will not hit the y-z plane, if the radius of the circular path is smaller than $a$. For maximum value of $v,$ the radius of circular path is just equal to $a$.
Hence, $\frac{mv}{Bq} = a\ $
Or $v\ \ = \ \frac{B\ q\ a}{m}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.