Q. A particle of mass $m$ and charge $q$ released from the origin in a region occupied by electric field $E$ and magnetic field $B$, $B = \ - B_{0},\ \widehat{j}\ ;E = E_{0}\widehat{i}$ The velocity of the particle will be
A) $\sqrt{\frac{2qE_{0}}{m}}\ $
B) $\sqrt{\frac{qE_{0}}{m}\ }$
C) $\sqrt{\frac{qE_{0}}{2m}\ }$
D) None of these
Explanation
(a) Since, the magnetic field does not perform any work, therefore, whatever has been gain in kinetic energy it is only because of the work done by electric field. Applying work-energy theorem,
$W = \ \mathrm{\Delta}E$
$qE_{0}\ = \frac{1}{2}\ mv^{2} - 0\ $
Or $v\ = \ \sqrt{\frac{2qE_{0}}{m}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.