Question

A particle of charge $q$ and mass $m$ moves in a circular path of radius $r$ in a uniform magnetic field $B$.
The particle is replaced with a particle of identical charge and mass $\frac{1}{2}m$.
The radius of the new circular path the particle makes is:

• A. $\frac{1}{4}r$
• B. $\frac{1}{2}r$
• C. $r$
• D. $2r$
• E. $4r$

Answer 1

The correct option is B $\frac{1}{2}r$

Radius of circular path, $r=\frac{mv}{Bq}$

Mass of new particle, $m^{\prime }=\frac{m}{2}$

$\therefore$ Radius of new circular path, $r^{\prime }=\frac{\frac{m}{2}v}{Bq}=\frac{r}{2}$