Q. A charged particle is moving in a circular orbit of radius 6 cm with a uniform speed of $3 \times 10^{6}m/s$ under the action of a uniform magnetic field $2 \times 10^{- 4}wb/m^{2}$ at right angles to the plane of the orbit. The charge to mass ratio of the particle is
A) $5 \times 10^{9}C/kg$
B) $2.5 \times 10^{11}C/kg$
C) $5 \times 10^{11}C/kg$
D) $5 \times 10^{12}C/kg$
Explanation
(b) Here, $v = 3 \times 10^{6}ms^{- 1},$
$B = 2 \times 10^{- 4}wb\ \ m^{- 2} = 2 \times 10^{- 4}T$
$R = 6cm = 6 \times 10^{- 2}m.$ As $Bqv = \frac{mv^{2}}{R}$ or $\frac{q}{m} = \frac{v}{BR}$
Substituting the given values, we get
$\frac{q}{m} = \frac{3 \times 10^{6}}{2 \times 10^{- 4} \times 6 \times 10^{- 2}} = 0.25 \times 10^{12}C/kg$
$= 2.5 \times 10^{11}C/kg$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.