Q. An electron having mass $(9.1 \times 10^{- 31}\ kg)$ and charge $(1.6 \times 10^{- 19}\ C)$ moves in a circular path of radius 0.5 m with a velocity $10^{6}\ {ms}^{- 1}$ in a magnetic field. Strength of magnetic field is
A) $1.13 \times 10^{- 5}\ T$
B) $5.6 \times 10^{- 6}\ T$
C) $2.8 \times 10^{- 6}\ T$
D) None of these
Explanation
(a) We have the relation
$\Rightarrow \ \ r = \frac{mv}{eB}$
Given, $\ m = 9.1\ \times 10^{- 31}\ kg,\ e = 1.6 \times 10^{- 19}\ C$
$r = 0.5\ m,\ v = 10^{6}\ {ms}^{- 1}$
$\therefore B = \frac{mv}{re} = \frac{9.1 \times 10^{- 31} \times 10^{6}}{0.5 \times 1.6 \times 10^{- 19}}$
$\ \ \ \ \ \ \ \ = \frac{9.1 \times 10^{- 25}}{0.8 \times 10^{- 19}} = \frac{91}{8} \times 10^{- 6}$
$\ \ \ \ \ \ \ \ = 11.3 \times 10^{- 6} = 1.13 \times 10^{- 5}\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.