Q. An electron rotates about a proton, the induced magnetic field is $14T$ at the centre, find out the angular velocity of electron if radius of rotation is $0.5\ nm$
A) $4.4 \times 10^{17}rad/sec$
B) $4.4 \times 10^{12}rad/sec$
C) $3.14 \times 10^{- 15}rad/sec$
D) $4.2 \times 10^{10}rad/sec$
Explanation
(a) $B = \frac{\mu_{0}I}{2r} \Rightarrow B = \frac{\mu_{0}}{2r} \times \frac{e\omega}{2\pi} = \frac{\mu_{0}e\omega}{4\pi r}$
$\Rightarrow 14 = \frac{10^{- 7} \times 1.6 \times 10^{- 19} \times \omega}{0.5 \times 10^{- 9}}$
$\Rightarrow \omega = \frac{14 \times 0.5 \times 10^{- 9}}{1.6 \times 10^{- 26}} = \frac{7}{1.6} \times 10^{26 - 9}$
$\Rightarrow \frac{70}{16} \times 10^{17} = \frac{35}{8} \times 10^{17} = 4.4 \times 10^{7}rad/sec$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.