Question

An electron describing a circle is in a magnetic field of ${10}^{-4}T$ . The angular frequency of revolution, if mass is $9.1\times {10}^{-31}kg$ and charge is $1.6\times {10}^{-19}C$, is :

• A. $1.24\times {10}^{7}rad/s$
• B. $2.42\times {10}^{7}rad/s$
• C. $1.62\times {10}^{7}rad/s$
• D. $1.758\times {10}^{7}rad/s$

Answer 1

Answer: (D)

$1.758\times {10}^{7}rad/s$

Equating the magnetic force with centripetal force we get, $\frac{m{v}^2}{r}=qvB$

where all the terms have their usual meanings.
$\Rightarrow$ $v=\frac{rBq}{m}$ ......(1)
Since angular frequency $w=\frac{v}{r}$

From (1), we get $\omega =\frac{Bq}{m}$

$\therefore$ $w=\frac{{10}^{-4}\times 1.6\times {10}^{-19}}{9.1\times {10}^{-31}}rad/s$
$⟹$ $w=1.758\times {10}^{7}rad/sec$