Question

An electron moves in a circular path of radius $15 \,cm$ in a magnetic field of intensity $B=4\times {{10}^{-4}}\,T$ . The velocity of electron is :

• A. $1.05\times {{10}^{7}}m/s$
• B. $5\times {{10}^{6}}m/s$
• C. $3.2\times {{10}^{3}}m/s$
• D. zero

Answer 1

Answer: (A)

$1.05\times {{10}^{7}}m/s$

Answer 2

Magnetic force provides- the necessary centripetal force.
The magnetic force acting on the electron is
$F=qvB$ ... (i)
Centripetal force is $F=\frac{m{{v}^{2}}}{r}$ ... (ii)
Equating Eqs. (i) and (ii), we get
$r=\frac{mv}{eB}$
$\Rightarrow$ $v=\frac{eBr}{m}$
Given, $B=4\times {{10}^{-4}}T$,
$e=1.6\times {{10}^{-19}}C$ ,
$r=0.15\,m$,
$m=9.1\times {{10}^{-31}}kg$
$\therefore$ $v=\frac{1.6\times {{10}^{-19}}\times 4\times {{10}^{-4}}\times 0.15}{9.1\times {{10}^{-31}}}$
$v=1.05\times {{10}^{7}}m/s$