Question

An electron having charge $1.6 \times 10^{-19} C$ and mass $9 \times 10^{-31} kg$ is moving with $4 \times 10^{6} m / s$ speed in a magnetic field of $2 \times 10^{-1} T$ in a circular orbit. The force acting on an electron and the radius of circular orbit will be

• A. $1.28 \times 10^{-14} N , 1.1 \times 10^{-3} m$
• B. $1.28 \times 10^{15} N , 1.2 \times 10^{-12} m$
• C. $1.28 \times 10^{-13} N , 1.1 \times 10^{-4} m$
• D. None of the above

Answer 1

The Correct Option is C

Electron moves in a magnetic field $(\vec{ B })$ in a circular orbit of radius $(r)$, hence Centripetal force
$=$ force due to magnetic field $(B)$
$\frac{m v^{2}}{r}=e v B$
$\Rightarrow r=\frac{m v}{e B}$
Given, $m=9 \times 10^{-31} kg , $
$e=1.6 \times 10^{-19} C ,$
$v =4 \times 10^{6} m / s ,$
$B=2 \times 10^{-1} T$
$\therefore r =\frac{9 \times 10^{-31} \times 4 \times 10^{6}}{1.6 \times 10^{-19} \times 2 \times 10^{-1}}$
$=1.1 \times 10^{-4} m$