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 $2\times {10}^{-1}$ tesla in a circular orbit. The force acting on an electron and the radius of circular orbit will be:

• A. $12.8\times {10}^{-13}N,1.1\times {10}^{-4}m$
• B. $1.28\times {10}^{-14}N,1.2\times {10}^{-3}m$
• C. $1.28\times {10}^{-13}N,1.2\times {10}^{-4}m$
• D. $1.28\times {10}^{-13}N,1.2\times {10}^{-3}m$

Answer 1

Answer: (C)

$1.28\times {10}^{-13}N,1.2\times {10}^{-4}m$

The force acting on electron
$F=q(v\times B)$
$=1.6\times {10}^{-19}(4\times {10}^6\times 2\times {10}^{-1}$)
$=1.28\times {10}^{-13}N$

Also, $F=\frac{m{v}^2}{r}$
$r=\frac{m{v}^2}{F}=\frac{9\times {10}^{-31}\times (4\times {10}^6{)}^2}{1.28\times {10}^{-13}}$
$=1.2\times {10}^{-4}$ m