Question

In an experiment electrons are accelerated,from rest, by applying a voltage of $500V$.Calculate the radius of the path if a magnetic field $100mT$ is then applied.[Charge of the electron =$1.6\times {10}^{-19}C$ Mass of the electron =$9.1\times {10}^{-31}kg$

• A. $7.5\times {10}^{-4}m$
• B. $7.5\times {10}^{-3}m$
• C. $7.5m$
• D. $7.5\times {10}^{-2}$m

Answer 1

The correct option is A $7.5\times {10}^{-4}m$

$r=\frac{\sqrt{2mk}}{eb}=\frac{\sqrt{2me\Delta v}}{eB}$
$r=\frac{\sqrt{\frac{2m}{e}.\Delta v}}{B}=\frac{\sqrt{\frac{2\times 9.1\times {10}^{-31}}{1.6\times {10}^{-19}\left(500\right)}}}{100\times {10}^{-3}}$
$r=\frac{\sqrt{\frac{9.1}{0.16}\times {10}^{-10}}}{{10}^{-1}}=\frac{3}{4}\times {10}^{-4}=7.5\times {10}^{-4}$