Question

In an experiment electrons are accelerated, from rest, by applying a voltage of $500 \,V$. Calculate the radius of the path if a magnetic field $100\, mT$ 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. $7.5 m $
• D. $7.5 \times 10^{-2} \; m $

Answer 1

Answer: (A)

$r= \frac{\sqrt{2mk}}{eB} = \frac{\sqrt{2me\Delta v}}{eB}$
$ r = \frac{\sqrt{\frac{2m}{e}.\Delta v}}{B} = \frac{\sqrt{\frac{2\times9.1\times10^{-31}}{1.6\times10^{-19}}\left(500\right)}}{100\times10^{-3}}$
$ r = \frac{\sqrt{\frac{9.1}{0.16}\times10^{-10}}}{10^{-1}}= \frac{3}{4} \times10^{-4} =7.5 \times10^{-4} $