Question

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

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

Answer 1

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

The radius of the circular path of an electron in a magnetic field is given by,

$r=\frac{mv}{qB}$

$\Rightarrow r=\frac{\sqrt{2mK}}{eB}$

$\Rightarrow r=\frac{\sqrt{2meV}}{eB}(\because K=eV)$

$\Rightarrow r=\frac{\sqrt{\frac{2m}{e}V}}{B}$

$\Rightarrow r=\frac{\sqrt{\frac{2\times 9.1\times {10}^{-31}}{1.6\times {10}^{-19}}\left(500\right)}}{100\times {10}^{-3}}$

$\Rightarrow r=\frac{\sqrt{\frac{9.1}{0.16}\times {10}^{-10}}}{{10}^{-1}}\approx \frac{3}{0.4}\times {10}^{-4}$

$\Rightarrow r=7.5\times {10}^{-4}\text{m}$

Hence, option $\left(D\right)$ is correct.