Magnetics 1 Question 5
5. 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.
(Take, charge of the electron $=1.6 \times 10^{-19} C$ and mass of the electron $=9.1 \times 10^{-31} kg$ )
(2019 Main, 11 Jan I)
(a) $7.5 \times 10^{-2} m$
(b) $7.5 \times 10^{-4} m$
(c) $7.5 \times 10^{-3} m$
(d) $7.5 m$
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Answer:
Correct Answer: 5. (b)
Solution:
- During the circular motion of accelerated electron in the presence of magnetic field, its radius is given by
$$ r=\frac{m v}{B e}=\frac{\sqrt{2 m e V}}{e B} $$
where, $v$ is velocity and $V$ is voltage.
After substituting the given values, we get
$$ \begin{aligned} & =\frac{\sqrt{2 \times 9.1 \times 10^{-31} \times 1.6 \times 10^{-19} \times 500}}{1.6 \times 10^{-19} \times 100 \times 10^{-3}} \\ & =10 \frac{2 \times 9.1 \times 500}{1.6} \times 10^{-12} 1 / 2 \\ r & =7.5 \times 10^{-4} m \end{aligned} $$
