Question 19

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]

$$p = \sqrt{2m eV}$$

$$r = \frac{p}{eB} = \frac{\sqrt{2m eV}}{eB} = \frac{1}{B}\sqrt{\frac{2mV}{e}}$$

$$r = \frac{1}{0.1}\sqrt{\frac{2 \times 9.1 \times 10^{-31} \times 500}{1.6 \times 10^{-19}}}$$

$$r = 10 \times \sqrt{\frac{9100 \times 10^{-31}}{1.6 \times 10^{-19}}} = 10 \times \sqrt{5687.5 \times 10^{-12}}$$

$$r \approx 10 \times 75.41 \times 10^{-6} = 7.54 \times 10^{-4}\ \text{m}$$

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