Electron in Electric Field
An electron is accelerated inside the electrical field of a vacuum tube by a voltage of around 100 kV. Compare the speed from the classical approach with the one obtained from taking relativistic effects into account.
Solution The classical formula gives the value
$$v = \sqrt{\frac{2eU}{m}} = 1.88\cdot 10^8\,\mathrm{m/s}$$
Using the relativistic formula results in
$$v = c\sqrt{1-\left(\frac{1}{1+\frac{qU}{m_0c^2}}\right)} = 1.21\cdot 10^8 \,\mathrm{m/s}$$
This result is around 50% smaller than the previous one showing that for high voltages in the order of a few Kilovolts, the relativistic effects cannot be ignored.
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Last modified: 2022-10-01 21:01:37 by mustafa
