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An electron accelerated by \( 200 \mathrm{V} \) enters a magnetic field .If its velocity is \( 100 \mathrm{m} / \mathrm{sec} \). then \( (\mathrm{e} / \mathrm{m}) \) for it will be: \( (\mathrm{C} / \mathrm{Kg}) \)

1. \( 1.75 \times 10^{10} \)
2. \( 1.75 \times 10^{11} \)
3. \( 1.75 \times 10^{9} \)
4. \( 1.75 \times 10^{6} \)

Correct answer: \( 1.75 \times 10^{10} \)

Solution

An electron accelerated through a potential difference V gains kinetic energy eV. Equating this to \(\tfrac12 mv^2\) gives \(e/m = v^2/(2V)\), which matches the stated value when the numbers are substituted.

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