Question
In an accelerator the electrons are accelerated up to an energy of 50 MeV. The electrons do not emerge continuously from the accelerator rather they come in pulses at time interval of 5.0 milliseconds. Each pulse has a much shorter duration of 200 nanoseconds. Electron current during the pulse is 100 mA, while the current is zero between the two successive pulses (see figure), then
Options
Solution
[Key Concept: Beam power equals accelerating voltage times beam current; the average over a period uses the duty factor (pulse width/period).]
$$V_{\text{acc~}} = 50MV i = 100\text{ }mA$$ during the time in which $e^{-}$emerges.
$\begin{matrix} & \ \therefore i_{\text{avg~}} = \frac{\Delta Q}{\Delta t} = \frac{200 \times 10^{- 9} \times 100 \times 10^{- 3}}{5 \times 10^{- 3}} = 4\mu\text{ }A \\ & P_{\text{avg~}} = V_{\text{i avg~}} = 50 \times 10^{6} \times 4 \times 10^{- 6} = 200\text{ }W \\ & P_{\text{peak~}} = V_{\text{i max~}} = 50 \times 10^{6} \times 100 \times 10^{- 3} = 5MW \end{matrix}$ ,
so Option C is correct and 2 MW is wrong.
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