Question

We define average current as $I_{av}=\frac{\Delta Q}{\Delta t}$ and instantaneous current as $I=\frac{dQ}{dt}$. Obviously, $Q=\int Idt$. Further, electric energy delivered per unit time by a source, i.e., power, $P=\frac{\Delta E}{\Delta t}$, where $\Delta E$ is the energy delivered by the source in time $\Delta t$.
In a certain accelerator, electrons emerge with energies of $40.0MeV\left(1MeV=1.60\times 10^{-13}J\right)$. The electrons do not emerge in steady stream, but in pulses that repeat 250 times per second.

This corresponds to a time between each pulse of $4.00ms$ in figure. Each pulse lasts for $200ms$ and the electrons in the pulse constitute a current of $250mA$. The current is zero between the pulses. While the pulse is on, the current is constant.
The maximum power delivered by the electron beam is

• A. $100W$
• B. $10kW$
• C. $1MW$
• D. $10MW$

Answer 1

Answer: (D)

Maximum power delivered by the electron beam
$P=\frac{\Delta E}{\Delta t}$
$=\frac{\left(3.13\times 10^{11}electrons/\text{ pulse }\right)(40.0MeV/electron)}{2.00\times 10^{-7}s/pulse}$
$=\left(6.26\times 10^{19}MeV/s\right)\left(1.6\times 10^{-13}J/MeV\right)$
$=1.00\times 10^{7}W=10.0MW$