Answer to Question #235243 in Electricity and Magnetism for Vic

Question

In a certain particle accelerator, electrons emerge with an energy of 40.0 MeV (1 MeV=

1.60 X 10-13 J). The electrons do not emerge as a steady stream but rather in pulses at the

rate of 250 pulses/s. This corresponds to a time interval between pulses of 4.00 ms (See

figure 5). Each pulse has duration of 200 ms, and the electrons in the pulse constitute a

current of 250mA. The current is zero between pulses

a) How many electrons are delivered by the accelerator per pulse?

b) What is the average current per pulse delivered by the accelerator?

c) What is the peak power delivered by the electron beam?

Answer 1

a)

$Q=It=250\cdot 10^{-3}\cdot 200^{-9}=5\cdot 10^{-8}~C,$

$N=\frac Qe=\frac{5\cdot 10^{-8}}{1.6\cdot 10^{-19}}=3.13\cdot 10^{11},$

b)

$I_{av}=\frac QT=\frac {5\cdot 10^{-8}}{4\cdot 10^{-3}}=12.5~\mu A,$

c)

$W=\frac{NE} t=\frac{3.13\cdot 10^{11}\cdot 40\cdot 1.6\cdot 10^{-13}}{2\cdot 10^{-7}}=10~MW.$