In the movie Back to the Future, Doc tells Marty that, to power his automotive t
ID: 1587330 • Letter: I
Question
In the movie Back to the Future, Doc tells Marty that, to power his automotive time machine, he needs at least 1.2 gigawatts (1.2 × 109 W) and that he can obtain this from a stroke of lightning. Suppose that a certain lightning stroke lasts 0.20 s and transfers 20 C of charge across a potential difference of 5.0 × 107 V.
(a) How much energy is delivered, and what is the power of the stroke?
(b) If the time machine uses energy at the rate of 1.2 gigawatts, how long will the energy obtained from the lightning last?
(c) The time machine uses a so-called “flux” capacitor. Assuming that it has characteristics similar to an ordinary capacitor, with a dielectric constant of 100 and a dielectric strength of 1.0 × 108 V/m, find the minimum volume it can have to store the energy from the lightning stroke.
(d) A typical automobile battery stores about 106 J in a volume of 102 m3 . How large would an automobile battery have to be to store the energy from the lightning?
Explanation / Answer
a)
energy U = 0.5*Q*V = 0.5*20*5*10^7 = 5*10^8 J
power = U/t = (5*10^8)/0.2 = 25*10^8 W
b)
time = U/P = (25*10^8)/(1.2*10^9) = 2.083 s
(c)
energy density = 0.5*k*eo*E^2 J/m^3
volume = energy/energy density
volume = (5*10^8)/(0.5*100*8.84*10^-12*(10^8)^2)
volume = 113.12 m^3
(d)
volume required = (10^-2/10^6)*(5*10^8) = 5 m^3
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