In the movie Back to the Future, Doc tells Marty that, to power his automotive t

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=q*V= 20C *5*107V= 109 Joules

Power = Energy/time=109 Joules/0.2 sec = 5 *109 Watt= 5 gigawatt

b) time to use the energy by machine= 109 Joules / 1.2*109 Watt= 5/6 seconds= 0.83 sec

c) d=V/E=5*107/108=0.5m

C=q/V=20/(5*107)=400*10-9=100*8.85*10-12 Area /0.5

Area=0.5*400/0.885=226m2

Required volume =d*Area=113m3

d) Number of small automobile batteries required of given size=109J/106J=1000

New size the automobile battery has to be =1000*10-2=10m3

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