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 × 10^9 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 × 10^7 V.

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 × 10^8 V/m, find the minimum volume it can have to store the energy from the lightning stroke.

Explanation / Answer

Here ,

c) charge , C = 20 C

time taken , t = 0.20 s

potential difference , V = 5 *10^7 V

here, for the minimum seperation

seperation, d = voltage/dielectric strength

d = 5 *10^7/(1 *10^8) m

d = 0.5 m

Now ,

as Q = C * V

20 = 8.854 *10^-12 * area/0.5 * 5 *10^7

solving for area

area = 22588.7 m^2

volume of capacitor = 22588.7 * 0.5

volume of capacitor = 11294 m^3

the volume of capacitor is 11294 m^3

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