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nirvana33 [79]
3 years ago
14

Air undergoes dielectric breakdown at a field strength of 3 MV/m. Could you store energy in an electric field in air with the sa

me energy density as gasoline? The energy content of gasoline 44* 10^6 J/kg and the density of gasoline is 670 kg/m^3. Yes or No.
Physics
1 answer:
slega [8]3 years ago
3 0

Answer:

No

Explanation:

The energy content of gasoline is

44\cdot  10^6 J/kg

while the density is

670 kg/m^3

So the energy density of gasoline is

u = (44\cdot 10^6 J/kg)(670 kg/m^3)=2.95\cdot 10^{10} J/m^3

The energy density of an electric field is given by

u_E = \frac{1}{2}\epsilon_0 E^2

where

\epsilon_0 = 8.85\cdot 10^{-12} F/m is the vacuum permittivity

E is the strength of the electric field

For air at dielectric breakdown,

E=3 MV/m = 3\cdot 10^6 V/m

Substituting into the equation,

u_E = \frac{1}{2}(8.85\cdot 10^{-12})(3\cdot 10^6)^2=39.8 J/m^3

We see that u_E < u, so the energy density of the electric field is much lower than the energy content of gasoline, so the answer is No.

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