Question

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

Answer 1

No

Step-by-step 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 = (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 = (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.