Professor Kraus reminds his readers in Electromagnetics , that \"we live inside

Question

Professor Kraus reminds his readers in Electromagnetics, that "we live inside a huge capacitor" between the earth's surface and the 'electrosphere' - a conducting region of the upper atmosphere, around 25 km up, in which cosmic rays ionise the air molecules.

He calculates the earth's capacitance at about 0.18 Farad, which seems surprisingly low, and from the known value of charge density at the surface of the earth (around 3 nC/sq.m) he shows that this capacitor holds a million Coulombs or so. Then it's a simple matter to calculate how much energy it's storing. So how much energy is stored in the Earth's Atmosphere.

Hint you will need to analyse these units to find the path to the answer, the dimensions of the Earth may come into play.

Explanation / Answer

here by using the formula

U = 0.5 * Q^2 / C

the charge denisty = 3 * 10^-9 C /m^2

sigma = charge / area

area of earth = 5.1 * 10^14m^2

3 * 10^-9 * 5.1 * 10^14 = charge

q = 1.53 * 10^6 C

then put in the first formula

U = 0.5 * (1.53 * 10^6)^2 / 0.18

U = 6.5025 * 10^12 J

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