Message-ID: <4D8FA9B3.1020303@toya.net.pl>
Date: Sun, 27 Mar 2011 23:18:43 +0200
From: Piotr Mlynarski <sq7mpj@toya.net.pl>
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Subject: Re: LF: Earth capacitance
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Andy Talbot pisze:
> Here's an interesting little thought excercise
>
> Consider the Earth as one plate of a capacitor, and the lower surface
> of the ionosphere as the other.   Without actually doing the
> calculation, what do you 'feel' the capacitiance might be?
>
> Then do the calculation; the result is rather surprising
>
>   

Dear Andy, LF

as i had completely no idea what might be the value of such defined 
capacitance
i immediately thought that this "interesting little thought excercise"  
could be added to
my sunday evening cup of coffee ... :)

Gauss theorem says that E field from charge Q on a sphere of radius R is
E = Q/(4*pi*eps*R*R)
having now two spheres: inner (earth) R1 and outer: ionosphere R2
the potential V = integral from R1 to R2 over EdR which immediately gives
 V = (Q/4*pi*eps)*(1/R1 - 1/R2) so as C = Q/V one gets
C  = 4*pi*eps/(1/R1 - 1/R2)
assuming R1 = 6370km ; R2 = 6370km + 60km = 6430 km; eps = 8.854*10^-12 F/m
C is about 0.076F or 76 miliFarad

                               pse, check my "homework"  :)   Piotr, sq7mpj

qth: Lodz /jo91rs/