Electric pressure: parallel plate vs. spherical capacitor (fwd)

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---------- Forwarded message ----------
Date: Mon, 6 Aug 2007 22:20:51 -0400
From: Jared Dwarshuis <jdwarshuis@xxxxxxxxx>
To: Pupman <tesla@xxxxxxxxxx>
Subject: Electric pressure: parallel plate vs. spherical capacitor

Electric pressure:  parallel plate vs. spherical capacitor





We will show that in both cases:   Pressure = ½ e Esqrd



Case # 1       Parallel plate capacitor   [Cap = e A/d]



F = ½ Cap Vsqrd / d           (this comes from work = force times distance)



F = ½  e A / (d sqrd) Vsqrd    But V= E d  and  Vsqrd = Esqrd  (d sqrd)
so….



F = ½ e A Esqrd      since       F/A = pressure   we get:



Pressure = ½ e Esqrd







Case # 2      Spherical capacitor with second plate at infinity   [Cap = 4
pi e R]



F = ½ Cap Vsqrd / R          (this comes from work = force times distance)



F = ½  4 pi e R Vsqrd / R    Or:



F =  2 pi e Vsqrd      But V= E d  and  Vsqrd = Esqrd  (d sqrd) so….



F = 2 pi e Esqrd Rsqd



Since   F/A = pressure and since area equals 4 pi Rsqrd  we get:



Pressure = ½ e Esqrd





Jared Dwarshuis Aug 07