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Joseph Bishop Keller.

Electrohydrodynamics I. The equilibrium of a charged gas in a container online

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G(r,r') ^ j ^ , 2/"* \

( L - r r'log L/r (r') ( i - i ) , r'< r ,



r



r



From (31), with v = a, we find for n = 3



(UU) V, - a - ~-^ erp ~ a r log L/r < v < a = v^ •



'l RT



2

The analogues of (kh) for n » 1 and n » 2 are obtained by replacing r log L/r

L^- r^ 2

by — X and r L - r respectively, ^his yields the bounds on p for n = 3

/ \i 2 - 2

(U5) Pi " p I ly < P < P •

Corresponding boimds can be foimd for n = 1 and n = 2, although exact solutions
are available in these cases. Here P " j[ijr ®^ RT '^ "^^ *^^ value of p on the
boundary r = L where v = a. Improved bounds can be obtained by continued
use of (31) •



- 17 -



References



W M. von Laue, Jahrb. f. RadioaktivitSt 15(1918) S, 20$-256,

L^J L, HLeberbach, Gbttinger Nach. 1912, S. 599-602, Math. Ann. 77(1916)

S. 173-212.

L^J H. Rademacher in Frank-von Mises, Die Differential und Integralgloichungen

der Mechanik und Physik, I, pp. 838-8U5, Second Edition,
Rosenberg, N.Y., 19U3.

L^-» Joseph B, Keller, " On the Solutions of Z^u - f(u)"^to be published.





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Elec troliyd.ro dynamicsj




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Electrchyd5?o dynamics. J.





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Online LibraryJoseph Bishop KellerElectrohydrodynamics I. The equilibrium of a charged gas in a container → online text (page 2 of 2)