3pi e/ln(b-a/a) ???
two long straight wires with equal cross-sectional radii a are located parallel to each other in air.the distance between their axes equals b.find the mutual capacitance of the wire per unit length under the condition b>>a.
-
UP 0 DOWN 0 0 5
5 Answers
3see E = σ/2 pi e [1/r + 1/b-r ]
integrate frm .. a to b-a .... get pd ...
sigma / V =the req ans ...
1solve this
long straight wire crosssectional radius a and a infinite plane are located parallel to each other in air.the distance between them equals b.find the mutual capacitance of the wire per unit length under the condition b>>a.
3detail soln..
E for an infinitly long conducter ...
let @ be charge density ////
drawing a cylindrical gaussian surface of radius r and length l .........
@l/e = 2 pi r l E ....
@/2 pi e r = E .....
now we have two of them of chargedensity say @ , -@
E(at r) = @/2 pi e r + @/2 pi r (b-r) ...
V = -∫E.dr !!
takin origin at 1 of the conducters ..
V(a) - V(b-a) = -@/2pie [2ln(a/b-a)]
@/pie [ln(b-a/a)]
now q in 1 unit length ........ @(1) /
C = Q/V ...
@pi e/@ln(b-a/a)
pi e /ln(b-a/a)...
as b>>a
pi e / ln(b/a)