## Capacitance Of A Cylindrical Capacitor

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# Capacitance of A Cylindrical Capacitor

The plates of capacitors of this type such as of a single core cable, are two co-axial cylinders, as shown in, that produces a non-uniform, but radically symmetric field. Assuming that the distance between te plates is very small in comparison with the length of capacitor plates, i.e. ignoring the field distortion occurring at the edges of the capacitor plates (fringe effect), let us denote the inner diameter by d, the outer diameter by D and relative permittivity of the dielectric by ∈r, Let the charge per meter length of the capacitor on the outers surface of inner cylinder be + q coulombs and all practical purposes, the charge of +q C/m on the surface of the inner cylinder can be assumed to be located along its axis. The outer cylinder is earthed.

Surface area of the co-axial cylinder of radius x metres and length one metre is 2πx metres

Therefore electric field intensity at a point x metres from the centre of the inner cylinder,

Surface area of the co-axial cylinder of radius x metres and length one metre is 2πx metres

^{2}Therefore electric field intensity at a point x metres from the centre of the inner cylinder,

Ex =

__q__

__=__

__q__

__.__

__1__V/m

2π∈

_{o}∈

_{r }2π∈

_{o}∈r x

Potential difference between the capacitor plates,

(between core and sheath),

=

__q__

__loge__

__D__

2π∈

_{o}∈r d

Capacitance of cytinderical capacitor,

C =

__q__=

__q__

__= 2π∈__

_{o}∈r F/m =

__2π x 8.854 x 10__

^{-12}∈rV

__q__

__loge__

__D__loge

__D__

__D__

__2π∈__d d 2.3 log

_{o}∈r_{10}d

=

__∈r x 10__F/m

^{-9}41.4 log

_{10}

__D__

d

=

__0.-24 ∈r__μ F/m

log

_{10}

__D__

d

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