Axial Electric Field of a Charged Disk

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The graphic shows the infinitesimal contributions to the electric field in a point at a distance above the center of a charged disk with uniform charge density and radius
. In cylindrical coordinates, each contribution is proportional to
, where
and
are the radial and angular coordinates.
Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA
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Integrating, the electric field is given by
,
where is the permittivity of free space and
is a unit vector in the
direction.
The result depends only on the contributions in , because the angular contributions cancel by symmetry.
When , the value of
is simply
, which corresponds to the electric field of a infinite charged plane.
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