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Axial Electric Field of a Charged Disk

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.

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DETAILS

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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