Axial Electric Field of a Charged Disk

​
ϕ
0
s
0.5
z
0.5
The graphic shows the infinitesimal contributions to the electric field in a point at a distance
z
above the center of a charged disk with uniform charge density and radius
R
. In cylindrical coordinates, each contribution is proportional to
s'ds'dϕ'
, where
s'
and
ϕ'
are the radial and angular coordinates.

Details

Integrating, the electric field is given by
E=
σ
2
ϵ
0
1-
z
2
R
+
2
z

z
​
,
where
ϵ
0
is the permittivity of free space and

z
is a unit vector in the
z
direction.
The result depends only on the contributions in

z
, because the angular contributions cancel by symmetry.
When
R∞
, the value of
E
is simply
σ/2
ϵ
0
, which corresponds to the electric field of a infinite charged plane.

External Links

Charge (ScienceWorld)
Permittivity of Free Space (ScienceWorld)
Electric Field (ScienceWorld)
Cylindrical Coordinates (Wolfram MathWorld)

Permanent Citation

Enrique Zeleny
​
​"Axial Electric Field of a Charged Disk"​
​http://demonstrations.wolfram.com/AxialElectricFieldOfAChargedDisk/​
​Wolfram Demonstrations Project​
​Published: November 16, 2010