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Electric field of a disc
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Integrate rings to get the disc's field.
Integrate rings: E = (σ/2ε₀)(1 − x/√(x² + R²)). As R → ∞ it approaches the infinite sheet result σ/2ε₀.
Close to the centre the disc acts like a plane.
Check the limits.
In more detail
On the axis of a uniformly charged disc, the field is E = (σ/2ε0)(1 − z/sqrt(z² + R²)). It approaches the infinite sheet result when the disc is large compared with the distance.
Real-world uses
- Estimating fields near charged electrodes shaped like discs.
- Modelling capacitors with circular plates.
- Physicists model a charged disc, such as a sample holder or an electron source, by adding the fields from many thin rings.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What does the limit mean?
For points very close to a large disc, the field approaches σ/2ε0.
Is the field zero at the centre?
No, it is largest at the centre and decreases with distance.
Is the field of a disc the same as an infinite plane?
Only near the disc. Far away the field falls off like a point charge, while close to a large disc it approaches the plane value.
Related topics in Electrostatics
Electrostatic energy of a sphere · Earnshaw's theorem · Electric field of a ring