Calculator Input
Plotly Graph
This graph shows the constant electric field and the linearly changing potential across the gap.
Example Data Table
| Case | Mode | σ (μC/m²) | V (V) | d (m) | εr | Area (m²) | Expected E (V/m) |
|---|---|---|---|---|---|---|---|
| Vacuum Plate Pair | Charge density | 5.00 | — | 0.010 | 1.00 | 0.050 | 564704.534 |
| Air Gap Design | Voltage distance | — | 120.00 | 0.010 | 1.00 | 0.050 | 12000.000 |
| Dielectric Filled Gap | Charge density | 3.20 | — | 0.006 | 2.30 | 0.080 | 157309.784 |
Formula Used
Field from two oppositely charged infinite plates: E = σ / ε
Field from voltage and plate spacing: E = V / d
Permittivity in a medium: ε = ε₀ × εr
Capacitance approximation: C = εA / d
Charge on one plate: Q = C × V
Energy density: u = ½ εE²
Stored energy: U = ½ C V²
Potential variation in the gap: V(x) = Vcenter − E x
The ideal infinite plate model assumes uniform charge spread and no edge fringing. Because each single sheet contributes σ / 2ε, two oppositely charged sheets create a combined field magnitude of σ / ε between plates.
How to Use This Calculator
- Select whether you want to calculate from charge density or from voltage and separation.
- Enter the plate separation in meters.
- Enter the medium relative permittivity.
- Enter plate area if you want capacitance and energy results.
- Enter a position inside the gap for local potential evaluation.
- Choose the preferred field direction wording.
- Press Calculate Now to display the result above the form.
- Use the CSV or PDF buttons to export the current result set.
Frequently Asked Questions
1. Why is the field constant between infinite plates?
Infinite plates create a uniform charge distribution. That symmetry makes the field strength constant everywhere between them, as long as the ideal model ignores fringing and boundary distortions.
2. Why does the calculator ask for relative permittivity?
Relative permittivity changes the medium permittivity. A larger value reduces the field created by a fixed surface charge density and changes capacitance and stored energy results.
3. When should I use charge density mode?
Use charge density mode when the plate charges are known or specified by electrostatic design. It is useful in physics problems focused on field generation from surface charge.
4. When should I use voltage distance mode?
Use voltage distance mode when the applied voltage and gap are known. This is common in engineering setups, capacitors, and dielectric field calculations.
5. Does plate area affect the electric field here?
In the ideal infinite plate model, field strength depends on charge density or voltage and spacing, not area. Area is included here for capacitance and stored energy estimates.
6. Why is the potential graph linear?
Potential changes linearly because the field is constant. Since electric field equals the spatial rate of potential change, a uniform field produces a straight potential profile.
7. What does the position input represent?
The position value marks a point inside the gap, measured from the center plane. It helps estimate local electric potential under the ideal uniform field assumption.
8. Are edge effects included in this calculator?
No. This tool follows the ideal infinite plate approximation. Real finite plates show fringing near edges, so measured fields can deviate from these theoretical results.