Calculator Inputs
This calculator supports direct charge-volume calculations, field-based methods from Gauss's law, potential-based calculations from Poisson's equation, carrier-density evaluation, and a one-dimensional field gradient model.
Formula Used
1) Direct charge and volume
ρ = Q / V
Use this when total charge inside a known volume is already available.
2) Electric field divergence
ρ = ε0 εr ∇·E = ε0 εr (∂Ex/∂x + ∂Ey/∂y + ∂Ez/∂z)
Use this for isotropic media with approximately uniform permittivity.
3) Potential Laplacian
ρ = -ε0 εr ∇²V
This is the Poisson equation form, useful when potential curvature is known.
4) Carrier concentration
ρ = s z e n
Here, s is the sign, z is valence, e is elementary charge, and n is carrier density.
5) One-dimensional field gradient
ρ = ε0 εr (dEx/dx)
Useful for slab-like or nearly one-dimensional field distributions.
How to Use This Calculator
- Choose the method that matches your available physics data.
- Enter charge, field derivatives, potential derivatives, or carrier values.
- Select consistent units for charge, volume, and carrier concentration.
- Pick a material preset or type a custom relative permittivity.
- Press Calculate to view the result above the form.
- Review the summary table, sign interpretation, and graph trend.
- Export the result as CSV or PDF for reports or records.
- Compare methods when you want to validate experimental and theoretical values.
Example Data Table
These sample rows show typical inputs and corresponding output values.
| Method | Sample Inputs | Result |
|---|---|---|
| Direct charge and volume | Q = 2 μC, V = 40 cm³ | ρ = 0.050000 C/m³ |
| Field divergence | ∂Ex/∂x = 250, ∂Ey/∂y = 300, ∂Ez/∂z = 350 V/m², εr = 2.5 | ρ = 1.992192e-8 C/m³ |
| Potential Laplacian | ∂²V/∂x² = -600, ∂²V/∂y² = -500, ∂²V/∂z² = -400 V/m², εr = 4 | ρ = 5.312513e-8 C/m³ |
| Carrier concentration | n = 2.5×10¹² per cm³, z = 1, positive | ρ = 0.400544 C/m³ |
| 1D field gradient | dEx/dx = -1200 V/m², εr = 3 | ρ = -3.187508e-8 C/m³ |
FAQs
1) What is space charge density?
Space charge density is the net electric charge stored per unit volume. It is usually expressed in coulombs per cubic meter and may be positive, negative, or nearly zero.
2) When should I use the direct Q/V method?
Use the direct method when total charge and occupied volume are already known. It is the simplest route and is often useful for laboratory measurements or known trapped-charge regions.
3) Why does permittivity appear in field-based methods?
Permittivity links electric field behavior to charge through Gauss’s law in matter. For a linear isotropic medium with uniform permittivity, charge density equals permittivity multiplied by field divergence.
4) What does a negative result mean?
A negative result means the net local charge density is negative. In many physical systems, this suggests an excess of electrons or negatively charged ions within that region.
5) Can I use this for semiconductors?
Yes. The carrier concentration method is especially useful for semiconductors when you know carrier density, sign, and valence. It can help estimate net volumetric charge behavior inside a region.
6) What units are used in the calculator?
The final result is reported in C/m³. The calculator also shows the same numerical magnitude as μC/cm³, because 1 C/m³ equals 1 μC/cm³ after unit conversion.
7) Is the potential method based on Poisson’s equation?
Yes. The potential method comes directly from Poisson’s equation, where charge density is proportional to the negative Laplacian of electric potential in a medium of constant permittivity.
8) Why does the graph matter?
The graph shows sensitivity. It helps you see whether charge density changes linearly, changes sign, or grows sharply as the main driving variable increases or decreases.