Select a Maxwell relation, choose the variable to solve, then enter the remaining values in SI units.
| Mode | Sample Inputs | Sample Output |
|---|---|---|
| Gauss’s Law for Electricity | Q = 1e-6 C, ε = 8.854187817e-12 F/m | ΦE ≈ 1.129409e+5 N·m²/C |
| Gauss’s Law for Magnetism | Outward = 0.03 Wb, Inward = 0.03 Wb | Net Flux = 0 Wb |
| Faraday’s Law | Φ1 = 0.018 Wb, Φ2 = 0.006 Wb, Δt = 0.02 s | ℰ = 0.6 V |
| Ampère-Maxwell Law | μ = 1.2566370614e-6 H/m, I = 5 A, ε = 8.854187817e-12 F/m, dΦE/dt = 2e7 V·m/s | ∮B·dl ≈ 6.283408e-6 T·m |
1) Gauss’s Law for Electricity
ΦE = Q / ε
Closed-surface electric flux equals enclosed charge divided by permittivity. Optional area can estimate average normal electric field using Eavg = ΦE / A.
2) Gauss’s Law for Magnetism
ΦB,net = Φoutward − Φinward
A perfectly closed magnetic surface has zero net flux. This mode solves one balance term and reports the closure error percentage.
3) Faraday’s Law of Induction
ℰ = −ΔΦB / Δt
Induced EMF depends on how quickly magnetic flux changes. The negative sign represents Lenz’s law and the direction of opposition.
4) Ampère-Maxwell Law
∮B·dl = μ ( I + ε · dΦE/dt )
Magnetic circulation depends on both conduction current and displacement current. Optional path length estimates average magnetic field.
- Choose one of the four Maxwell-equation modes from the top selector.
- Select the variable you want the solver to calculate.
- Enter the remaining known values in SI units.
- Press Calculate to show the result under the header and above the form.
- Use Download CSV for tabular export or Download PDF for a printable report.
1) What does this calculator solve?
It solves four major Maxwell relations: electric flux, magnetic flux balance, induced EMF from changing flux, and magnetic circulation with displacement current.
2) Which units should I enter?
Use SI units. Charge is in coulombs, flux in webers or N·m²/C, time in seconds, permeability in H/m, and permittivity in F/m.
3) Why can Faraday results be negative?
The sign follows Lenz’s law. A negative value indicates the induced EMF acts in a direction that opposes the change in magnetic flux.
4) Why is net magnetic flux expected to be zero?
Gauss’s law for magnetism states that magnetic field lines do not begin or end at isolated monopoles, so total closed-surface magnetic flux is zero.
5) What is displacement current here?
It is the term ε·dΦE/dt in the Ampère-Maxwell equation. It behaves like an effective current produced by changing electric flux.
6) Can I export the results?
Yes. CSV creates a compact data table, while PDF captures the visible result section for printing, archiving, or sharing.
7) What does the graph represent?
The graph shows how one important variable changes with another for the selected law. The highlighted point marks your current solved result.
8) Can this replace full electromagnetic simulation software?
No. It is ideal for analytical calculations, quick checks, education, and design estimates, but not for full spatial field simulation.