Electromagnetic Field Solver Calculator

Model sources, then evaluate fields at points fast. Superpose contributions with consistent SI units easily. Download tables to share calculations with your team today.

Solver Inputs

Evaluation Point
Coordinates where net fields are computed.
Field Sources
Enable multiple rows to use superposition.
Source 1
row 1
Choose an idealized model per row.
For line/wire, z is ignored.
Used by Coulomb law for E.
Infinite line along z through (x,y).
Infinite wire along +z through (x,y).
Approx: E about sigma/eps0 between plates.
Approx: B about mu0 n I inside long solenoid.
Adds directly to net E vector.
Adds directly to net B vector.
Source 2
row 2
Choose an idealized model per row.
For line/wire, z is ignored.
Used by Coulomb law for E.
Infinite line along z through (x,y).
Infinite wire along +z through (x,y).
Approx: E about sigma/eps0 between plates.
Approx: B about mu0 n I inside long solenoid.
Adds directly to net E vector.
Adds directly to net B vector.
Source 3
row 3
Choose an idealized model per row.
For line/wire, z is ignored.
Used by Coulomb law for E.
Infinite line along z through (x,y).
Infinite wire along +z through (x,y).
Approx: E about sigma/eps0 between plates.
Approx: B about mu0 n I inside long solenoid.
Adds directly to net E vector.
Adds directly to net B vector.
Tip: keep the evaluation point away from source axes to avoid singularities.

Example Data Table

Sample inputs and typical magnitudes in SI units. Use them to validate wiring and unit conversions.

Scenario Source Parameters Point (m) Expected order
Point charge q at origin q = 1 uC (0.10, 0, 0) E about 9e5 V/m
Wire current I along +z I = 5 A (0.02, 0, 0) B about 5e-5 T
Line charge lambda along z lambda = 1 uC/m (0.05, 0, 0) E about 3.6e5 V/m
Solenoid Long solenoid n = 1000 1/m, I = 1 A Inside B about 1.26e-3 T
Plates Parallel plates sigma = 1 nC/m^2 Between E about 113 V/m

Formula Used

  • Point charge: E = k q rhat / r^2, with k = 1/(4 pi eps0).
  • Infinite line charge: |E| = (1/(2 pi eps0)) (lambda/rho), radial in the x-y plane.
  • Infinite wire current: |B| = (mu0 I)/(2 pi rho), direction phihat by the right hand rule.
  • Parallel plates (approx): E about sigma/eps0 along the chosen normal.
  • Long solenoid (approx): B about mu0 n I along the solenoid axis.
  • Energy density: u = 0.5(eps0|E|^2 + |B|^2/mu0).
  • Poynting vector: S = (1/mu0)(E x B).

These models assume vacuum and ideal geometries. Near boundaries and finite devices, real fields can differ.

How to Use

  1. Set the evaluation point coordinates and distance unit.
  2. Add one or more sources, select a type, and enter parameters.
  3. Enable only the rows you want included in superposition.
  4. Click Solve Fields to view net E, net B, u, and S.
  5. Use Download CSV or Download PDF to export results.

Article

Field Superposition and Source Modeling

This solver uses linear superposition, summing individual electric and magnetic contributions from enabled sources at one evaluation point. Point charges use kq/r^2, infinite line charge uses (1/(2 pi eps0)) lambda/rho, and infinite straight wire current uses (mu0 I)/(2 pi rho). These closed forms let you sanity-check magnitudes before exporting results.

Interpreting Vector Outputs in SI Units

Results are reported as E in volts per meter and B in tesla, with components [x,y,z] and magnitudes |E| and |B|. For example, a 1 uC point charge at 0.10 m produces about 9x10^5 V/m along the radial direction. A 5 A long wire at 0.02 m gives about 5x10^-5 T, tangential around the wire.

Energy Density as a Comparative Metric

The calculator reports electromagnetic energy density u = 0.5(eps0|E|^2 + |B|^2/mu0) in joules per cubic meter. When E dominates, u scales with |E|^2; doubling distance from a point charge reduces E by 4x and u by 16x. When B dominates, u scales with |B|^2, useful for comparing current-driven setups.

Poynting Vector and Power Flow

Power flux is estimated with S = (1/mu0)(E x B) in watts per square meter. S is zero when E and B are parallel, and maximized when they are perpendicular. With uniform fields, you can model plane-wave-like cases by setting E and B orthogonal with the ratio |E|/|B| near c about 3x10^8.

Using Plots to Spot Dominant Components

The Plotly charts display component bars for E and B so you can immediately see whether the field is primarily axial, radial, or transverse. A strong Ez with small Ex,Ey suggests plate-like or uniform inputs, while large Bx,By with near-zero Bz often indicates wire geometry. Plot trends across repeated runs help document design iterations.

Exportable Reporting and Practical Boundaries

CSV export captures the net vectors and per-source contributions for audit trails, while PDF export provides a compact summary for reviews. Remember these are idealized vacuum models: finite conductor size, dielectrics, and boundary conditions can shift results materially. Use the solver for fast screening, then validate with detailed simulation when precision matters. Document assumptions with units, and keep sources separated from evaluation points.

FAQs

1) What does this solver actually compute?

It computes net electric field E and magnetic field B at one point by summing idealized source models. It also reports |E|, |B|, energy density u, and Poynting magnitude |S| for quick comparisons.

2) Why do I see a singularity warning?

Some formulas diverge when the evaluation point lies on the source, such as r=0 for a point charge or rho=0 on a wire axis. Move the point slightly away to get finite values.

3) Can I mix electric and magnetic sources?

Yes. Each enabled row contributes either E, B, or both (uniform fields), and the solver sums them. This is useful for estimating combined effects in quasi-static scenarios and for computing the cross product in S.

4) Are the plate and solenoid models exact?

No. They are common long-geometry approximations: E about sigma/eps0 between large parallel plates and B about mu0 n I inside a long solenoid. Edge effects and finite sizes can change real fields.

5) What units should I use for inputs?

Use the unit selectors provided. Distances convert to meters internally, charge converts to coulombs, current to amperes, and uniform fields to V/m or T. Outputs are always in SI units.

6) How should I use the plots in reports?

Use the E and B component bars to show directionality and the derived plot to compare |E|, |B|, u, and |S|. Pair plots with CSV exports for traceable design notes.

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