Force Field Generator Calculator

Example Data Table

Formula Used

• Gravity (point mass): g(r) = −G M r / |r|³, and F_g = m g.
• Electric field (point charge): E(r) = k Q r / |r|³, and F_e = q E.
• Magnetic field (straight wire): |B| = μ₀ I /(2πρ), with direction around the wire.
• Lorentz force: F = q (E + v × B).
• Total force: F_total = F_g + F_e + F_mag.

How to Use This Calculator

1. Enter the observation point where you want the field.
2. Enable the sources you want to combine.
3. Set source strengths and positions for your scenario.
4. Provide test particle mass, charge, and velocity.
5. Optionally enable the line scan to generate a dataset.
6. Press Compute Force Field to see results above the form.

Force Field Generator: Technical Overview

1) What this calculator generates

This tool superposes gravitational acceleration g, electric field E, and magnetic field B from selectable sources, then evaluates forces on a test particle. Outputs include vector components, magnitudes, and energy diagnostics at a user-defined observation point.

2) Constants and unit system

All computations use SI units. The calculator applies G = 6.67430×10⁻¹¹ N·m²/kg², k = 8.9875517923×10⁹ N·m²/C², and μ₀ = 4π×10⁻⁷ N/A². Enter meters, kilograms, coulombs, amperes, and meters per second to keep results consistent.

3) Point-source gravity model

For a point mass M located at (x_s,y_s,z_s), the calculator uses g(r)=−GM r/|r|³. The force on the test mass is F_g=m g. For Earth-scale checks, a mass near 5.972×10²⁴ kg at large distance yields realistic orders of magnitude.

4) Coulomb electric field model

For a point charge Q at the same source position, the calculator uses E(r)=kQ r/|r|³, with force F_e=qE. As a practical reference, a 1 μC source produces about 9.0×10³ V/m at 1 m along the axis.

5) Magnetic field from an infinite straight wire

When the wire source is enabled, the calculator assumes an infinite conductor along the +z direction through (x_w,y_w). The magnitude follows |B|=μ₀I/(2πρ). The direction wraps azimuthally around the wire, and the Lorentz term uses v×B. For example, I=10 A at ρ=0.10 m gives roughly 2.0×10⁻⁵ T.

6) Total force and energy diagnostics

The combined force is F_total=m g + q(E + v×B). The tool also reports gravitational potential energy U_g=m(−GM/|r|) and electric potential energy U_e=q(kQ/|r|). Magnetic potential energy is not uniquely defined without a gauge choice, so it is intentionally omitted.

7) Numerical softening and recommended ranges

Point models diverge as |r|→0, so the calculator replaces distances with max(|r|, r_min). A typical setting is r_min=10⁻⁶ m. For smooth exploration, keep observation distances above 10⁻³ m and avoid extreme charges unless you intentionally study near-field behavior.

8) Data generation via line scans

The optional scan sweeps one coordinate while holding the other two fixed, producing a table of E, B, and F components plus |F|. With 21–51 steps you can build plots for validation, such as verifying the expected 1/r² trend for point-source fields or the 1/ρ trend for the wire field.

FAQs

1) What does “force field generator” mean here?

It means the calculator synthesizes vector fields from selectable analytical sources, then evaluates the net force on a test particle at a point, using superposition and the Lorentz force.

2) Can I use non-SI units?

The formulas are implemented in SI. If you use other units, convert inputs first (e.g., centimeters to meters). Otherwise the results will scale incorrectly and comparisons to references will fail.

3) Why do results change when I adjust r_min?

r_min softens singularities near sources by limiting the minimum distance. Larger values reduce extreme near-field magnitudes and can stabilize scans close to the source position.

4) Why is magnetic potential energy not shown?

A unique scalar potential energy for magnetic forces generally requires additional structure (like a chosen vector potential and gauge). The calculator reports magnetic force directly to avoid misleading energy values.

5) What is the wire direction assumed by the model?

The wire is assumed infinite and aligned with +z. Its position is set by (x_w, y_w). The resulting field circles the wire in the xy-plane according to the right-hand rule.

6) How do I validate the calculator quickly?

Disable all but one source, pick a simple geometry (e.g., on-axis), and compare with a hand calculation. Use the scan table to confirm scaling like 1/r² for point sources or 1/ρ for the wire.

7) What does the CSV/PDF export include?

Exports include a compact point-summary table (g, E, B, and force components). If a line scan is enabled, the exported file also contains the full scan dataset for plotting or reporting.