Maxwell Stress Tensor Calculator

Maxwell Stress Tensor Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Science & Education
Input types: number, select
Output type: text
Sample coverage: 4
API ready: Yes

Overview

The Maxwell Stress Tensor Calculator computes the 3×3 electromagnetic stress tensor matrix, electric and magnetic energy densities, trace consistency check, and surface traction vector from three-dimensional electric and magnetic field components. By evaluating Maxwell stress expressions across configurable field units, it helps quantify electromagnetic momentum flux, radiation pressure, and field line tension in physical media and vacuum.

When to use

Determining radiation pressure and momentum flux exerted by electromagnetic waves on planar boundaries.
Evaluating electrostatic or magnetostatic forces and field line tension on charged or magnetized surfaces.
Validating electromagnetic field calculations with energy density breakdowns and tensor trace checks.

How it works

1Input the Cartesian vector components for both the electric field (Ex, Ey, Ez) and magnetic field (Bx, By, Bz), selecting appropriate measurement units.
2Select the surface normal orientation (+x, +y, or +z) to evaluate directional mechanical traction across a boundary.
3The tool computes the full 3×3 stress tensor matrix in N/m², electric and magnetic energy densities (u_E and u_B), the tensor trace check tr(T) = -(u_E + u_B), and the resulting surface traction vector.

Use cases

Calculating radiation pressure on solar sails and optical components under incident electromagnetic waves.
Analyzing mechanical stress and electrostatic tension near high-voltage electrodes approaching dielectric breakdown.
Verifying electrodynamics assignments and research models against analytical stress tensor formulas.

Examples

1. Sunlight Radiation Pressure on a Solar Sail

Aerospace Propulsion Engineer

Background

An engineer is sizing the solar radiation pressure acting along the propagation axis of an interplanetary solar sail.

Problem

Determine the total energy density, stress tensor matrix, and normal traction for sunlight characterized by an electric field of 614 V/m and magnetic flux density of 2.0474 µT.

How to use

Set Ex to 614 V/m, By to 2.0474 µT, remaining field components to 0, and choose +z as the surface normal.

Outcome

Calculates a total energy density of 3.34 µJ/m³ and a pure axial radiation pressure of 3.34 µPa directed along the +z propagation normal.

2. Electrostatic Tension at Atmospheric Breakdown

High-Voltage Systems Researcher

Background

A researcher is studying the mechanical pull exerted by strong static electric fields near conductor surfaces at the breakdown limit in air.

Problem

Compute the electrostatic pull and transverse compression generated by an electric field of 3 MV/m aligned along the x-axis.

How to use

Enter Ex = 3 with unit MV/m, set magnetic fields to 0, and select the +x normal.

FAQ

What is the physical meaning of the Maxwell stress tensor?

It represents the electromagnetic momentum flux density and mechanical force per unit area exerted by electric and magnetic fields on matter.

What does the tensor trace check verify?

In vacuum, the trace of the 3×3 Maxwell stress tensor equals the negative of the total electromagnetic energy density, confirming mathematical consistency.

What does a negative diagonal value in the tensor indicate?

Negative diagonal elements represent isotropic or directional pressure compressing the surface, whereas positive diagonal elements represent tensile stress.

Which field measurement units are supported?

Electric field inputs support V/m, kV/m, and MV/m, while magnetic field inputs support T, µT, and nT.

How is the surface traction vector calculated?

Traction is obtained by multiplying the 3×3 stress tensor by the unit normal vector chosen for the target surface.

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Sunlight Radiation Pressure on a Solar Sail

2. Electrostatic Tension at Atmospheric Breakdown

FAQ

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