Formulate Maxwell Equations

Analyze electromagnetic phenomena by stating the relevant Maxwell equations in appropriate form (integral or differential), applying boundary conditions and symmetry to reduce the system, solving the resulting partial differential equations for the fields, computing derived quantities such as the Poynting vector, radiation pressure, and wave impedance, and verifying the solution against known static and wave limits.

When to Use

• Solving a boundary value problem for E and B fields in a region with sources and material interfaces
• Deriving the electromagnetic wave equation from first principles
• Computing energy flow (Poynting vector) and momentum density of electromagnetic fields
• Applying boundary conditions at interfaces between different media (dielectrics, conductors, magnetic materials)
• Analyzing displacement current and its role in completing the Ampere-Maxwell equation
• Connecting the static limits (Coulomb's law, Biot-Savart) to the unified time-dependent framework

Inputs

• Required: Physical configuration (geometry, source charges and currents, material properties)
• Required: Quantity to solve for (E-field, B-field, wave solution, energy flux, or boundary field values)
• Optional: Symmetry information (planar, cylindrical, spherical, or no special symmetry)
• Optional: Time dependence specification (static, harmonic at frequency omega, or general time-dependent)