Practical Electron Microscopy and Database

The laws of classical electromagnetics can be summarized into a concise collection called Maxwell's equations.

In point form, the first of Maxwell’s equations, called Gauss’ law (electric), is a similar expression for the electric field  , but its divergence is not zero,

            ----------------------- [4285a]

where,
           ρ -- Charge
           ε₀ -- Permittivity of of vacuum, 8.854 × 10⁻¹² farad/m

The second of Maxwell’s equations, called Gauss’ law (magnetic), comes directly out of the quantum mechanical description, given by,

            ----------------------- [4285b]

where,
            -- Magnetic field

The third of Maxwell’s equations, called Faraday’s law, is given by,

            ----------------------- [4285c]

The fourth of Maxwell’s equations, called Ampère-Maxwell law, is a similar expression for the curl of the magnetic field, given by,

            ----------------------- [4285d]

where,
            c -- = 3 × 10⁸ m/s (the speed of light)
            µ₀ -- permeability of vacuum, 4π × 10⁻⁷ henry/m