The Continuum — Part V: Electromagnetism from the Continuum

We show that the electric and magnetic fields emerge from two distinct components of the same velocity field generated by the toroidal vortex: E from the poloidal component (pressure gradient), B from the toroidal component (curl of the field). With these definitions, E and B correctly share the same physical dimensions. We state honestly the different nature of the four Maxwell equations: Faraday's law and the absence of magnetic monopoles follow directly from the definitions via vector-calculus identities valid for any field - self-consistency checks, not independent derivations. Ampere-Maxwell's law and Gauss's law are stated in their expected final form; both are proven, for the case of discrete charges, from the universal Coulomb force and Helmholtz's theorem. The electromagnetic constants epsilon0 = rho0/c and mu0 = 1/(rho0c) correctly satisfy the structural relation c = 1/sqrt(epsilon0*mu0) - not a postulate, but a consequence. Checked individually against SI units, they are not dimensionally consistent - not a gap in the model, but because the International System requires charge to be an independent dimension (the Ampere), while in the Continuum charge is a dimensionless topological label (+/-1). The physically meaningful electromagnetic quantity, alpha_fs, independent of any unit convention, has already been derived elsewhere in this series to 0.37 ppm precision. Photons emerge as waves of the velocity field at J = rho_e = 0, with particle-like behavior from quantization determined by delta_min. We further construct the electromagnetic energy density in the Continuum's native language - not an adaptation of the International System's formula, but a form forced by dimensional analysis once E is recognized to carry the dimensions of a force: u_EM = E^2/(hbar*c) + c*B^2/hbar. For an elementary charge, the field energy integrated up to the proton's radius amounts to roughly 0.0167% of its rest mass; the magnetic contribution, from the structure's intrinsic rotation, is real but negligible. We finally show that the Coulomb force is not a separate fundamental interaction, but the superfluid's Bernoulli effect applied to the bubbles' chiral flows: attraction and repulsion share the same origin - the pressure P0 - differing only in the relative direction of the flows in the gap between particles. This work constitutes Part V of a series.