Maxwell's equations

There were equations written on a table in one of the habitation hubs of Sanctuary Base 6. (TV: The Impossible Planet)

Behind the scenes
Maxwell's equations are named for James Clerk Maxwell, whom the Fifth Doctor once identified as a friend. (AUDIO: The Haunting of Thomas Brewster)

In the real world, Maxwell's equations are a series of equations used in classical electrodynamics. Put heuristically, they can be described as saying "an electric charge generates an electric field", "there are no magnetic monopoles" (magnetic charges analogous to electric charges), "a change in a magnetic field over time creates an electric field", and "magnetic fields can be created either by a changing electric field over time or by an electric current".

The version of these equations given in the episode are in their differential form. The variables, vectors and operators written include $$D$$ (the electric displacement field), $$\rho$$ (the free electric charge density) , $$B$$ (the magnetic field in Teslas) , $$H$$ (the magnetic field in $$\frac{Amperes}{m^{2}}$$ ) , and $$\nabla$$ (the differential operator). In addition, the fourth equation may or may not include Maxwell's Correction, and thus include $$J_{f}$$ (the free current density), all shots shown of these equations in the episode are from an angle and distance that make it impossible to tell. Covariant versions of the equations would potentially be more useful to the crew of Sanctuary Base 6, being in a shorter form, but they are absent.