Toronto Lectures on Physics

3 The permittivity of space-time is a metric on u(1). 8 3.1 Electrostatics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.1 The electric field. . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.2 The dielectric displacement. . . . . . . . . . . . . . . . . . 8 3.1.3 The dielectric operator and the dielectric coefficient. . . . 9 3.1.4 The dielectric coefficient. . . . . . . . . . . . . . . . . . . 10 3.1.5 Rotationally invariant solutions of Laplace’s equation. . . 10 3.2 Magnetoquasistatics. . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2.1 Objects: The magnetic induction and the magnetic excitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2.2 The laws. 1: Faraday’s law of induction. . . . . . . . . . . 12 3.2.3 The laws. 2: There are no magnetic poles. . . . . . . . . . 12 3.2.4 The laws. 3: Ampère’s law. . . . . . . . . . . . . . . . . . 12 3.2.5 The force on a moving charge. . . . . . . . . . . . . . . . 12 3.2.6 The permeability. . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.7 The units of ∫ S B. . . . . . . . . . . . . . . . . . . . . . . 13 3.3 The Maxwell equations. . . . . . . . . . . . . . . . . . . . . . . . 13 3.3.1 The equation dF = 0. . . . . . . . . . . . . . . . . . . . . 13 3.3.2 The equation dG = 4πj. . . . . . . . . . . . . . . . . . . . 14 3.4 Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4.1 The units of the integral of F over a surface. . . . . . . . 14 3.4.2 The units of the integral of G over a surface. . . . . . . . 15 3.4.3 The integral of F ∧G over a four dimensional region is a scalar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4.4 The units of the permittivity. . . . . . . . . . . . . . . . . 15