Electromagnetic theory, Lecture — I.
This lecture, the web version of the first lecture given in the electromagnetic theory paper of the physics honors degree class, was delivered on 21st December 2017. All electromagnetic theory lectures of this series, will be found here.
Also read part-2 of the linked lecture. That describes the subject matter of this lecture, in a good deal of depth.
A. Maxwell’s equations — basic form
B. Displacement current — Correction to Ampere’s law
C. Maxwell’s equations — in material media
Maxwell’s equations the basic forms
The Maxwell’s equations without the corrections to the Ampere’s law can be written as the following;
Electrostatics is when the electric charge and electric current densities, that produce these field, known therefore also, as the sources of the field, do not explicitly depend on time, that is, are constants. These sources or distributions depict the behavior of the field, and their independence from time means the fields do not vary in time, but vary only under spatial transformation.
Note that we are not talking about sources in the Maxwell’s equations above, but the ones that actually produce the E and B fields of the equations. The sources present in the equations above would alter these static fields though.
Accordingly the Maxwell equations would change their behavior in dynamic — i.e. time varying conditions, than they exhibit in the static conditions.
Equation (ii) has no names, but sometimes given a name, Gauss law — of magneto-statics.
Equation (iii) is known as Faraday’s law — of electromagnetic induction.
Equation (iv) is known as Ampere’s law.
Inconsistency in Maxwell’s equation
The Maxwell’s equations in this form are not the most general form of the eponymous set of equations. Also they are fraught with some degree of inconsistency.
Lets gaze deeper.