Maxwell’s equations LEC 6

Understand the need to make Ampere's law consistent with the charge conservation law (Maxwell's fix), understand the concept of the displacement current, appreciate the fundamental Maxwell's equations of electromagnetism, understand the concept of free space and derivation of the wave equations, learn how to use wave functions to describe electromagnetic wave solutions, appreciate relative directions of the electric and magnetic fields in a plane wave.

How do dielectric materials affect electric fields?

In dielectric materials, polarization (P⃗) creates a volume charge density (−∇⋅P) that adds to the free charge density when calculating the electric field.

what the method for calculating error for neglecting displacement current in a solenoid

• The displacement current arises due to the changing electric field produced by a time-varying magnetic flux in the solenoid.

• Using Faraday’s Law, the induced electric field is calculated, and the displacement current is then computed through integration.

• The displacement current is much smaller than the total current for typical frequencies and solenoid radii.

What happens when electromagnetic fields vary rapidly in time

The displacement current becomes significant and cannot be neglected, leading to new solutions of Maxwell's equations, specifically the propagation of electromagnetic waves.

what does induce mean?

In simple terms, to induce means to cause something to happen or to create an effect.

What is a plane wave in electromagnetic radiation?

A plane wave is an electromagnetic wave with wavefronts that are planes perpendicular to the direction of propagation.