# Course: Fundamentals of Electrodynamics

Maxwell equations and electromagnetic waves
1. 1

## What is Multipole Expansion?

What is multipole expansion of charge density in electrodynamics and what it is useful for.

2. 2

## The 4 Maxwell's Equations: Important Basics You Need to Know

Simple explanation of the Maxwell's equations for beginners. The divergence integral and the curl integral theorems are also explained.

Questions & Answers What is the Difference Between Differential and Integral Form of Maxwell's Equations?
Derivations & Experiments

## Displacement Current for the 4th Maxwell Equation

Derivation of the displacement current as a correction to the fourth Maxwell equation. For this purpose we use a plate capacitor.

## Coulomb's Law using 1st Maxwell Equation

Here you will learn how to derive Coulomb's law for two point charges from divergence theorem and Maxwell's first equation.

Related formulas

3. 3

## Electromagnetic wave and its E-field and B-field components

Here you will learnthe wave equations for the E-field and B-field of an electromagnetic wave and how it can be simplified to a plane wave.

Derivations & Experiments

## Wave Equation for E-field and B-field

Derivation of the wave equation for the electric and mangetic field from the decoupled Maxwell equations in vacuum.

## Energy of the Electric Field

Derivation of the energy of the electric field (E-field) using the charging process of a sphere (and a plate capacitor).

## Energy of the magnetic field

Derivation of the magnetic energy and energy density of the B-field using a current-carrying coil. The formulas are also valid in general.

Related formulas

4. 4

## B-Field inside a Current-Carrying Coil

In this derivation, the magnetic field inside a long coil is calculated using Ampere's law when N, l, and I are given.

Related formulas

5. 5

## Magnetic Field Inside and Outside a Coaxial Cable

Derivation of the magnetic field (B-field) of a coaxial cable, inside and outside, by exploiting Ampere's law.

6. 6

## Magnetic Field of a Helmholtz Coil

Derivation of the homogeneous magnetic field in the center (on the symmetry axis) of the Helmholtz coil with radius R and distance d.

Related formulas

7. 7

## Linearly and Circularly Polarized Electromagnetic Waves

Here you will learn about polarized light, i.e. linearly or circularly polarized electromagnetic waves, and what characterizes them.

8. 8

## Dielectric Polarization: How Charges are Shifted in a Dielectric

Here, dielectric polarization is simply explained and how it can be used to explain the weakened E-field in the dielectric.

Questions & Answers How Does an Electric Dipole Move in the (In)Homogeneous E-Field?
Related formulas

9. 9

## Magnetic Dipole in a External Magnetic Field

Magnetic dipole (as a conductor loop) is simply explained and what happens to it when the is placed in an external magnetic field.

Derivations & Experiments

## Magnetic Dipole - Torque, Energy and Force

Derivation of the potential energy (potential), torque and force on a magnetic dipole - expressed with the magnetic dipole moment.

Related formulas

10. 10

## Self-Inductance of Two Current-Carrying Wires

Derive the self-inductance and magnetic flux of two parallel current carrying conductors with opposite currents.

Related formulas

11. 11

## What is the Magnetization of a Material?

How is magnetization defined and and what does it have to do with diamagnetic, paramagnetic and ferromagnetic materials?

Related Questions What is the Difference Between Electric and Magnetic Fields? How Does an Electric Dipole Move in the (In)Homogeneous E-Field?

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