# Course Fundamentals of Electrodynamics

Maxwell equations and electromagnetic waves
Level 3 (with higher mathematics)
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.
1. 1
Video

## Maxwell Equations. Here You Get the Deepest Intuition!

1. What is the Difference Between Differential and Integral Form of Maxwell's Equations?
Derivations & Experiments
Derivation

## 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.

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## Biot-Savart Law for a Thin Wire (Magnetic Field)

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2. 2
Lesson

## 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.

Video

## Electromagnetic Wave Equation Simply Explained

Derivations & Experiments
Derivation

## 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.

Derivation

## 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).

Derivation

## 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.

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## Wave Equation for B-Field

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3. 3
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## Induced Voltage (Inductance, Current)

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4. 4
Derivation

## 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.

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5. 5
Derivation

## 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.

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## Helmholtz Coil (B-Field, Same Current Direction)

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6. 6
Lesson

## 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.

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7. 7
Lesson

## 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
Derivation

## 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.

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## Magnetic Dipole (Force)

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8. 8
Derivation

## Self-Inductance of Two Current-Carrying Wires

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