Electromagnetism, waves, action on a field, least action on a field and gauge theory

Introduction

Introduction

Electric fields

\(\overrightarrow{\mathbf F} = e\overrightarrow{\mathbf E}\)

\(div \overrightarrow{\mathbf E}=\dfrac{\rho}{\epsilon_0}\)

Electic fields of point charges: Column’s law

\(\overrightarrow{\mathbf F}=k_e\dfrac{q_1q_2}{r^2}\)

Electic fields of continuous charges

Electric potential

Magnetic fields of point charges

Magnetic fields of continuous charges

Magnetic fields

\(\overrightarrow{\mathbf F} = e\overrightarrow{v}\times \overrightarrow{\mathbf B}\)

\(div \overrightarrow{\mathbf B}=0\)

Magnetic potential

Electromagnetism

\(\overrightarrow{\mathbf F} = e{\overrightarrow{\mathbf E}+\overrightarrow{v}\times \overrightarrow{\mathbf B}}\)