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

Introduction

Introduction

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

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

Electric fields

Magnetic fields

Electric potential

Magnetic potential

Column’s law

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