In this lecture, Leonard Susskind dives into the topics of magnetic and electrostatic forces. He derives these forces to show their relationship to magnetic fields and potential. He introduces the static electric and magnetic fields with the associated Lagrangian and the Lorentz force. The vector potential, it's gauge field and gauge invariance are also introduced. Topics: - Magnetic and electric fields - The concept of field - The “del” or “nabla” symbol - Vector calculus: Gradient, Divergence and Curl - The Levi-Civita symbol - Algebra: div curl and curl grad vanish - The vector potential and why it's needed - Gauge field: "Gauge" is a misnomer - Lorentz force. Lorentz force compared with the Coriolis force - Lagrangian for charged particles in a electro-static and magneto-static fields - Gauge invariance of the equations of motions associated to the electro-magneto-static Lagrangian Recorded on November 21, 2011.

1. State diagrams and the Nature of Physical Laws
2. Newton's Law, Phase Space, Momentum and Energy
3. Lagrangian, Least Action & Euler-Lagrange Equations
4. Symmetry and Conservation Laws
5. The Hamiltonian
6. Hamilton's Equations
7. Liouville's Theorem & Phase Spaces
8. Poisson Brackets
9. Lagrangian of Static Electric and Magnetic Fields
10. Particles in Static Electric and Magnetic Fields

This is the first course in a collection of 6 core physics courses by renowned physicist Leonard Susskind's series, The Theoretical Minimum. Our exploration of the theoretical underpinnings of modern physics begins with classical mechanics, the mathematical physics worked out by Isaac Newton (1642--1727) and later by Joseph Lagrange (1736--1813) and William Rowan Hamilton (1805--1865). We will start with a discussion of the allowable laws of physics and then delve into Newtonian mechanics. We then study three formulations of classical mechanics respectively by Lagrange, Hamiltonian and Poisson. Throughout the lectures we will focus on the relation between symmetries and conservation laws. The last two lectures are devoted to electromagnetism and the application of the equations of classical mechanics to a particle in electromagnetic fields.