Leonard Susskind wraps up the lecture series by finishing his talk on particles and both electric and magnetic fields and how they relate to physics. Topics: - Review of the vector potential, concept of gauge and gauge invariance - Lorentz force law - Example of different vector potentials for a constant magnetic field and the gauge transformation that relate them - Importance of gauge invariance and choice of gauge - Lagrangian of a particle in a static magnetic field. Review of the related action gauge invariance - Distinction between mechanical and canonical momentum: only the canonical momentum is related to symmetries and invariance - Derivation of the Euler-Lagrange equation of motion from the magneto-static Lagrangian and rediscovery of the Lorentz force - Justification of the vector potential as an essential tool for the least action principle - Derivation of the magneto-static Hamiltonian - Smart choice of gauge and derivation of the Lorentz force from symmetry arguments only, “cyclic coordinates” - Circular motion of a charged particle in a static magnetic field - Monopoles discussion as part of the questions session - Brief Quaternions discussion as part of the questions session Recorded on November 28, 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.