Download Introduction to electromagnetism - Pierre

PHY 042: Electricity and Magnetism
Introduction
Prof. Pierre-Hugues Beauchemin
The Structure of Sciences I
 E&M offers a clear way to see how physics laws are obtained from
simple experimental setups, and how they evolve and get generalized
following new experimental results and richer mathematical formalism
 This is a great opportunity to understand, at least partly, how sciences
work, and how an established theory is structured
 Studying E&M has an high epistemological value
 In this class, I will heavily insist on the elucidation of the connections
between theoretical ideas, formalism and instrumental setups.
 These connections are generally applicable to other field of physics, and
often demystify a theory
 For example, quantum mechanics is not describing a bizarre reality, it
proceeds from a similar interplay between experiments, math and physics
concepts as in E&M.
The Structure of Sciences II
 We will see that:
 Every laws or equations in physics have CONDITIONS OF
APPLICABILITY
 They are valid only under certain circumstances;
 Theoretical statements serve to describe or make predictions for
experimental setups or technological devices to which the laws can
be applied;
 Laws of physics are often generalized by some more powerful
mathematical and conceptual apparatus;
 Concepts are not really equivalent, even if one formula converts one
into another; they express different empirical conditions
 Generalization means an extension of the conditions of
applicability of the laws, which, in turn, will describe new
experiments, new devices and provide new phenomena
The Structure of Sciences III
 No physics law or equation of state is meaningful without an
experimental context

This experimental context may or may not be actually realized, but
it must at least be conceivable

The same equation might be applicable to various incompatible
experimental contexts, but in this case they have different meaning
and often the identity of formula is just a simplification
 The narrative of the course will be organized in a way to make
such structure obvious!
Context in physics I
 In mechanics, you learned to quantify the motion of an object:
 Description (kinematic)
 Effects of forces on the kinematic of an object (dynamic)
 Symmetry of the system in motion  conserved quantity
 The mathematical framework of classical mechanics is
inadequate in describing the motion of systems which:
 Travel closed to the speed of light
 Are microscopic
Context in physics II
Classical mechanics
(Newton)
Quantum mechanics
(Bohr, Heisenberg,
Schrödinger, Fermi)
Special and general
Relativity
(Einstein)
Quantum field theory
(Dirac, Schwinger,
Feynman)
Where does E&M fit?
Fundamental forces
 The electromagnetism is the interaction between matter particles
that we describe in mechanics.
 It is the cause of a change in the state of motion of a system
 There are 4 fundamental forces in Nature:
 Gravitational
 Long range, very weak classical and relativistic description
 Nuclear Weak and Strong
 Short range, quantum and relativistic description
 Electromagnetic
 Long range, can be described in all 4 realms
This course focus on the non-relativistic classical description
of the E&M interaction
Unification
 Special relativity description of E&M contains a fundamental feature:
 The complete unification of the E and B fields

Lorentz transformations leave Maxwell equations invariant
 Light is also an E&M wave (crucial to relativity too)
 Unification of E, M and optics
 Further unification?

Kaluza-Klein, Glashow-Salam-Weinberg, GUT?, Superstring?
 Unification is not a formal or epistemological requirement for physics
theories, but provides theories with rich structures extending the
known laws of physics to a broader range of phenomena.
 Unification also serve as guiding principle for theory development, and
provide a simple and beautiful picture of the world
Crucial Concepts in E&M I
 Fields:
 The space around an electric charge is permeated by electric and
magnetic fields which are responsible for transmitting the effects of
a set of charges on another
 Destroy the idea of distant action
 Keep causality
 Mediator of an interaction
 Fields are not passive:
 They carry energy, momentum and angular momentum
 They can be a system (radiation)
 Extend the concept of force to the concept of interaction
Crucial Concepts in E&M II
 Charges:
 Property of matter that is responsible for the interaction via a field
 It is related to the very powerful concept of symmetry
 0 net charge does not mean no E&M interaction…
 Each fundamental interaction comes from a fundamental symmetry
of Nature and thus with a charge associated
 Noether’s theorem
 They are quantized
 They are involved in the experimental aspects of probing E&M :
 Preparation  produce a field
 Observation  detect test charges