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PHY 415: Electromagnetic Theory I
Prof. S. Teitel: stte@pas.rochester.edu ---- Fall 2021

Unit 4

Unit 1 • Unit 2 • Unit 3 • Unit 4 • Unit 5 • Unit 6 • Unit 7 • Unit 8

Electromagnetic Energy and Momentum

October 14 to 22

You should review the notes and videos below by October 22.
Questions on the material of Unit 4 may be posted on the Unit 4 Discussion Board, or on the Unit 4 Slack channel.

Your response to Discussion Question 7 is due Tuesday, October 19, at 5pm
Your solutions to Problem Set 7 are due Thursay, October 21, at 5pm

In this unit we extend the ideas of energy and momentum to electromagnetic fields, defining the energy and momentum densities, and the energy and momentum currents. We show how these enter conservation laws for the total energy and momentum of a system of interacting charges. We also discuss the capacitance of a system of conducting bodies, and the inductance of a system of current carrying loops. We discuss the electromagnetic and magnetostatic energies stored in these configurations. We review the properties of electromagnetic waves in a vacuum, and discuss the energy and momentum carried by such waves. In supplemental notes, we discuss the force, torque, and interaction energy of electric and magnetic dipoles.

Below is a list of links to the course notes for each topic in this unit, followed by links to recorded video lectures.

Notes and Video Lectures

• Notes 4-1 - Electromagnetic energy density and the Poynting vector
  Video 4-1.1 - Electromagnetic energy and energy conservation [22 min]

  Video 4-1.2 - Energy conservation and the macroscopic Maxwell equations [20 min]

  Video 4-1.3 - Electrostatic and magnetostatic energy [22 min]

• Notes 4-2 - Electromagnetic momentum density, the Maxwell stress tensor, and the force on a conductor's surface
  Video 4-2.1 - Electromagnetic momentum and momentum conservation [35 min]

  Video 4-2.2 - Meaning of the Maxell stress tensor and the force on a conductor's surface [22 min]

• Notes 4-2-supp - Magnetic monopoles, electromagnetic angular momentum, and the quantization of electric charge

• Notes 4-3 - Capacitance and Inductance
  • Video 4-3.1 - Capacitance matrix between conducting bodies [33 min]

  • Video 4-3.2 - Mutual inductance matrix between current carrying loops [13 min]

• Notes 4-3-supp - Supplemental: Forces, Torques, and Interaction Energy of Electric and Magnetic Dipoles

• Notes 4-4 - Energy and momentum of an electromagnetic wave in a vacuum
  • Video 4-4.1 - Harmonic plane electromagnetic waves in a vacuum [40 min]

  • Video 4-4.2 - Energy and momentum in harmonic plane waves [16 min]