Homework14 - Homework 14 Answers 95.657 Fall 2011...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 14 Answers, 95.657 Fall 2011, Electromagnetic Theory I Dr. Christopher S. Baird, UMass Lowell Problem 1 Jackson 6.9 Discuss the conservation of energy and linear momentum for a macroscopic system of sources and electromagnetic fields in a uniform, isotropic medium described by a permittivity ε and a permeability μ . Show that in a straightforward calculation the energy density, Poynting vector, field-momentum density, and Maxwell stress tensor are given by the Minkowski expressions: u = 1 2 (ϵ E 2 +μ H 2 ) S = E × H g =μ ϵ E × H T ij =[ϵ E i E j +μ H i H j − 1 2 δ ij (ϵ E 2 +μ H 2 )] What modifications are made if ε and μ are functions of position? SOLUTION: As derived in class, the energy density and energy flow in linear, low-dispersion, low-loss materials are given by: u = 1 2 ( H ⋅ B + E ⋅ D ) and S = E × H For linear material, B = μ H and D = ε E so these become: u = 1 2 ( ϵ E 2 +μ H 2 ) and S = E × H The field-momentum density is given by: g = S...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

Homework14 - Homework 14 Answers 95.657 Fall 2011...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online