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## Homework Statement

A dielectric material has the following properties:

electrical conductivity [tex]\sigma = 0 [/tex]

relative permittivity [tex]\epsilon_r = 3 [/tex]

relative permeability [tex]\mu_r =1 [/tex]

The electric field in the dielectric is given by

[tex] \mathbf{E} = E_0 cos(kz-\omega t)\hat{x} [/tex]

There are no time independent magnetic fields in the dielectric:

i) Write down maxwell's equation in matter in differential form

ii) find an expression for the polarization vector [tex] \mathbf{P} [/tex]

iii) find an expression for the volume density of bound charge

iv) find an expression for the volume density of free charge

v) find an expression for [tex] \frac{\parital \mathbf{E}}{\partial \mathbf{t}} [/tex]

iv) find an expression for [tex] \nabla \times \mathbf{E} [/tex], and hence deduce an expression for the magnetic field [tex] \mathbf{B} [/tex], in the dielectric.

vii) find [tex] \nabla . \mathbf{B} [/tex] and explain what this means physically

viii) What is the magnetization vector M in the dielectric?

ix) Find an expression for the phase speed [tex] \frac{\omega}{k} [/tex]

## Homework Equations

## The Attempt at a Solution

i) Maxwells equations in differential form (THOUGH i'm not sure what they are in matter???)

curl/divergence of both magnetic and electric fields:

[tex] \nabla . \mathbf{E} = \frac{\rho}{\epsilon_0} [/tex] gauss's law

[tex] \nabla . \mathbf{B} = 0 [/tex]

[tex] \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} [/tex] faraday's law

[tex] \nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}[/tex] maxwells fixed ampere's law

the question does say it wants the equations in matter,

so should I be using the auxhillary magnetic field and electric displacement field vectors H and D?

or would the equations in the form I gave be enough?

ii) (writing it up now)

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