Electromagnetic Fields and Waves: Notes, Solved Problems and Interactive Lab

3.4 Electrostatic Fields in Material Media

Matter answers an applied field with bound charges of its own: this section introduces polarisation, the flux density and the permittivity, the boundary conditions at interfaces, conductors and the image principle, the energy stored in the field and the capacitance of a pair of conductors.

17 solved examples and exercises6 interactive tools

In this section you will learn

how a material answers an applied field with bound charges of its own, and how the polarisation $P$ , the flux density $D = ε_{0} E + P$ and the permittivity $ε$ describe this answer,
the two boundary conditions ( $E_{τ}$ continuous, $D_{n}$ jumps by $ρ_{S}$ ) and how field lines bend at an interface,
why the field inside a conductor is zero, and what follows from it,
how to solve a problem with a conductor by the image method, and why the uniqueness theorem allows it,
how much energy an electrostatic field stores, and where it is stored, and
what capacitance is and how to compute it for any pair of conductors.

Look inside any electronic device and you will find matter between and around the charges: the ceramic of a capacitor, the plastic insulation of a cable, the glass of a window, the copper of the tracks. Until now (Sections 3.1 to 3.3) our charges lived in an empty universe. In this section we let matter in. We shall see that matter is not a passive spectator: it answers the field with charges of its own, and these charges change the field. A dielectric between two plates lets them hold more charge at the same voltage, and a metal surface pulls a nearby charge towards itself. All of this follows from a few simple ideas, which we develop step by step.

The plan is as follows. We first describe how a material reacts to a field (polarisation, bound charges, $D$ and $ε$ ). Then we find what happens where two materials meet (the boundary conditions), look at the special case of conductors, and learn a beautiful trick for solving problems with conductors (the image method). Finally we compute the energy stored in a field and define capacitance. Two applications, capacitor dielectrics and electrostatic energy storage, are placed right after the theory they use.

3.4 Electrostatic Fields in Material Media

Contents of Section 3.4

Problems · 1

Home exercises · 4

Further exercises · 10

Worked examples · 2