# Chapter 4 Summary

# Concepts

- Maxwell’s equations are the fundamental tenets of electromagnetic theory.

- Under static conditions, Maxwell’s equations separate into two uncoupled pairs with one pair pertaining to electrostatics and the other to magnetostatics.

- Coulomb’s law provides an explicit expression for the electric field due to a specified charge distribution.

- Gauss’s law states that the total electric field flux through a closed surface is equal to the net charge enclosed by the surface.

- The electrostatic field E at a point is related to the electric potential V at that point by E=−∇V with V often being referenced to zero at infinity.

- Because most metals have conductivities on the order of 10 6 (S/m), they are treated in practice as perfect conductors. By the same token, insulators with conductivities smaller than 10−10 (S/m) often are treated as perfect dielectrics.

- Boundary conditions at the interface between two materials specify the relations between the normal and tangential components of D, E, and J in one of the materials to the corresponding components in the other.

- The capacitance of a two-conductor body and resistance of the medium between them can be computed from knowledge of the electric field in that medium.

- The electrostatic energy density stored in a dielectric medium is w e=1 2 ε E 2 (J/m 3).

- When a charge configuration exists above an infinite, perfectly conducting plane, the induced field E is the same as that due to the configuration itself and its image with the conducting plane removed.

# Mathematical and Physical Models

Maxwell’s Equations for Electrostatics

Mathematical and Physical Models Full Alternative Text
Current density J = ρ v u Poisson's equation∇2 V=−ρ v ε Laplace's equation∇2 V=0 Resistance R=−∫l E⋅d L∫S σ E⋅d s Boundary conditions Table 4-3 Capacitance C=∫S ε E⋅d s−∫l E⋅d L R C relation R C=ε σ Energy density w e=1 2 ε E 2 Electric Field Point charge E=R^q 4 π ε R 2 Many point charges E=1 4 π ε∑i=1 N q i(R−R i)|R−R i|3 Volume distribution E=1 4 π ε∫υ′R^′ρ v d υ′R′2 Surface distribution E=1 4 π ε∫S′R^′ρ s d s′R′2 Line distribution E=1 4 π ε∫l′R^′ρ l d l′R′2 Infinite sheet of charge E=z^ρ s 2 ε 0 Infinite line of charge E=D ε 0=r^D r ε 0=r^ρ l 2 π ε 0 r Dipole E=q d 4 π ε 0 R 3(R^ 2 cos θ+θ^sin θ)Relation to V E=−∇V

# Important Terms

Provide definitions or explain the meaning of the following terms:

- boundary conditions

- capacitance C

- charge density

- conductance G

- conduction current

- conductivity σ

- conductor

- conservative field

- constitutive parameters

- convection current

- Coulomb’s law

- current density J

- dielectric breakdown voltage V br

- dielectric material

- dielectric strength E d s

- dipole moment p

- electric dipole

- electric field intensity E

- electric flux density D

- electric potential V

- electric susceptibility χ e

- electron drift velocity u e

- electron mobility μ e

- electrostatic energy density w e

- electrostatic potential energy W e

- electrostatics

- equipotential

- Gaussian surface

- Gauss’s law

- hole drift velocity u h

- hole mobility μ h

- homogeneous material

- image method

- isotropic material

- Joule’s law

- Kirchhoff’s voltage law

- Laplace’s equation

- linear material

- Ohm’s law

- perfect conductor

- perfect dielectric

- permittivity ε

- Poisson’s equation

- polarization vector P

- relative permittivity ε r

- semiconductor

- static condition

- superconductor

- volume, surface, and line charge densities