# Chapter 6 Summary

# Concepts

- Faraday’s law states that a voltage is induced across the terminals of a loop if the magnetic flux linking its surface changes with time.

- In an ideal transformer, the ratios of the primary to secondary voltages, currents, and impedances are governed by the turns ratio.

- Displacement current accounts for the “apparent” flow of charges through a dielectric. In reality, charges of opposite polarity accumulate along the two ends of a dielectric, giving the appearance of current flow through it.

- Boundary conditions for the electromagnetic fields at the interface between two different media are the same for both static and dynamic conditions.

- The charge continuity equation is a mathematical statement of the law of conservation of electric charge.

- Excess charges in the interior of a good conductor dissipate very quickly; through a rearrangement process, the excess charge is transferred to the surface of the conductor.

- In the dynamic case, the electric field E is related to both the scalar electric potential V and the magnetic vector potential A.

- The retarded scalar and vector potentials at a given observation point take into account the finite time required for propagation between their sources, the charge and current distributions, and the location of the observation point.

# Mathematical and Physical Models

Faraday′s Law

V e m f=−d Φ d t=−d d t∫S B⋅d s=V e m f t r+V e m f m

Transformer

V emf tr=−N∫S∂B∂t⋅d s (N loops)

Motional

V e m f m=∮C(u×B)⋅d l

Charge–CurrentContinuity

∇⋅J=−∂ρ v∂t

EM Potentials

E=−∇V−∂A∂t B=∇×A

Current Density

Conduction

J c=σ E

Displacement

J d=∂D∂t

Conductor Charge Dissipation

ρ v(t)=ρ v o e−(σ/ε)t=ρ v o e−t/τ r

# Important Terms

Provide definitions or explain the meaning of the following terms:

- charge continuity equation

- charge dissipation

- displacement current I d

- electromagnetic induction

- electromotive force V e m f

- Faraday’s law

- Kirchhoff’s current law

- Lenz’s law

- motional emf V e m f m

- relaxation time constant

- retarded potential

- transformer emf V e m f t r

- wavenumber k