Chapter 8 Electricity

á      Charge

á      Coulomb Force

á      Electric field

á      Electric potential (volt)

á      Voltage sources (potential difference, conductors)

á      Electric current

á      OhmŐs law

á      Circuits (series, parallel, diagrams, overloading)

á      Power

Chapter 9 Magnets

á      Poles N,S

á      Fields

á      Materials (iron, regions)

á      Currents  Magnets 

á      E  M (forces, meters, motors)

á      E  M  induction (FaradayŐs law: E field induced by changing B)

á      Generators, alternators

á      Power production

á      Tranformers

á      E  M  B field induced by changing E


Students are not required to know the details of MaxwellŐs equations or the general force law as shown in the following aside.

Aside  Fundamental structure of E&M

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits.

    Lorentz force

Formulation in terms of total charge and current, differential form



Differential form

Gauss's law

Gauss's law for magnetism

Maxwell–Faraday equation

(Faraday's law of induction)

Ampre's circuital law

(with Maxwell's correction)


Formulation in terms of total charge and current, integral form



Integral form

Gauss's law

Gauss's law for magnetism

Maxwell–Faraday equation

(Faraday's law of induction)

Ampre's circuital law

(with Maxwell's correction)




A qualitative understanding of each law is important and provided below.



Define the field in terms of the force experienced per unit source

General force law     Lorentz force.

For electric charge we can see the field is the force per unit charge.


GaussŐs law


There is a force between electric charges that satisfies CoulombŐs law (with the Lorentz Force)


GaussŐs law


Same for magnets (no fundamental monopoles)

Faraday equation

A changing magnetic field induces and electric field. A magnet pushed and pulled through a loop of wire drives a current around the loop. Since there are no monopoles there is no Ňmagnetic analog of currentÓ.  All N, S are ultimately created by moving electric charge so fundamental fields are generated ultimately by electric charge.

AmpereŐs law with displacement current.

-Currents produce magnetic fields

-Changing electric fields produce magnetic fields.


Field- Let us take the definition of the field and find the field at some points,



Postive point charge

Electric dipole field

Parallel plate capacitor (plates must be large compared to the gap)

Magnetic field of a wire (What field does an electric current generate § AmpereŐs Law

Magnetic field of a loop

Magnetic field of a coil



N-S dipole field

Several loop coil field

Electric charge moving in a circular path can produce a similar ŇexternalÓ field as that due to a N-S dipole.  So to build a actual bar magnet we can line up a set of small loops (atoms)

For a magnetic material you can align the atoms. These atoms need to have some overall rotating charge that can be considered as a loop.  The combined movement of all the electrons in an atom does not always create such a pattern but if it does then the atom possesses a magnetic dipole field. If you can line up these small dipoles there sum will be a large dipole (bar magnet).  Permanent magnets have these dipoles aligned without external fields.  The mechanism that keeps regions aligned to form permanent magnets is called ferromagnetism.

ASIDE (not important) ferro, dia, para are the three ways materials can behave magnetically. For ferromagnets, at short distances, the exchange interaction (Pauli exclusion) is much stronger than the dipole-dipole magnetic interaction. As a result, in a few materials, the ferromagnetic ones, nearby spins tend to align in the same direction. In simple terms, the electrons, which repel one another, can move "further apart" by aligning their spins, so the spins of these electrons tend to line up.


The plastic block with filings suspended in liquid provides a visualization of the field.


Energize a coil of wire we see that it behaves like a N-S bar magnet.  This demonstrates what the pictures above show.



Electric charges attract/repel they are the source of  electric fields.

N,S poles attract and repel and show a similar but different force, the magnetic force.

Moving charges create magnetic fields (attract and repel N, S poles) and are moved (pushed or pulled) by magnetic forces.

There are no fundamental N,S poles but the way moving charges behave they act almost in the same way that N,S poles behave. However the simplest configuration (loop) possesses 2 poles a N and a S pole.  If N,S are simply a manifestation of moving charge there will always be a N_S combination and there is no way to create an isolated effective N or S pole.

The fields E, B are also linked because a changing E or B produces a B or E.  This is easy to demonstrate for the case of changing B.

The complementary relation changing E creates B is critical to the nature of the fields but is not so easily demonstrated nor does it become essential when evaluating many applications. However it is critical to the understanding of light and how energy in the form of the E and B fields can move.  This explains how light reaches us from the sun and how cell phones can launch your messages to your colleagues.