Bringing It All TogetherBringing It All Together

This WeekThis Week

Today-Today-– No Clickers – sell them back to the bookstore No Clickers – sell them back to the bookstore

unless you are planning to take my section of unless you are planning to take my section of the course next semester. Bad idea!the course next semester. Bad idea!

– We tie the stuff together and do the candle We tie the stuff together and do the candle trick right in front of you. (Remember the trick right in front of you. (Remember the video??)video??)

The rest of the week: FINAL EXAMSThe rest of the week: FINAL EXAMS

My scheduleMy schedule

Tuesday – Not on CampusTuesday – Not on Campus

Wednesday – FridayWednesday – Friday– Giving examsGiving exams– Grading PapersGrading Papers– In foul mood! Stop by if you need to.In foul mood! Stop by if you need to.

Grades will be completed as fast as I can.Grades will be completed as fast as I can.– Grader has finals this week to, so it may be a Grader has finals this week to, so it may be a

slow process.slow process.

The Last LectureThe Last LectureCovering 5 Additional ChaptersCovering 5 Additional Chapters

We have been looking at the properties of We have been looking at the properties of Electric Fields.Electric Fields.

We have been looking at the properties of We have been looking at the properties of Magnetic FieldsMagnetic Fields

We looked at a few situations where there was We looked at a few situations where there was some kind of connection between the two.some kind of connection between the two.

We saw that ALL of what we discussed could be We saw that ALL of what we discussed could be explained by one set of equations.explained by one set of equations.– MAXWELL’s EquationsMAXWELL’s Equations

James Clerk MaxwellJames Clerk Maxwell

1831 – 18791831 – 1879Scottish physicistScottish physicistProvided a mathematical Provided a mathematical theory that showed a theory that showed a close relationship close relationship between all electric and between all electric and magnetic phenomenamagnetic phenomenaHis equations predict the His equations predict the existence of existence of electromagnetic waves electromagnetic waves that propagate through that propagate through spacespace

SMART DUDE

Almost MaxwellAlmost Maxwell

Gauss

Faraday

Ampere

Bindell

E&B Together Problem

Remember the Lowly Capacitor?Remember the Lowly Capacitor?

AC Current=I

Id 0 sB ???0 sB d

AmpAmpère’s Law is used to analyze magnetic ère’s Law is used to analyze magnetic fields created by currents:fields created by currents:

But this form is valid only if any electric But this form is valid only if any electric fields present are constant in timefields present are constant in time

Maxwell modified the equation to include Maxwell modified the equation to include time-varying electric fieldstime-varying electric fields

Maxwell’s modification was to add a termMaxwell’s modification was to add a term

od μ IB s

Maxwell Fixed the Problem!Maxwell Fixed the Problem!

The additional term included a factor called the The additional term included a factor called the displacement currentdisplacement current, I, Idd

This term was then added to AmpThis term was then added to Ampère’s Lawère’s Law– Now sometimes called Ampère-Maxwell LawNow sometimes called Ampère-Maxwell Law

This showed that magnetic fields are produced both This showed that magnetic fields are produced both by conduction currents and by time-varying electric by conduction currents and by time-varying electric fieldsfields

Ed o

dI ε

dt

MAXWELL’S EQUATIONSMAXWELL’S EQUATIONS

VacuumVacuum

There ain’t nuttin there.There ain’t nuttin there.– No ChargesNo Charges– No CurrentsNo Currents– Can there be electric or magnetic fields Can there be electric or magnetic fields

present??present??

Maxwell’s equations say YESMaxwell’s equations say YES– And they add some serious requirements to And they add some serious requirements to

what is there.what is there.

Sorry it’s crooked!

PropagationDirection

Back to MaxwellBack to Maxwell

E & M fields can propagate from a region E & M fields can propagate from a region where there are charges/currents to where there are charges/currents to regions far away where they do not regions far away where they do not contain these sources.contain these sources.

The fields propagate as WAVESThe fields propagate as WAVES– Shape moves at the speed of the wave.Shape moves at the speed of the wave.– Because the E field is changing (moving Because the E field is changing (moving

charge example), there will be a B field there charge example), there will be a B field there as well.as well.

Enter:Enter:Heinrich Rudolf HertzHeinrich Rudolf Hertz1857 – 18941857 – 1894German physicistGerman physicistFirst to generate and First to generate and detect electromagnetic detect electromagnetic waves in a laboratory waves in a laboratory settingsettingThe most important The most important discoveries were in discoveries were in 18871887He also showed other He also showed other wave aspects of lightwave aspects of light

Hertz Hertz ExperimentExperiment

So far we can assume:So far we can assume:

Extended View – Sine ShapeExtended View – Sine Shape

The Magic From M’s 4The Magic From M’s 4

Mathematically these equations describe Mathematically these equations describe waves traveling thought space.waves traveling thought space.E and B are perpendicular to each other E and B are perpendicular to each other and to the direction of propagation.and to the direction of propagation.The velocity of the wave must beThe velocity of the wave must be

2 2 2 2

2 2 2 2o o o o

E E B Bμ ε and μ ε

x t x t

1

o o

v cμ ε

The Velocity is “c:The Velocity is “c:

This must describe light waves …..This must describe light waves …..

It can be shown that the wave It can be shown that the wave carries carries energyenergy and momentum, and momentum,

How??How??