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Basic Physics III Lecture 9

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Title Basic Physics III Lecture 9
Title of Series Basic Physics III
Part Number 9
Number of Parts 26
Author Smy, Michael
License CC Attribution - ShareAlike 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license.
DOI 10.5446/12945
Publisher University of California Irvine (UCI)
Release Date 2013
Language English

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So we will stop order and new chapter today perhaps the most A difficult chapter in the book some sense also 1 of the utmost importance area will start discussing an electromagnetic waves and before we talk about ways that we briefly discuss electric and magnetic fields
We have the observation that things like like charges electrical charges
Yuri have Wunsch obj Here we have another shot in the observation There's that there is a force are interacting between those 2 Chondrus so for example the ghost will charges can attract each other repel each other this is the attractive Case and there isn't action happens even where those A toe charges are quite a distance apart from each other and uh that seemed a rather mysterious to physicists and so they invented a new concept they imagined that Instead of Were faced with challenges Each other with some distance that there is a new entity called electric field and each charge surround themselves with Such an electric field and banned the interaction is actually an electric field at this point That Points in the same direction us Electric field and that then can simply write that electric field the charge time on Saudi forces Be Charged times The electric field so now we have no longer an interaction at a distance of about dozen interactional the child with the field charges Between themselves and of course a discharge also produces some electric field versus field from our a little fuel midfield from a big Q and This force he on the other Q. What times The electric field cup of originating from a from the other child so now we have no longer a spooky action over dissidents But we have those Fields or electric field this as a mediator actually tools such fields and electromagnetism and 1 is the electric field where the forces proportional with the charm and Then there's a magnetic field Bouvier force is proportional to the charge and the velocity of the charm of so-called Moran's force force there's the charge times fast product of velocity magnetic field so now we have those New entities electric and magnetic fields and they can represent them by field lines so for example a on the field Lions All for a of farmland magnetic field lines remote field lines mean simply indicates the direction of The field director Uh each point through the forces Our The force field is a vector also saw it as a vector a functional since position is also solo act if if he drops the electric fields around over on the charge in this manner news or little charged few of them
Their man We elect Eddie electric field lines radiate all that and depending on the size of the charm efforts of positive charge they go or what if it's a negative charge they go in this is the the case for so once redefining such a field lines which represents these electrical magnetic field we density over
Those few appliances actually related 2 were intends before you know how much how much force that would solar magnetic force there In the case of the bomb and this time around the polls or if you can actually go inside and is somewhat weaker If you go off perpendicular to the bomb But So we can also defined Something called the UK flux For example for the electric field if have some area and defined the normal vector of that Area that vector perpendicular will be the then defying the influx going so that area as We value of the electric field in this case I'm using electric fields dotted with this area vector or another works The size of the area times the size of the electric fields times the cosine of the angle of post will be made with huge so that These electric flux for the electric field and the Temple same thing
For these magnetic field the only difference differences we replace electric field lines the magnetic field lines and the definition is exactly the same so the question is what are those fluxes If these mumble field lines are sending actually varies as go across America So for example if I if I have a field where the line is sort of like this where in some area more that and so than others and I have a large area with
Burying their field strength Crossed Will be doing that Can't cases subdivided that area Many small area Although small area must be field will be approximately constant and demand we add up all the fluxes from those little pieces and that is
What is meant by an area into Rich symbolically it's been order by By this a former integral with little pieces of Of area DAT If we Electric field theories as functional position and then we we can still define electric shocks and that if the area is closed surface for example Or CEO or permit them drawn little circle around the symbol indicated that closed lot of them are 1 of these cases he wrote the surface doesn't uh wrapped around some the definition of electric flux and of course can Have a similar definition for the magnetic flux Ready for doses launched a magnetic fields theirs That if you have a closed surface This magnetic flux Always comes up to P Europe No matter what and that's a their Watts It was status as the reasoning behind it there on all of the charges And Why do you say that I will become clearer and more moment when I talk about electric flux equivalent because in the case of electric flux if you have a close surfers if you'd this be electric flux where you get The enclosed charges all the charges that are inside the volume of close divided by Messer said should be
A sort of Uh make this a visual in the case of you just have 1 charged will if I A CEO of a wrong wrong that Charles sphere has a radius Than I care can actually a calculated electric flux of you know all that these electric force But the electric force between 2 charges of a small Q and a Q there's 1 almost 4 times that of 1 0 of the product of the charges A divided by the radio scripts and combat Yukon crew would that Electric field electric fields A strength must simply be Cuomo ask rail 1 will for four-part 0 so if I choose a C O around Around the challenge this distance are from the charges the same for Points the same as year In this formula for another A moment where there which little piece of surface I chose a always get the same answer for amendment would be field and since the electric field is pointing out Everywhere and A almost a direction for office surface also point out what in and everywhere we can immediately right Be electric flux As the eat times for Pine fast grip And if it like map this formula for each of the 4 pi Cancels the radio script councils and The only thing that's left the fuel and the Epson so in this simple case Dulcis law holds a baguette about all the charges that are in an area located in the sphere And even tho it's harder to show just take my word for word if you have a charges of sent off this year it said it would still therefore if you go now back to the magnetic case the fact that This integral always comes up with Zero means And There are no magnetic charges charges don't exist In electromagnetism so let's not talk about something else You may remember that The way you generate magnetic fields It is that if you have a wife and A letter current overloaded that wife Excel wireless wrongs itself with a circular magnetic field now Maxwell on That issue interrupt this and for the parallel slate capacitors For example this man initially you get some current are charging up capacity which after a while stopped but while you get this current you ought to produce A magnetic field just like for the wire and that is true even in between Who plays and call that to a displacement sell it is sort of Annan allergies and we have our current he'll making a magnetic field even those that are the physical current is interrupted should still get the circular circular magnetic field but what does it mean if charge up the capacitor What it means is if we charge the capacitor A glance at this site becomes positive this Becomes negative demanded electric field Between the 2 plates of the capacitor this is generated so we have a changing electric field between those 2 plates of the capacity therefore The displacement current is basically a changing electric field so Sowerby ever-changing electric field that surrounds itself The circular magnetic field that is summed up in an amputee law now have dropped the wire and the capacity moving charges or if he had changing electric fields we generate a circular magnetic field around And that is called on long and symbolically to write again this funny symbol Magnetic fields are Parliament daughter half women equals enclosed current plus some constant times a electric not talk about this If you look at Some close Then We can define a small piece of that And we can define a vector which points Along the path for its tangential and now we can just like what we did with electric magnetic flux weekend actually Formed the dot product of the magnetic field With this path Parliament he now and then he's every some some over the entire park and of course if the magnetic field is constant among the cast member we can simply say that this is A B times the the total path length Times of a really the average angle but if said if the magnetic field changes riders Before that New Hanover be started The PLO and performance and if this is a closed tasks like a drop wrong he then indicate that With a little circle wrong Otherwise it Said it could be any old time if it's a closed pass that it also defines an area in between and we can you was that area to defy a toe define the electric flux passing through that And so let us what
That means Reform the electric corresponding electric all of this Grow And the time derivative off That gives them the contribution from the and also any physical current passing through would also give the the country in this case As a symbol mean some closed part there's also parodies law which is universal Amperes law Basically what it means is that changing magnetic field makes a circular electric field and you'll probably encounter that before because this is nothing else But Induction of induced voltage that That's what it means you produce amid an electric field from what changing magnetic field that is called Faraday's law and we can arrive in the same form this and the only differences Such constancy and there's a minus sign and at this time is missing And that is because since no armored medic charges they also normally currents of such charges all of these things sewn together are called Maxwell's Equation So if you have long magnetic field and for electric field and then And his law days then those former together we uniform next And Electric and magnetic fluxes that And armpits and us open surfaces Bounded by close Pumps And the equations Look symmetric but there are no magnetic currency and Normal medic someday asymmetry Maxwell will end The good news is you actually don't need to know how to exactly who the Maxwell equations as long as still remember that the changing electric field makes a circular magnetic field and vice-versa meaning that a changing magnetic field makes a circular electric field so let's not look That
A similar case the capacity only this Kayseri just Connectors about when antenna antenna is basically just a straight loss and they're connected and positive about child was rolled out appeal and negative charges for alike as indicated in the picture below and therefore We make an electric field was goes from the positive charges the negative charges on books on all sides of the wife and because we have the displacement current why this is happening we also have a magnetic field that surrounds the wife of 1 what these little symbols mean those of us opposed Depict Also was back The have This is to so magnetic fields coming out of the plane like this loop around and then go back on on the other side and that is because of the displacement since all of those fields are changing may have merit Changing electric fields which make it turned our changing magnetic fields which then dent electric bills and so on and actually feel separated from the antenna and The move space we can actually do this as an experiment so I wanna have healer sitting on the table is uh microwave And a microwave receiver And The strength Of the microwave Received is shown But can but Dialog he should be able to see a A little black lying close to 100 And Michael ways or elect degrees So we have a transmission electron wounded warriors from this But And will sort of demonstrated that I can send waves somewhere else believes the caution of called this if a if I send them somewhere else this There's normal signal signal ghost And ASIA debate a receiver then we see This signal more can interrupt such digital vote Pretty much understood So a piece of paper with them the same piece of metal for of medal will actually stop it and the reason is because It's sorting out the electric field so when you have the circle electric field it's it's induction and the voltages shoulder by currents flowing matter if I have a lot of sick a piece of metal that is Small enzyme than most of These electromagnetic waves will be interrupted because they'll waves they actually floor on the obstacle But the waves and a little bit remains so the way we can imagine we waived Propagation happening on 10 his like this so this is exactly what would be discussed
Before we have a metal aren't the only differences I'm not connecting it anymore toward static a battery constant voltage But what changing vault So alternating lead the top will be positively charged and negative charm and what USC get rid of the ball Green Arrow those are the electric field vectors and what is indicated by the EU and green and red Area its media magnetic Molson magnetic solves and that and you see that generate an alternating electromagnetic waves Magnetic field is a circular surrounding an otherwise and then traveling out space and The electric field sort of Performs a little lower Which outgoing mostly India could equatorial plane but also a little bit The polls show if you connect and AC source form antenna he actually leader electromagnetic waves and media buyer antenna the structures were a complex funny looking loops for electric field and also the magnetic field its field strength Has a funny became But if you look far away After the hosts Field Separate themselves from the antenna trouble out Then things get a little bit easier and they opened some rules 1st of all you find that Electric And magnetic fields On perpendicular to each other and their perpendicular to the direction of wave So in other words electromagnetic waves of France was waves but are transfer laced with 4 kinds of displacement in an electric field and magnetic then if we go even further away eventually the curvature of Those of us who was straight out and we have our plane so this is the picture are sold at the beginning our plane electromagnetic wave looks like and assume that the plane wave Travels Plus extra rich and we also assumes the electric field is pointing and a plus or minus y direction the magnetic field is finding the parcel And this is actually a scientist audio plainly see from some sort of British of electric field as I said before and the far field electric and magnetic fields are perpendicular to and Show the propagation direction And we can use our right hand will to get her propagation direction you is that we are pointing fingers and the middle finger for the electric and magnetic field we found pointing in the direction of motion for an electric grid and we can describe this mathematically E. the these white component of the electric Field rector by tool Not times assigned KX minds on the team and busy component of the magnetic field It's not time signed KX my and both electric field and magnetic field on phase Used No additional angle Um between most of those to call home We can now look A Feira days lawful this electromagnetic waves and featureless particularly convenient cast which was this half-year that goes Along the direction propagation but just a small distance He X and then it goes in the white direction goes back an X and then goes back As In line And what that means for this Open to grow The electric field disappointing along Dollar against the so I really get kind of the same thing but with a plus sign he and a minus sign here and of course this is the electric field a slightly different positions for another works Look at will get me why component at position X plus DX and time minus a white component Position next time And then be multiplied by a length Of this part of the Delta wine for both be up and down part of the book and you know all this must be the time derivative of the magnetic flux going and But for that we need be area of this The area simply X times Dr. wine and banned and this doesn't change with time so the only thing that changes the magnetic field so this time derivative is simply derivative of the using Component we get from Curtis law that this peace must be equal to about 10 however what is just B EX times the spatial derivative of the white but basically the definition of the word Therefore if you look at this Equals that noticed that the DX cancels And I'm just left with this piece and we can now plug-in our work EYE and easy and get Uh assigned functions become cosine functions for the spatial derivative getaway And for the time derivative again angular frequency and the call sign in this equation cancels and we can relate electric and magnetic field amplitude On a goal Paid which is the velocity of delectable or can simply saving the cosine and that The entire ratio of The tow fields he wire would be be easy is the same as the ratio of armored OK way Do the same thing with all onto a small band Chose a similar looking only this time the scope in the plane of the magnetic field rather than face electric because amperes law has those additional Constance and get this Additional concert and their corresponding wage And Are damaged garden where they function for electric field member get a similar relations which relates Abbott told of the medical aid and electric And Get additional constant in him and orders that this ratio is opposite the water before we multiplied both And the easier the easy or cancels out just 1 on the left hand side and on the right hand side figured you will not That is not at times these For another words we have our relations between the No. 1 of magnetic and constant An the electric constant and the velocity square off The way or another These which is Buffalo electric rates typically called square just 1 of you not at finale plugging the numberless formula not of not new for pi times 10 to the minus 7 test data and epsilon not this 8 . 8 5 times 10 to the minus 12 square meters Korea regarding those numbers we get an interesting result this is sweet times 10 to the 8 meters and that Ms. Lee value for the speed of light So the great triumph of 19th century physics of finding equations That govern both Electricity and magnetism and also you will find
The optics 110 actually shall I'm not going to our home and you that The electric fields All 3 components as well as all 3 components of the magnetic fields separately satisfy awaited with seas with waves and zooms sees gray areas Also the speed of light which means that light troubles at the same velocity as seems natural to assume that light is an electromagnetic as it happens Light is actually a small A a small portion of the year an electromagnetic waves spectrum so this is the entire range of electromagnetic waves as far as we have explored at hand A visible light just this tiny little portions and this is a logarithmic scale and frequency and this is a logarithmic scale in weight over a tiny portion between 400 not only And 700 mountain is actually visible 12 And each portion of That spectrum and has a different name for example and this is the domain of radio waves this of microwaves and microwaves The system for example Then I have infrared radiation than the visible spectrum ultraviolet X-rays And finally Belmont will illustrate that That's finished with the a small example so let's calculate the wavelength of
A over 60 hertz electromagnetic feed and 93 . 3 megahertz Frequency modulated radio CEO 1 . 6 7 times 10 to the 15 hurts Heat radiation that can be detected by by a rattlesnake for a then media at a wavelength of My laser pointer riches a frequency of 6 . 7 4 times 10 of the 14 of them want Punto times 10 to the 19 medical X-ray and finally 1 . 5 times 10 20 1 hurts Look you down The way we solve this problem As usual the wavelength times frequency equals the Which is the speed of light Times 8 from an as the 2nd toward those who take times 10 the 8 meters per 2nd and divided for example the 60 votes for part AT and together wavelength of 5 thousand kilometers this is roughly half the size of long wait for the yeah FM radio waves to divide By 93 points they megahertz 193 . 3 times 10 The 6 and this Give the wavelength of 3 . 2 2 meters sold roughly twice my height Then that for me Peter radiation Snakes are able to detect when go hunting for mammals In this Paisley divided by 1 . 6 7 times 10 of 13 and that gives us a wavelength of 18 and Michael so weary a tiny wavelength Michael leaders 1 thousands of willing which is 1 thousand or so and next hair my laser pointer and a fire truck in 6 . 7 4 times 10 of the 14 then I get an even smaller number for the wavelength 445 and not only needles and not only does want thousands of miles from my if you go to air their medical X-rays we divided by 1 . 2 times 10 19 hurts and begets at 25 people The pickle meters 1 thousand Course not only There are getting very small actually smaller than the size of an unhappy and finally a year no clear the 1 . 5 times since the 21 votes that gives us Sure And Tomiko firmly and 1 cm 1 thousands of people and the size of a phone book Lewis This aboard 1 So this is 400 times the the size of the Berbers small and Actually Now don't stop with that frequency can go several orders of magnitude highest electromagnetic Range of frequencies and wavelength is Jerry lot so our with that
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