Electomagnetism PHYSICS 151 Notes fo Online Lectue #36 Thee ae fou fundamental foces in natue: 1) gavity ) weak nuclea 3) electomagnetic 4) stong nuclea The latte two opeate within the nucleus of an atom and we e not going to discuss them vey much. Gavity, we ve seen, opeates on eveything, although we ve applied it pimaily to macoscopic objects. You ve pobably head of both electicity and magnetism. These two phenomena ae elated vey closely they ae diffeent aspects of the same phenomenon. We goup them togethe and call the topic electomagnetism. This foce is significant at the level of an atom, so let s emind ouselves of what an atom looks like. Neutons potons electon Stuctue of the Nucleus. The atom is made up of a nucleus, which in tun is made up of potons and neutons. The potons have a chage of 1 we call them positive. Suounding the nucleus ae a numbe of electons usually the same numbe of electons as thee ae potons. Electons also have a chage, but they ae negatively chaged and cay a 1 chage. Neutons no chage Potons 1 Electons 1 If we have an atom like, say, Cabon which is numbe 6 on the peiodic table we know that thee ae 6 potons, 6 neutons and 6 electons. If we add up the chage that is caied by all of the atomic components, we find net chage = 6 (1)6(0)6(1) = 0 In othe wods, thee is no net chage on the atom. We call this a neutal atom. Some atoms like gabbing electons off othe atoms. Some atoms like giving up electons to othe atoms. Those of you with some chemisty backgound know that the electons fill up shells and that Chage Page 1
the electons left in the outemost shell ae called valence electons and can be donated to othe atoms o can eceive moe electons. In ou cabon atom, fo example, we have two electons in the 1s shell and fou in the 1 p shell. Let s say that the cabon inteacts with anothe atom and loses one of these oute electons. The net chage now is: 6(1)6(0)5(1) = 1 Anytime the net chage on an atom is nonzeo, we call it an ion. When we put atoms togethe to fom solids, the atoms all line up in a patten, but typically the whole atom is dawn as a dot. If we look a little deepe, we find that the nuclei stay petty much in one place, but that some electons ae fee to move all ove the mateial. Because the electons ae chaged, they will espond to extenal stimuli. In some cases, you can actually move these electons fom one place to anothe. Tansfeing Chage. o example, let s say that you shuffle you feet along the capeting. Initially, both the capeting and you feel ae neutal. As we ll see, things like to be neutal. ecognize that Chage is tansfeed fom the foot to the capeting, but no new chages ae ceated, no ae any destoyed. This is a consevation law, just like the consevation of othe quantities we ve studied, such as enegy o momentum. The same # of electons that ae ubbed off the foot appea on the capet. Note that I m dawing only a few chages in eality, a huge numbe of chages ae tansfeed about 10 10 chages at a time. NO NET CHARGE IS GAINED OR LOST As you shuffle along, thee is fiction between you foot and the capeting. The capet ubs electons off you foot and collects them. This leaves the capet with excess electons, thus giving it a net negative chage. You foot has lost electons, and it is thus positively chaged. Now and this is impotant you must # electons = # potons # electons = # potons # electons < # potons net positive chage # electons > # potons net negative chage Anothe ule that will become impotant to you, now that you e walking aound with a net positive chage is that Chage Page
THINGS DON T LIKE HAVING A NET CHARGE So somehow, you foot is going to have to attact some exta electons to make it neutal again. Thee ae two ways this can happen: 1) If it s humid, the wate in the ai can help neutalize unbalanced chages. Wate is what we call a pola molecule: The net chage on the wate molecule is zeo it is indeed a neutal molecule. Why then can it help neutalize chage? The answe is because of its pola chaacte. It tuns out that the electons like to hang out aound the oxygen atom moe than they like to hang out aound the H atoms. This gives the oxygen end of the molecule a negative chage and the hydogen ends a positive chage. The contact of wate vapo with you foot allows the chage to be caied away. This is the pefeed method fo idding you foot of excess chage. ) If, howeve, it is not humid, thee ae not sufficient wate molecules in the ai to take away excess chage. The chage has to get out some othe way. If you touch something metal with you foot, fo example, the diffeence in chage will be so lage that electons will jump fom the metal to you foot, giving you a shock. The type of electicity poduced by fiction is called static electicity. In you dye, clothes ub against each othe continuously. Dye sheets, like Bounce, contain lots of pola molecules to help keep the chage of you clothes neutal, thus avoiding static electicity. When you e thinking about the chages being tansfeed, emembe that it is the electons that ae tansfeed the nuclei stay in place and don t get tansfeed. A net positive chage means that thee is a lack of electons. A net negative chage means that thee is an excess of electons. Anothe good example of static electicity with which you e pobably familia is the electicity poduced when you ub a balloon on you hai. In this case, the electons fom the balloon ae attacted to you hai. Afte ubbing, you hai has a net negative chage and the balloon has a net positive chage. Attaction and Repulsion. You ll note that the balloon and the wall seem to attact each othe. This is an illustation of anothe fundamental popety of chaged things. attact If I ub a PVC od with a pape towel, electons leave the PVC and move onto the towel, so the PVC is left with a net positive chage. If I take anothe epel PVC od and do the same thing, both ods ae positively chaged. If I bing epel them nea each othe, they epel. A simila effect is found fo negative chages, which leads us to anothe fundamental popety of chages: LIKE CHARGES REPEL: UNLIKE CHARGES ATTRACT A comment hee that the assignment of the negative chage to electons is eally vey abitay Ben anklin decided on this convention and we ve stuck with it. Thee is no eason why we couldn t have gone the othe way and called the chage on an electon positive but we didn t. Chage Page 3
Going back to my example about shuffling you feet on the capeting and touching something metal. What would happen if you instead touched something wood? You won t get a shock, o at least, not much of one. This is because thee ae some big diffeences between diffeent types of mateials. Conductos and Insulatos. In metals, the electons ae not as tightly bound to the nuclei and they ae moe fee to move. If I have a chage on my finge and I bing it nea a metal dooknob, the electons ae attacted to the chages and move ove towad the finge: This is what allows the electons to jump onto the hand, poducing a shock. In an insulato such as wood, plastic, ubbe, etc. electons ae moe closely bound to the nucleus, so the electons can t move as easily. This esults in thee being less chages available fo neutalization. This is why wie is usually coppe (although silve actually conducts electicity bette, it is moe expensive) and has ubbe o plastic on it as an insulato. Thee ae also mateials that ae in between conductos and insulatos we call them semiconductos. Unde the ight conditions, they can conduct electicity, but not as well as metals. Conduction and Induction Now I want to addess the pocess by which things acquie chage. I m going to use ods to symbolize whateve objects we e looking at. Thee ae two diffeent ways to tansfe electons: 1) induction ) contact o conduction Chage Page 4
Let s say that I have a od I ve aleady chaged with positive chages. When I bing this od close to the neutal od, the electons in the neutal od will move towad the positive od end. This leaves a positive chage at the othe end of the od, whee the electons ae deficient. This pocess is called chaging by induction. The peviously neutal od is still neutal no chages have been tansfeed but thee is now a chage sepaation so that one end of the od is negative and the othe end is positive. Now let s bing the two ods in contact being in contact allows chages to actually move fom one od to the othe. The electons wee aleady ove by the end neaest the positive chage and they now jump ove to the positively chaged od. This leaves a lack of electons, which gives a positive chage to the second od. This is called chaging by conduction o contact. Induction Conduction You may have head the tem gound in conjunction with electicity. You also hea gound efeed to as Eath because a eal gound is often a long metal pipe stuck in the gound. The Eath is so massive that it acts like a souce o sink of electons. You can deposit o withdaw many electons and not change the oveall chage of the Eath. The thid pong you see on plugs is a gound it is thee because, if thee is a need fo the electons that ae being caied in the othe two wies to leave those wies, you want them to go somewhee othe than you body. The gound plug helps to funnel them safely away fom people. The electoscope is a device that can be used to tell if two things have the same o diffeent chages. (it consists of a metal electode attached to two pieces of foil. The contaption is usually placed in a glass bulb with a ubbe stoppe (why? both glass and ubbe ae good insulatos of electicity and isolate the system.) If you chage the electoscope with a known chage (say by touching it with a chaged od), you now have a known chage, let s say a negative one. You can then take you unknown chaged object and bing it nea. If the chage is the Chage Page 5
same as the one aleady on the equipment, the leaves move futhe apat. If it is diffeent, they will move close togethe. Now we want to quantify the inteaction between chages. A scientist named Coulomb (1750 s 1800 s) used a tosion balance to investigate inteactions between chages. By chaging a sphee and binging it nea one of the sphees on the tosion balance, a cetain deflection is obseved. To quantify this, though, you have to know how much chage is on the sphee. What Coulomb easoned is that if you chage up a sphee with some chage, then touch anothe conducting sphee, the chage will be split equally between them. Now you at least know the atio of the chage on the two sphees. By vaying the chage atio, he found that: If the chage on eithe of the sphees is doubled, the foce is doubled If the distance between the sphees is doubled, the foce deceases by a facto of fou. We abstact the balls as point chages an imaginay point that contains the same amount of chage as that on the ball. If one of the point chages has chage q 1 and the othe has q, and they ae sepaated by a distance, the foce between them is given by Coulomb s Law: q q = k If we wanted to, we could choose to wok in a system of units whee k = 1 (and some people do) howeve, in the SI system, we use the coulomb (C) as the unit fo chage, so that the constant k has the value k = 8.988 x 10 9 Nm /C, o appoximately 9 x 10 9 Nm /C One C is thus the amount of chage that, if placed on two objects a distance of 1 m apat, will cause each object to exet a foce of 9 x 10 9 N on each othe. Diection of the Coulomb oce: Remembe that foce is a vecto, so in addition to the magnitude, we also have to think about the diection. o two chages, the foce will always lie along the line connecting the two chages. If thee ae moe than two chages, we find the foce on a chage due to all of the othe chages by doing a vecto sum. Static electicity caused by fiction poduced about a micocoulomb o less of chage. How many electons is this? Chage on an Electon: The chage of an electon has been measued. It is a fundamental quantity and has the value 1.60 x 10 19 C but note that it is a negative numbe. We define 1 e = 1.60 x 10 19 C so that the chage on an electon is e. The chage on a poton is e. An inteesting consequence of this value is that chage only comes in these little packets. You can have a chage of e, e, 3e, 4e, etc. but you can t have 5/ e. In geneal, e is such a small numbe and we deal with so many electons at a time, that we don t notice that thee ae jumps; howeve, as electonics get smalle and smalle, this becomes a poblem as the stuctues that cay cuent Chage Page 6
(electons) get so small that they only let one electon pass though at a time and then you do see the effects of the quantization of chage. If q 1 > 0 and q > 0, then will be positive. This coesponds to the two chages tying to epel each othe. Note that the foce the two chages exet will be equal and opposite in all cases. The same situation applies when the two chages ae both positive. When the sign on the foce is positive, the foce is epulsive. If the two chages have opposite signs, the foce will be a negative numbe, which coesponds to attaction between them. We sometimes wite Coulomb s law slightly diffeently: q q = k 1 whee ε o is called the pemittivity of fee space. 1 k = 4πε ε o o 1 = 4πε o q 1 1 C = = 885. x10 1 4πk Nm q As usual, thee ae some estictions on this law it only woks when the sizes of the objects ae much smalle than the distance between them. Notation: We will use the notation ab to mean the foce on object a due to object b That woks fo two chages: what if thee ae moe? Ex. 1: A chage of 3 µc and a chage of 7 µc ae a distance of 0.5 m apat. Which of the following is tue: a) 1 is to the ight and 1 is to the ight b) 1 is to the left and 1 is to the left c) 1 is to the left and 1 is to the ight d) 1 is to the ight and 1 is to the left e) Since 1 = 1, the foces sum to zeo Chage Page 7
Ex. : A chage of 3 µc and a chage of 7 µc ae a distance of 0.5 m apat. ind 1 and 1 1 1 1 q1q = k = 9 ( 9x10 Nm ) =.76N C ( 3x10 C)( 7x10 ( 0.5m) C) 3µC 7µC 1 0.5 m The negative sign means that the foces ae attactive. If we daw the pictue as shown at left, the foce that 1 exets on ( 1 ) is to the left. The foce that exets on 1 ( 1 ) is of the same magnitude and to the ight. Ex. 3: A thid chage of magnitude 1 µc is placed 0.7 m to the left of the 3 µc chage and colinea with both chages. ind the total foce on each chage. 1 1 1 µc 3µC 7µC 3 1 0.7 m 0.5 m Hee, we ae going to be inteested only in the magnitudes of the Coulomb foce: the sign tells us the diection of the foce. We aleady have fom above that 1 = foce on 1 due to is 0.76 N to the ight 1 = foce on due to 1 is 0.76 N to the left Chage Page 8
13 13 13 q1q = k = 3 9 ( 9x10 Nm ) = 0.66N C ( 3x10 C)( 1x10 ( 0.7m) These two chages ae the same, so thei inteaction will cause 13 = foce on chage 1 due to chage 3 is 0.66 N to the ight 31 = foce on chage 3 due to chage 1 is 0.66 N to the left Now 3 3 3 q q = k = 3 9 ( 9x10 Nm ) = 0.53N C ( 7x10 ( 1.m) C)( 1x10 The sign is negative the foce hee is attactive. 3 = foce on chage due to chage 3 is 0.53 N to the left 3 = foce on chage 3 due to chage is 0.53 N to the ight In sum: 13 = foce on chage 1 due to chage 3 is 0.66 N to the ight 31 = foce on chage 3 due to chage 1 is 0.66 N to the left 3 = foce on chage due to chage 3 is 0.53 N to the left 3 = foce on chage 3 due to chage is 0.53 N to the ight 1 = foce on 1 due to is 0.76 N to the ight 1 = foce on due to 1 is 0.76 N to the left We now want to assign signs to these foces: let s take left to be negative 13 = 0.66 N 31 = 0.66 N 3 = 0.53 N 3 = 0.53 N 1 = 0.76 N 1 = 0.76 N C) C) The total foce on chage 1 is thus: Chage Page 9
on 1 = 1 13 = 0.76 N 0.66N = 1.4 N (to the ight) on is 1 3 = 0.76 N0.53 N = 1.9 N (to the left) on 3 = 31 3 = 0.66 N 0.53 N = 0.13 N (to the left) Ex. 4: One model of the hydogen atom (which has one poton and one electon) is called the Boh model. In this model, the electon obits the poton similaly to how the eath obits the sun. The distance between the poton and the electon is 5.3 x 10 11 m. What is the electostatic foce between the two paticles? ep ep ep q eq = k = p 9 ( 9x10 Nm ) = 4.3x10 C 18 ( 1.6x10 N 19 C)(1.6x10 11 ( 5.3x10 m) 19 C) Chage Page 10