1.1 THE ELECTRIC CHARGE

Transcription

1 1.1 THE ELECTRIC CHARGE - In a dy day, one obseves "light spaks" when a wool pull is taken out o when the finges touch a metallic object. Aound the yea 1600, one classified these effects as electic phenomena. Also, one could obseve that an object that is electically neutal (does not poduce electic effects) may become electically active afte fiction with othe objects. Obsevations: Nomally, a glass od does not attact o epeal othe objects; but, afte ubbing a glass od to a fu (o silk), the od attacts electically neutal light objects. One says that, without fiction, the glass od is electically inactive and afte ubbing it becomes electified and electically active. The scientific eseach has shown that electic action is at the oigin of light, chemical eaction, nevous system function, mateial popieties,. Some mateials, known as magnetic mateials, do not need fiction to attact ion objects. As we will see in this couse, the oigin of magnetic behaviou is elated to electic phenomena. - Newton intoduced the gavitational mass "m" to quantify and measue the gavitational action of an object on othe objects. Similaly, one has intoduced the net electic chage "q o Q" to quantify and measue the electical action of an electically active object on othe objects. - Electostatics deals with the electic action of an chaged object at est. In the second pat of this couse, we will see that a chaged object in motion, besides the electical effects, pesents magnetic effects, too. - Expeiments showed that the same chaged object may attact o epel anothe chaged object. One has intoduced the sign of electic chage to explain its two opposite possible actions. Thee exist only two kind of chages; positive and negative. Two chages of the same sign (+/+ o -/-) epel each othe and two chages of diffeent sign (+/-) attact each othe. Fig1 (a- zeo net chage ) (b- same sign chage) (c- opposite sign chage) Exp: (a) Two neutal polystyene balls (b) A glass od is chaged by ubbing with silk. Then, the chaged od touches the two balls. (c) The od touches one ball and the silk the othe one. Comment: When ubbed, the glass od gets a positive chage and silk a negative chage. (This is a abitay labelling by Benjamin Fanklin). Next, when touching the balls, the od tansmits a pat of its chage to the polystyene balls. (b)as two balls get chaged with the same sign they epel each othe; (c) As one of balls gets negative chage fom the silk, the two balls get chaged with diffeent sign and attact each othe. 1

2 - The eseach about the amount of electic chage contained in objects evealed that: Electons and potons ae both electically chaged with the minimum amount of chage (elementay chage e) but the electon chage is negative and poton chage is positive (q ele. = - e; q pot. = + e ). The neutons have no electic chage ( q neuton = 0 ). A neutal atom contains equal numbe of electons and potons and consequently, a zeo net electic chage (Ex. He has [ p +neut] +el; its net. el. chage= [+e+0]+[-e]) = 0). A macoscopic object contains a huge numbe of atoms; so, it comes out that it contains a big numbe of elementay electic chages. An object that contains only neutal atoms is electically unchaged. Electically chaged atoms (o molecules) ae called ions. An atom (o molecule) that have lost one o seveal electons becomes a positively chaged ion; if it hosts additional electons it becomes negatively chaged ion. An object may contain ions but if its total chage is zeo it will be electically neutal. An object is electically chaged only if its total chage is unbalanced. When two neutal mateials but "electically diffeent " ( i.e. located fa to each othe in tiboelectic table ) get in touch to each othe, a small amount of electic chage is tansfeed fom one to the othe, even without fiction. If one ub them to each othe, the tansfe of electic chage is enhanced and the effects elated to the electic chage become visible. The same object may get the two kinds of chages depending on the othe object in contact. Ex: (a) glass od ubbed on silk --- glass od (+) and silk (-) (b) teflon od ubbed on silk --- teflon od (-) and silk (+) Note that a diect outcome of this conventional sign labelling chosen by B. Fanklin is the (-) sign of electon chage and (+) sign of chage of poton. Table #1 The tiboelectic effect table. Human hands (usually too moist, though) Acquies a positive chage + Rabbit Fu Glass Human hai Nylon Wool Fu (This list is adapted fom Natue's Electicity, by Chales K. Adams.) Lead Silk The tiboelectic effect is the tansfe of electic chages between two Aluminum diffeent neutal mateial bought into contact. Pape The elative position of two substances in the tiboelectic table tells Cotton what sign of chage they will get. Steel Glass ubbed by silk causes a chage tansfe such that they get chaged Wood glass +q and silk -q. Ambe The fathe is the sepaation in the table, the geate is the amount of the Had ubbe chage q tansfeed. Nickel, Coppe Bass, Silve Gold, Platinum Polyeste Styene (Styofoam) Saan Wap Polyuethane Polyethylene (like Scotch Tape) Polypopylene Vinyl (PVC) Silicon Teflon Acquies a negative chage -

3 1. THE QUANTITATIVE DEFINITION OF ELECTRIC CHARGE -The definition of mass unit (1kg) is based on a standad, which does not change with time. One would pefe to define the unit of electic chage in the same way but it is vey difficult to keep it constant in time because the electic chages leak easily. So, the electic chage unit is deived fom anothe quantity which can be measued with high pecision in any time; the cuent ate. The unit of electic chage is called Coulomb (C) and it is the amount of electic chage tansfeed duing 1 sec though the coss section of a conducto by a cuent with 1Ampee ate. This definition is based on the cuent definition: dq I (1) dt Note that 1C coesponds to a big amount of electic chage. Typically, the chage acquied by a body though ubbing is of ode ~ 10-8 C and lightning bolts tansfe aound 0C of electic chage. -As the minimum amount of chage is e, it is clea that any electical chage is a multiple of e. Milliken measued fo the fist time (1909 ) the chage of electon (basic amount e) and found that it is Remembe that ; q electon = -e ; q poton = +e ; q neuton = 0e 19 e 1.60*10 C () -The expeimental measuements have shown that: If a chaged object is pefectly isolated (no contact with wies o damp ai) its chage is conseved. Also, an isolated system containing seveal chaged objects conseves its total electic chage. Actually, the chage can be tansfeed fom one object to anothe inside the system, but the net chage of the whole isolated system does not change with time. Note that, the electic chage consevation law is equally valid in micoscopic wold. Ex: a) Chemical eaction: The system of two ions inside an electolytic solution (Na + and Cl - ) Befoe the chemical eaction (ions fa to each othe) and afte eaction (ions tightly bound togethe). If an inteaction between system pats (inside system) happens Na Cl NaCl(neutal) The total chage of system does not change: befoe (+e) + (-e) = 0C ; afte 0C b) Beta (β - ) adioactivity; One neuton is decomposed in a poton, an electon and an antineutino. n p e Total chage of system: befoe the event 0C : afte the event (+e) + (-e) + (0e) = 0C 1.3 CONDUCTORS AND INSULATORS -The following classification of mateials is based on the ability of electic chages to move though them. a) Insulatos; mateials whee the chage cannot move feely (ubbe, plastic, distillated wate,..) b) Semiconductos; essentially insulato mateials which conducting ability is inceased in a contolled manne by adding small amounts of impuities (cabon, siliceous, gemanium,..) that bing a esticted numbe of fee electic chages into main mateial. c) Conductos; mateial whee chages move almost feely (metals, ionic solutions, tap wate, human body, eath,.) d) Supeconductos; mateials whee the chage moves pefectly feely (special mateials) When electic chages ae tansfeed on a conducto, due to ecipocal electic epeal and the fee motion possibility, they ae distibuted instantaneously ove its entie suface. In the case of a pefect insulato the chages emain concentated aound the aea of contact with chaging object (fig ). 3

4 Fig. - The conductivity of a mateial depends on oute and loosely bound valence electons of its atoms. a) In the case of metals, the valence electons escape easily fom atom stuctues and pactically move feely though the metal volume. These fee electons ae at oigin of conductivity of metal. b) In case of insulato mateials, valence electons ae bound stongly and thee is no chage that can move easily though the mateial volume. c) The impuities in semiconducto mateials ae souces of fee electons and the amount of impuities decides about the numbe of available fee electons in semiconducto. d) A fluid (liquid o gas) may be a vey good insulato (if thee ae no ions inside it) o a good conducto (if thee ae fee ions inside it) but its conductivity is always lowe compaed to that of a metal because the ions ae less mobile that electons (due to much highe mass). Ex. (tap wate is a conducto of electicity because it contains fee ions, but the distilled wate is an insulato because it does not contain fee ions) - One may eliminate the excess chage of a conducto by gounding i.e. connecting it via a wie to the eath which is a conducto behaving as lage containe of chages. If the excess chage is - the gounding tansfes fee e- in excess to the eath; if the excess chage is + the gounding tansfes fee e- fom the eath to the object allowing the object to get a neutal (zeo) net chage. (Ex: lighting-ods) Note: The human body is a good conducto but its skin is an insulato which insulates petty well fo low values of electic fields. Note that the skin cannot insulate fo high values of field. 1.4 CHARGING BY INDUCTION - Due to the mobility of chages inside it, a conducting object can get polaization of chage by induction; that is without touching othe chaged objects. In fig.3, a negatively chaged plastic od will attact eithe end of an isolated neutal coope od. This happens because many of fee electons in the close end of coope od ae epelled by the negative chage of plastic od. Moving to the othe end of coope od, these electons leave the close end with unbalanced positive chage; consequently, the plastic od attacts this end. The same would happen when the plastic od is appoached to the othe end of coope od. Note that the total chage of coope od is still zeo but it has opposite chages induced at its ends. One says that the induction poduces a polaized chage in a neutal object o simply polaizes the object. Besides, by a middle cut of coope od, one can get two half ods chaged equally but with opposite sign. Fig. 3 4

5 Notes: a) In solid conductos, only the fee electons (-e) can move; the positive ions ae fixed to the cones of lattice aay cells. b) In the case of insulatos, the induction polaizes the chages inside each molecule because the electons cannot escape out of molecules. This does poduce a polaization of the object but it is much smalle compaed to that of conducto mateials. Also, one cannot poduce two chaged pieces by cutting a polaized insulato. - The electoscope is a device that makes use of on electic induction to detect the pesence of chage in an object without touching it (fig4.a). Also, one may use it to compae the sign of chage of two diffeent chaged objects (fig4.b/c afte touch to the fist object). Meanwhile, one cannot measue the magnitude of electic chage in an object by an electoscope. Fig COULOMB S LAW In 1785, Chales Coulomb discoveed by expeimental measuements the basic law of electostatics; i.e. the mathematical expession fo the inteaction foce between two point electical chages. The magnitude of electical foce exeted on each of two point chages (q, Q) at a distance is The vecto fom of Coulombs law is witten as follows q * Q F k (3) q * Q F F * k * (4) The unit vecto has no dimensions, has unit magnitude and is diected fom the chage that exets the foce to the chage on which the foce is applied. Q q F Fig.5 Q the souce of foce; q expeiences the foce; If Q&q have the same sign, the foce is epulsive. 5

6 One must include the signs fo q and Q in expession (4) to find the diection of the exeted foce F. If the two chages have the same sign, then F > 0 and thee is a epulsion foce; fo opposite signs F < 0 and thee is an attactive foce. Only the foce acting on chage q is shown in figue 5. The foce acting on chage Q is applied on Q, has the same magnitude but it is diected in opposite diection. 9 - The magnitude of electostatic constant "k" in SI system is k 9*10 Nm / C. In majoity of electicity 1 books this constant is expessed as k 1/ 40 whee C /( Nm ) is the electic pemittivity constant of vacuum and expession (3) appeas in the fom F 1 q * Q (5) 4 0 This substitution is widely used because it simplifies geatly the mathematical expession of all elations in electicity, especially in the theoy of electo magnetic fields (Maxwell s theoy). - It is inteesting to mention that Coulomb: a) Measued the electic foce by using a tosion balance (fig.6) b) Woked with elative values of electic chage. He used the fact that the chage on a metallic sphee (Q) is distibuted equally (Q/, Q/) afte touching it with anothe identical sphee. By this pocedue he could tansfe diffeent quantity of chage (Q/,Q/4,Q/8,..) on seveal sphees. Figue 6 - Impotant notes: a) In electostatics, all electical chages ae consideed to be at est. b) When an excess chage is given to a conducting sphee, the chage elements tent to go fa fom each othe because of the same sign epeal. Due to sphee symmety, the chage is unifomly distibuted ove the sphee suface. One may pove that: 1. the electic foce exeted on a point chage out a chaged sphee is the same as if the total chage of sphee wee located at its cente.. the electic foce exeted on a point chage placed somewhee inside the sphee is zeo. c) If the sepaation between two chaged objects is much bigge than thei dimensions one may apply the Coulomb s law as if they wee point chages, even if they have not a sphee fom. 6

7 d) One has poved expeimentally that Coulomb s law povides accuate esults fo electic foces at molecula and atomic level. It does descibe coectly the electic inteactions between electons and potons inside an atom, the contibution of electic foces on binding of atoms into a molecule and binding of molecules into a liquid o solid. THE SUPERPOSITION PRINCIPLE - If one electical chage q 1 is unde the electic action of N othe chages, the total foce exeted on q 1 is found by using the pinciple of linea supeposition (fig 7): F1 F1 F13.. F1 N... (6) Fig 7 The notation F ij means the foce exeted on point chage i by the point chage j. It is impotant to emind that in any situations (attaction o epulsion) the inteaction between two point chages obeys to the ecipocal elation (thid law of Newton). ( Example: Fo i=1 and j= F 1 F 1 ) F ij F ji (7) 7