Foces of Natue Electic Chages, Foces and Fields Chapte 17 Electic Chage Coulomb s Law Electic Field Electic Field Lines Flux of an Electic Field Physics 111: Analysis of motion - 3 key ideas Pat 1 Foces of natue o A shot jouney back to Physics 111 Newton s laws of motion Consevation of Enegy Consevation of Momentum 4 Newton s laws of motion Newton s Fist Law: If no foce acts on a body, then the body s velocity cannot change Newton s laws of motion (applications) Special case: motion with constant acceleation (1D, D o 3D motion) Newton s Second Law: F = ma Newton s laws of motion allow us to analyze many kinds of motion. F = ma at x = x + vt + v = v + at Obsevables: time foce position velocity acceleation 5 Examples of poblems: pojectile motion, 6 1
Consevation of enegy The total enegy of an isolated system cannot change In an isolated system whee only consevative foces cause enegy changes, the kinetic enegy and potential enegy can change, but thei sum cannot change K + U = K + U i i f f 7 Consevation of momentum Consevation of linea momentum If no net extenal foce acts on a system of paticles, the total linea momentum of the system cannot change P = m v + m v +... + m v 1 1 n n = const Consevation of angula momentum If the net extenal toque acting on a system is zeo, the angula momentum of the system emains constant, no matte what changes take place within the system L i = L f 8 What foces do we know fom ou expeience and Physics 111 Thee ae ONLY fou fundamental foces of natue Gavitational Foce Fictional Foce Sping Foce (Hook s Law) Nomal Foce Tension foce in a sting Aeodynamic Dag Foce 9 1 FOUR o ONE Many scientists think that all fou of the fundamental foces ae, the manifestations of a single foce which has yet to be discoveed. Gavitational and electo-magnetic foces: this what we expeience!!! Fictional foce, sping foce, nomal foce, tension foce in a sting, aeodynamic foce ae esults of electomagnetic foce Just as electicity, magnetism, and the weak foce wee unified into the electoweak inteaction, they wok to unify all of the fundamental foces. 11 1
Electic chage Pat Electic Chage Electic Chage is an intinsic chaacteistic of the fundamental paticles making up objects aound us (including us). The odinay matte consists of thee (only!) paticles: electon (e) poton (p) neuton (n) mass 9.11 1-31 kg 1.67 1-7 kg 1.67 1-7 kg chage -1.6 1-19 C 1.6 1-19 C. The SI unit of electic chage is the Coulomb 14 Impotant chaacteistic of electic chage An electic chage has a magnitude and sign. It is eithe positive o negative. Electon has negative electic chage Poton has positive electic chage Atoms and molecules ae made up fom electons, potons and neutons! A classical (sola system) model of an atom (Lithium) A quantum model of an atom (Lithium) If the chages have the same sign, the foces between them ae epulsive Chages of opposite sign Atoms ae combinations of equal amounts of electons and potons. expeience attactive foces15 16 Sizes and masses Atoms ae combinations of equal amounts of electons and potons. The neutons povide the glue to stick togethe the potons in the nucleus. The poton and the neuton ae about times heavie than the electon, so the vast majoity of an atom s mass esides in the nucleus. Atoms ae mostly empty. We live in almost empty space Net electic chage fo a system of n paticles net = q1 + q + q3 + Kq n The total (net) electic chage of an isolated system is conseved. The only way to change it is to add o emove chaged paticles. Example: tennis ball and a gain of sand 17 18 q The total electic chage of the univese is constant. the net electic chage of atoms and molecules is zeo (equal amounts of electons and potons) emoving an electon fom a neutal atom ceates a positive ion negative ions 3
Example: 19 Maco objects (many atoms o molecules) To make an unchaged object have a negative chage we must: A) add some atoms B) add some potons C) add some electons D) add some neutons E) wite down a negative sign Mateials two exteme models Insulatos a mateial in which chages do not move feely though the inteio of the sample. Examples: Glass, wood, ubbe, plastics, stone, bick, etc Conductos mateial whee fee chages can move though the mateial. Examples: Ionized gases (plasmas), metals, ionic solutions if salts in wate Semi-conductos a mateial intemediate between the two exteme models GaAs, Ge, Si, ae the classic examples. 1 Maco objects can be chaged by chage tansfe o chage sepaation Chage tansfe happens when electic chages (usually electons) tansfe fom one object to anothe Chage sepaation occus when two mateial ae ubbed togethe o when objects collide Chage is quantized Expeiments show that any positive o negative chage q that can be detected can be witten as q = n e, n = ± 1, ±, ± 3, K e = 1.6 1 19 C whee e is the elementay chage. 3 4 4
fom a simple to complex Univese human beings cells condense matte, gases molecules atoms Note: ALL electons ae identical, as well as potons, neutons Pat 3 A foce between chages electons, potons, neutons fundamental paticles: electons, quaks, 5 Coulomb s Law The electostatic foce between two chages q 1 and q sepaated by a distance has the magnitude q F = k 1 q 1 9 k = = 8.99 1 N m /C 4 πε k is the electomagnetic constant ε is the pemittivity constant The diagam shows two pais of heavily chaged plastic cubes. Cubes 1 and attact each othe and so do cubes 1 and 3. Which of the following illustates the foces of on 3 and 3 on Whee is the 3 d Newton s law 7 8 Compaing the gavitational and electostatic foces Let s calculate the atio of the electical to the gavitational foce inside a hydogen atoms. GM pm e keq pqe Fg =, F e = R kqq e p e Fe kqq e p e = = F GM g pm e GM pm e 9 19 Fe (9 1 )(1.6 1 ) = 11 7 31 Fg (6.67 1 )(1.67 1 )(9.11 1 ) 39 =.7 1 So we can foget gavity as compaed to electostatic A contadiction to a simple obsevation If F e /F Gl =.7 1 39 then, why the gavity foce plays any obsevable ole The foce of gavity play essentially NO ole in atomic and molecula systems Howeve macoscopic objects ae neutal o almost neutal (the net electic chage is close to zeo) Theefoe the foce of gavity play stong ole fo macoscopic objects foces at least on the atomic scale 9 3 5
An example with two coins Let s find an electostatic foce between two coins sepaated by a distance of 1 mete a) foce between electons b) foce between electons in the two coins c) the net foce between electons and potons in the two coins about 5 millions!!! q q F = k 1 9 k = 8.99 1 N m /C -19 e = 1.6 1 C N 1 electons coin.3*1-8 N.3*1 16 N. N 31 Coulomb s law and the pinciple of supeposition The pinciple of supeposition: the net effect is the sum of the individual effects Fo n inteacting paticles the net foce on paticle 1 can be witten as = F + F + F + K F1, net 1 13 14 F1 n being pactical see chapte 3 Vectos in Physics (adding vectos using components) 3 Net Foce and the supeposition pinciple Net Foce Chages Q, Q, and q ae placed at the vetices of an equilateal tiangle as shown. The total foce exeted on the chage q is: A) towad chage Q B) towad chage Q C) away fom chage Q D) at ight angles to the line joining Q and Q E) paallel to the line joining Q and Q Two point chages ae aanged as shown, whee Q 1 = -C, Q = 1C. In which egion could a thid chage +1 C be placed so that the net electostatic foce on it is zeo A) I only B) I and II only C) III only D) I and III only E) II only Always daw a fee body diagam! What if the thid chage is q=-1c What if the paticles have chages Q and -Q 33 What if the paticles have chages Q and Q 34 Net Foce Net Foce Conside the thee electic chages shown in the figue. List the chages in ode of the magnitude of the foce they expeience, stating with the smallest (Note: the distance fom A to B is the same as the distance fom B to C.) Fou identical point chages ae placed at the cones of a squae. A fifth point chage placed at the cente of the squae expeiences zeo net foce. Is this a stable equilibium fo the fifth chage good to use PhET compute simulation as an illustation 35 36 6
Example: 3 electic chages in a line poblem poblem Given that q = +1 mc and d = 16 cm, (a) find the diection and magnitude of the net electostatic foce exeted on the point chage q in Figue below (b) How would you answes to pat (a) change if the distance d wee tipled F blue F ed 1 3.q.q 9 3.q.q = = 9 1 4πε d d 1 1.q.q 9 1.q.q = = 9 1 4πε d d F 3.q.q 1.q.q = 9 1 to the ight d d 9 esultant 37 38 poblem A tale of two paticles poblem An electon and a poton ae eleased fom est in space, fa fom any othe object. The paticles move towad each othe, due to thei mutual attaction. When they meet, is the kinetic enegy of the electon geate than, less than, o the same as the kinetic enegy of the poton Explain. 39 4 A couple simple questions Pat 4 Electic Field The Coulomb law q q F = k 1 How does q 1 know of the pesence of q Since the chages do not touch, how can q 1 exet a foce on q Action on a distance! Othe examples 4 7
Electic Fields o Action on a Distance We can say that q 1 sets up an electic field in the space suounding it. 1. At any given point P in that space the field has both magnitude and diection.. The magnitude depends on the magnitude of q 1 and the distance between P and q 1. 3. The diection depends on the diection fom q 1 to P and the electical sign of q 1. 4. Thus when we place q at P, q 1 inteacts with q 43 though the electic field at P. The electic field is a vecto field The electic field consists of a distibution of vectos, one fo each point in the egion aound a chaged object. A way to define the electic field at some point P 1. Place a positive chage q, called a test chage, at the point P. Measue the electostatic foce F that acts on the test chage 3. Define the electic field at the point P due to the chaged object as F E = q The SI unit fo the electic field is 44 the newton pe coulomb (N/C) A paticle in an electic field The electic field due to a point electic chage 1. If we know the electic field vecto at a given point, the foce that a chage q expeiences at that point is F = qe. The diection of the foce: positive paticles in the diection of the field negative paticles in the opposite diection of the field F F + E 45 Fom Coulomb s law, the magnitude of the electostatic foce acting on q is q q 1 q q F = k = 4πε The diection of the foce is diectly away fom the point chage if q is positive, and diectly towad the point chage is q is negative. Then the magnitude of the electic field fom a point chage is q 1 q E = k = 4πε 46 Example Electic field aound a positive electic chage The electic field due to moe than one point electic chage Using the supeposition pinciple we can find the net foce F, net = F1 + F + F3 + KF n Theefoe the net electic field at the position of the test chage is F, net F1 F F3 F n E = = + + + K q q q q q E = E 1 + E + E 3 + KE n 47 48 8
Net Field A poton p and an electon e ae on the x axis. Find the diections of the electic field at points 1,, and 3 espectively Conside two identical negative chages as shown. At which letteed point is the magnitude of the electic field geatest Least a b c d Go to PhET 49 5 Conceptual question Conceptual question A poton moves in a egion of constant electic field. Does it follow that the poton s velocity is paallel to the electic field Does it follow that the poton s acceleation is paallel to the electic field The foce expeienced by chage 1 at point A is diffeent in diection and magnitude fom the foce expeienced by chage at point B. Can we conclude that the electic fields at point A and point B ae diffeent 51 5 Example: a point chage in an electic field Tools (equations) to descibe motion of electons The essential featues of an ink-jet pinte atoms molecules quantum mechanics Schodinge equation Diac equation F = qe = ma then motion with constant acceleation (see physics 111) gases, plasma, classical mechanics Second Newton s law F = qe = ma 53 54 9
Pat 5 Electic Field Lines Electic field lines povide a nice way to visualize pattens in electic fields 1. At any point, the diection of a staight field line gives the diection of the electic field at that point. Electic fields extend away fom positive chage and towad negative chage 3. No field lines coss. 4. The field lines ae dawn so that the numbe of lines pe unit aea is popotional to the magnitude of the electic field. 56 Examples Poblem The electic field lines suounding thee chages ae shown in the Figue. The cente chage is q = - 1. mc. (a) What ae the signs of q 1 and q 3 (b) Find q 1. Note that twice as many field lines oiginate fom the +q chage than the +q o q chages. 57 (c) Find q 3. 58 Flux Pat 6 Flux of an Electic Field Example: a wide ai steam of unifom velocity at a small squae loop of aea A. Let Φ epesents the volume flow ate (volume pe unit time) at which ai flows though the loop. The ate depends on the angle between the velocity and the plane of the loop. Φ = ( v cosθ ) A = vacosθ 6 1
Flux of an Electic Field Φ = EAcosθ θ is the angle between the electic field and the line pependicula to the suface. SI units: N m /C Fo a non-unifom fields we have to integate ove a suface The electic flux though a suface is popotional to the net numbe of electic field lines passing though that suface. 61 Gauss Law Gauss law elates the net flux Φ of an electic field though a closed suface to the net chage q enc that is enclosed by that suface ε Φ = q enc Gauss law and Coulomb s law Demonstation fo a point chage 1 q 1 q q E = Φ = EA = 4π = 4πε 4πε ε A = 4π 6 Example In the following figue, the dashed line denotes a Gaussian suface enclosing pat of a distibution of fou positive chages. (a) Which chages contibute to the electic field at P (b) Is the value of the flux though the suface, calculated using only the electic field due to q1 and q, geate than, equal to, o less than that obtained using the field due to all fou chages A pactical conclusion fom the Gauss s Law Faaday s cage 63 Duing a thundestom stay in you ca!!! 64 Epilogue Inteactive Compute Simulation A vey good collection of inteactive simulations to lean physics fom the Physics Education Technology poject at the Univesity of Coloado http://www.coloado.edu/physics/phet/ 65 11