Electric Charge. Electric charge is quantized. Electric charge is conserved

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Blanche Wheeler
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1 lectstatics

2 lectic Chage lectic chage is uantized Chage cmes in incements f the elementay chage e = ne, whee n is an intege, and e =.6 x 0-9 C lectic chage is cnseved Chage (electns) can be mved fm ne place t anthe, but the ttal chage emains the same In pai pductin, electn and psitn (eual and ppsite chage) ae ceated simultaneusly, cnseving the ttal chage in the univese

3 Culmb s Law lectic Fce The electstatic fce between tw pint chages and sepaated by a distance has a magnitude f F e N m 9 4 k N m C 4 Als tue f spheical chages whse centes ae sepaated by Oppsite chages attact Like chages epel C

4 F Me Than Tw Chages Detemine the fce n a chage due t each f the the chages in the vicinity. D a vect additin. When yu ae detemining electstatic fce, yu fcus n ne chage. It s all abut me! Wh is neaby wh can affect me?

5 lectic Fce Find the electstatic fce acting n : =.0 C =.0 C 3 = -3.0 C 0.4 m 0.3 m 3

6 lectstatic Fce (dwnwad) 0. ) (0.4 ) )( ( ) 0 ( N m C C m N C F ight) the (t ) (0.3 ) 3 )( ( ) 0 ( N m C C m N C F m 0.3 m

7 lectstatic Fce Ttal fce is: F N iˆ.0 N ˆj Which has a magnitude f: F N N 3.00 N F 3 θ 3 F F And an angle f: tan.0 N / (belw the x - axis) N

8 The lectic Field A chage distibutin changes the empty space aund it such that this empty space will affect the chages bught neaby. We say that a chage distibutin ceates an electic field in the empty space suunding it.

9 lectic Field lectic field Analgus t gavitatinal field Tells the stength and diectin f the electic fce n a psitive test chage at that pint Pints fm t chage High density f lines = high electic field Is a vect F 4 (f a pint chage)

10 lectic Field Lines

11 lectic Field Lines

12 lectic Field Lines

13 lectic Field Lines What is the diectin f the electic field at pint P? Q P Q P Q -Q

14 lectic Field Lines What is the diectin f the electic field at pint P? Q P P -Q Q

15 lectic Diple chaged paticles ual magnitude Oppsite sign Distance d apat Cente is a distance z fm P z d P -

16 lectic Diple Calculate the electic field at pint P, a distance z away fm the midpint f the diple n the diple axis. P 4 z Will need t use the binmial theem. d -

17 Binmial Theem F x < : nx! n( n ) x! n( n )( n ) x 3! x n 3 A useful euatin. Geneally nly use the st and nd de tems.

18 lectic Field due t an lectic Diple ) ( ) ( ) ( ) ( ) ( 4 ) ( d z d z 4 z d z d z Massage int the fm f the binmial theem

19 lectic Field due t an lectic Diple Using the binmial theem: d z ( )! d z d z d z ( )! d z d z Plug these tems int the euatin f : 4 z 4 z d z d z d z 3 d z 4 z d z d z

20 lectic Field due t an lectic Diple The electic field due t an electic diple is: d z We call the uantity d the diple mment p: p is in C m Diectin f p is fm t 3 Used t specify the ientatin f a diple p z 3

21 lectic field due t a cicula line f chage If the chage pe unit length is λ then an element f chage is P d = λ ds d 4 d 4 ds θ z R ds

22 lectic field due t a cicula line f chage Ntice the symmety: the ttal electic field is nly in the z diectin, s nly calculate the z-cmpnent f the electic field. csd z 4 4 ds z(r) 3 cs 4 z 3 z R 0 ds ds P R θ z

23 lectic field due t a cicula line f chage Final answe: Wite the electic field in tems f z and R (nt ) P Replace the chage density: λ = / (πr) θ z 4 4 z(r) 3 z ( z R ) 3/ ds R

24 lectic field due t a linea line f chage Detemine the magnitude f the electic field at a pint P alng the axis f a d f length L at a distance d fm the cente f the d if thee is a chage Q unifmly distibuted alng its length. P L d Q

25 lectic field due t a linea line f chage Use the linea chage density λ = /L and wite: d = λ dx d 4 d 4 dx x P L d Q

26 lectic field due t a linea line f chage Nw integate d fm (d-l/) t (dl/) t find the electic field. 4 dx x P d L Q 4 4 d d L L dx x x d d L L

27 lectic field due t a linea line f chage 4 ) )( ( L d L d L d L L d d L L L d P Q

28 lectic field due t an ac f chage A cicula ac has a unifm linea chage density f 5 nc/m. What is the magnitude f the electic field at the cente f the ac s cicle? R = m θ = 300º

29 lectic field due t an ac f chage Redaw the ac s that it is symmetical abut an axis: Nw the y-cmpnents cancel. The electic field at the igin pints t the ight. Only calculate the x-cmpnent f the electic field 30º 330º

30 lectic field due t an ac f chage F a small element s f an ac s = θ ds = dθ Wite λ = linea chage density Then an element f chage is = λ s d = λ ds = λ dθ 30º 330º

31 lectic field due t an ac f chage The x-cmpnent f the electic field is x = csθ Integate t find the ttal field: x cs d 4 4 cs d cs d 30º 330º csd

32 lectic field due t an ac f chage Slve the definite integal: csd sin (50 C / m) 4 (8.850 C / N m.5n / C )(m) sin( 330) 30º 330º sin( 30) Fm the iginal pblem, the diectin is -30º.

33 Gauss Law Culmb s Law Finds the electic fce Gd f a small numbe f discete pint chages Des nt explit symmety Gauss Law Relates electic field t chage enclsed by a clsed (imaginay Gaussian ) suface xplits symmety

34 Flux Φ lectic flux is a measue f the numbe f electic field lines passing thugh an aea. It is the electic field multiplied by the pependicula cmpnent f the suface. Thugh a (clsed) Gaussian suface the flux Φ is: da Integate ve a clsed suface.

35 Flux calculatin What is the flux f the electic field passing thugh a cylinde that is aligned paallel t the field? da da da da left end ight end sides A A 0 0

36 Flux: pint chage Calculate the flux f electic field thugh a clsed sphee f adius R if thee is a pint chage at the cente. da R R R da da (4R )

37 Gauss Law Relates the electic fields at pints n a (clsed) Gaussian suface and the net chage enclsed by that suface. da da Q Gauss Law = st f 4 Maxwell s uatins

38 Gauss Law = Culmb s Law Use Gauss Law t deive Culmb s Law: Find the electic field a distance away fm a pint chage. da enc Thee is spheical symmety is cnstant n the suface f a sphee, but nt n the suface f a cylinde cube aund the chage Pick the Gaussian suface t be a sphee

39 Gauss Law = Culmb s Law is cnstant n the suface: da da The aea f a sphee is 4π :

40 Gauss Law: line f chage Find the electic field at a adial distance fm a lng cylindical plastic d f psitive linea chage density λ. What is the symmety? What shape shuld the Gaussian suface be? cylindical

41 Gauss Law: line f chage Stat with Gauss Law and integate ve the suface f the cylinde: h h da da Nte: thugh each end is 0 since θ=90 at the ends. igne the ends

42 Slid cnducts If an islated cnduct has an excess chage, the chage will mve t the suface f the cnduct The electic field inside a cnduct is ze lectic field lines stat and end at chages lectic field lines intesect a cnduct pependiculaly

43 Spheical symmety A shell f unifm chage attacts epels a chaged paticle that is utside the shell as if all the shell s chage wee cncentated at the cente f the shell A shell f unifm chage exets n electstatic fce n a chaged paticle that is lcated inside the shell

44 lectic field lines Detemine whee the excess chage (if any) will g, and daw the electic field lines: Q Q Slid sphee Slid spheical shell

45 lectic field lines Detemine whee the excess chage (if any) will g, and daw the electic field lines: - - Neutal spheical shell; chage in cente Neutal spheical shell; chage ff-cente

46 Gauss Law pblem # A sphee f chage Q unifmly distibuted thughut its vlume is cncentic with a spheical cnducting shell f net chage Q. a) What ae the chages n the inne and ute sufaces f the shell? -Q a Q b c

47 Gauss Law pblem # b) Find an expessin f the electic field as a functin f the adius, within the sphee ( < a). da Fist pick a spheical Gaussian suface. Ttal chage n the inne sphee is Q, ttal vlume is 4 a 3 Chage pe unit vlume is at any adius (<a) is 3 V Q a -Q s the enclsed chage a Q b c V Q Q a a 3

48 Gauss Law pblem # At any given adius (<a), is cnstant n the suface f the chsen Gaussian sphee : da da 4 3 Q 4 a Q a 3 Q a Q a Q b c

49 Gauss Law pblem # c) Find an expessin f the electic field as a functin f the adius, between the sphee and the shell (a<<b). da da 4 Q 4 Q Q -Q Nte: the chage enclsed by the Gaussian sphee is Q a Q b c

50 Gauss Law pblem # d) Find an expessin f the electic field as a functin f the adius, inside the shell (b < <c). da da Q a Q b Nte: the chage enclsed by the Gaussian sphee is 0. c

51 Gauss Law pblem #. e) Find an expessin f the electic field as a functin f the adius, utside the shell (c < ). da da Q a Q Nte: the chage enclsed by the Gaussian sphee is 0. b c

52 Gauss Law pblem # A small, nncnducting ball f mass m=.0mg and chage =.0x0-8 C hangs fm an insulating thead that makes an angle f 30 with the vetical, unifmly chaged nncnducting sheet. a) Daw all fces acting n the ball.

53 Gauss Law pblem # b) Calculate the electical fce acting n the ball. m =.0mg = x0-8 C θ = 30 tan F e F F F e g g tan ( kg)(9.8m / N s ) tan(30)

54 Gauss Law pblem # c) Calculate the electical field acting n the ball. m =.0mg = x0-8 C θ = 30 F e = 5.66 x 0-6 N 6 F N 83N 0 C / 8 C

55 Gauss Law pblem # d) Use Gauss law t detemine the suface chage density f the sheet. What Gaussian suface? Ty a cylinde that passes thugh the sheet:

56 Gauss Law pblem #. Use Gauss law nclsed chage is σa = σ Sufaces ae sides left end ight end da 9 / ) / 0 )(8.85 / (83 0 ) ( ) ( m C m N C C N da da da sides ight left

57 lectic Ptential (V)

58 lectic Ptential (V) Als called Ptential Vltage lectic ptential Ptential diffeence Units: V (vlts) Is a scala

CHAPTER 24 GAUSS LAW

CHAPTER 24 GAUSS LAW CHAPTR 4 GAUSS LAW LCTRIC FLUX lectic flux is a measue f the numbe f electic filed lines penetating sme suface in a diectin pependicula t that suface. Φ = A = A csθ with θ is the angle between the and