= ΔW a b. U 1 r m 1 + K 2
|
|
- Everett Taylor
- 5 years ago
- Views:
Transcription
1 Chpite 3 Potentiel électiue [18 u 3 mi] DEVOIR : 31, 316, 354, 361, 35 Le potentiel électiue est le tvil p unité de chge (en J/C, ou volt) Ce concept est donc utile dns les polèmes de consevtion d énegie Il est ussi tès utile dns les cicuits électiues, vec les lois de Kichhoff, etc) Nottion: énegie cinétiue K, énegie potentielle U, potentiel V 31 Énegie potentielle électiue De fçon généle, si une chge test se déplce du point u point dns un chmp électiue E, los l difféence d énegie potentielle (due à E) ente ces deux points est U U = ΔW = E dl Au esoin, évise les concepts de tvil et énegie potentielle Si on connit l foce, los une intégle (ci-dessus) pemet d oteni l énegie potentielle P conséuent, si on connit l énegie potentielle, une déivée pemett d oteni l foce: l E (718) ui fit inteveni le gdient, ui eviend à l section 35 Lie l section Attention : ne ps oulie ue l E (39) n est vlide ue pou des chges ponctuelles! Si l souce du chmp n est ps ponctuelle, los il fut utilise l fomule ci-dessus Exemples: 34 IDENTIFY: The wok euied is the chnge in electicl potentil enegy The potons gin speed fte eing elesed ecuse thei potentil enegy is conveted into kinetic enegy () SET UP: Using the potentil enegy of pi of point chges eltive to infinity, U = (1 / )( / ) we hve W = ΔU = U U 1 = 1 e e 1 Fctoing out the e nd sustituting numes gives W = ( N m /C )( C) m 1 = J 1 15 m () SET UP: The potons hve eul momentum, nd since they hve eul msses, they will hve eul speeds nd hence eul kinetic enegy ΔU = K 1 + K = K = 1 mv = mv Solving fo v gives v = ΔU m = J kg = m/s EVALUATE: The potentil enegy my seem smll (comped to mcoscopic enegies), ut it is enough to give ech poton speed of nely 7 million m/s
2 311 IDENTIFY: Apply E(3) The net wok to ing the chges in fom infinity is eul to the chnge in potentil enegy The totl potentil enegy is the sum of the potentil enegies of ech pi of chges, clculted fom E(39) SET UP: Let 1 e whee ll the chges e infinitely f pt Let e whee the chges e t the cones of the tingle, s shown in Figue 311 Let c e the thid, unknown chge Figue 311 W = ΔU = (U U 1 ) U 1 = U = U +U c +U c = 1 d ( + c ) Wnt W =, so W = (U U 1 ) gives = U + c = nd c = / = 1 d ( + c ) EVALUATE: The potentil enegy fo the two chges is positive nd fo ech with c it is negtive Thee e two of the, c tems so must hve c < 3 Potentiel électiue Le potentiel électiue est l énegie potentielle p unité de chge Autement dit, l énegie potentielle U d une chge test en un point est otenue en multiplint l chge p l vleu du potentiel V en ce point En ce sens, le V est à U ce ue E est à F E L E (317) est l plus généle Attention: Les Es (314) à (315) ne sont vlides ue pou des chges souces ponctuelles Lie les exemples ux pp 791 à 794 Autes exemples : W 314 IDENTIFY: = V Fo point chge, V = k SET UP: Ech vcnt cone is the sme distnce, m, fom ech point chge Tking the oigin t the cente of the sue, the symmety mens tht the potentil is the sme t the two cones not occupied y the +5 µc chges This mens tht no net wok is done is moving fom one cone to the othe EVALUATE: If the chge moves long digonl of the sue, the electicl foce does positive wok fo pt of the pth nd negtive wok fo nothe pt of the pth, ut the net wok done is zeo
3 i 31 IDENTIFY: V = 1 i i SET UP: The loctions of the chnges nd points A nd B e sketched in Figue 31 () V A = A1 () V B = B1 A Figue 31 V A = ( N m /C ) C 5 m C = 737 V 5 m B V B = ( N m /C ) C 8 m C = 74 V 6 m (c) IDENTIFY nd SET UP: Use E(313) nd the esults of pts () nd () to clculte W W B A = ʹ (V B V A ) = (5 1 9 C)( 74 V ( 737 V)) = J EVALUATE: The electic foce does positive wok on the positive chge when it moves fom highe potentil (point B) to lowe potentil (point A) 33 IDENTIFY: Fo point chge,v = k The totl potentil t ny point is the lgeic sum of the potentils of the two chges SET UP: () The positions of the two chges e shown in Figue 33 () V = k k( ) + = (c) The potentil long the x-xis is lwys zeo, so gph would e flt (d) If the two chges e intechnged, then the esults of () nd (c) still hold The potentil is zeo EVALUATE: The potentil is zeo t ny point on the x-xis ecuse ny point on the x-xis is euidistnt fom the two chges Figue 33
4 34 IDENTIFY: Fo point chge,v = k The totl potentil t ny point is the lgeic sum of the potentils of the two chges SET UP: Conside the distnces fom the point on the y-xis to ech chge fo the thee egions y (etween the two chges), y > (ove oth chges) nd y < (elow oth chges) () y < :V = y < :V = k ( + y) k ( y) = ky y y > :V = k ( + y) k y = k y k ( + y) k ( y + ) = k y A genel expession vlid fo ny y isv = k y + y + () The gph of V vesus y is sketched in Figue 34 (c) y >> :V = k y k y (d) If the chges e intechnged, then the potentil is of the opposite sign EVALUATE: V = t y = V + s the positive chge is ppoched nd V s the negtive chge is ppoched Figue IDENTIFY: K + V = K + V SET UP: Let point e t the cthode nd let point e t the node K = V = 95 V An electon hs = e nd m = kg K = (V ) = ( C)( 95 V) = J K = 1 mv, so v = ( J) kg = m s EVALUATE: The negtively chged electon gins kinetic enegy when it moves to highe potentil 39 () IDENTIFY nd SET UP: The diection of E is lwys fom high potentil to low potentil so point is t highe potentil () Apply E(317) to elte V to E V = E dl = Edx = E(x x ) E = V +4 V = = 8 V/m x x 9 m 6 m (c) W = (V ) = ( 1 6 C)(+4 V) = J
5 EVALUATE: The electic foce does negtive wok on negtive chge when the negtive chge moves fom high potentil (point ) to low potentil (point ) 331 IDENTIFY nd SET UP: Apply consevtion of enegy, E(33) Use E(31) to expess U in tems of V () K 1 + V 1 = K + V (V 1 V ) = K K 1 ; = C K 1 = 1 m v = J; K e 1 = 1 m v = J e V 1 V = K K 1 = 156 V EVALUATE: The electon gins kinetic enegy when it moves to highe potentil () Now K 1 = J, K = EVALUATE: V 1 V = K K 1 = +18 V The electon loses kinetic enegy when it moves to lowe potentil 33 Clculs de potentiels Section ptiue Lie l encdé du s de l p 794 et l exemple 38 Lie les exemples de pp 796 à 798 Autes exemples : 334 IDENTIFY: Exmple 31 shows tht fo line of chge,v = λ πp ln( / ) Apply consevtion of enegy to the motion of the poton SET UP: Let point e 18 cm fom the line nd let point e t the distnce of closest ppoch, whee K = () K = 1 mv = 1 ( kg)( m/s) = J () K + V = K + V V = K K ln( / ) = πp λ ( 1175 V) = exp πp ( 1175 V) λ = J C = 1175 V = (18 m)exp πp (1175 V) C/m = 158 m EVALUATE: The potentil inceses with decesing distnce fom the line of chge As the positively chged poton ppoches the line of chge it gins electicl potentil enegy nd loses kinetic enegy 337 IDENTIFY: Fo points outside the cylinde, its electic field ehves like tht of line of chge Since voltmete eds potentil diffeence, tht is wht we need to clculte SET UP: The potentil diffeence is ΔV = λ ln( πp / ) () Sustituting numes gives ΔV = 1 cm ( )ln 6 cm λ ln( πp / ) = ( C/m) N m /C
6 ΔV = V = 78, V = 78 kv () E = inside the cylinde, so the potentil is constnt thee, mening tht the voltmete eds zeo EVALUATE: Cution! The fct tht the voltmete eds zeo in pt () does not men tht V = inside the cylinde The electic field is zeo, ut the potentil is constnt nd eul to the potentil t the sufce 341 IDENTIFY nd SET UP: Use the esult of Exmple 39 to elte the electic field etween the pltes to the potentil diffeence etween them nd thei seption The foce this field exets on the pticle is given y E(13) Use the eution tht pecedes E(317) to clculte the wok () Fom Exmple 39, E = V d = 36 V = 8 V/m 45 m () F = E = (4 1 9 C)(8 V/m) = N (c) The electic field etween the pltes is shown in Figue 341 Figue 341 The plte with positive chge (plte ) is t highe potentil The electic field is diected fom high potentil towd low potentil (o, E is fom + chge towd chge), so E points fom to Hence the foce tht E exets on the positive chge is fom to, so it does positive wok W = F dl = Fd, whee d is the seption etween the pltes W = Fd = ( N)(45 m) = J (d) V = +36 V (plte is t highe potentil) ΔU = U U = (V ) = (4 1 9 C)( 36 V) = J EVALUATE: We see tht W = (U U ) = U U 344 IDENTIFY: Exmple 38 shows tht the potentil of solid conducting sphee is the sme t evey point inside the sphee nd is eul to its vlue V = / πp R t the sufce Use the given vlue of E to find SET UP: Fo negtive chge the electic field is diected towd the chge Fo points outside this spheicl chge distiution the field is the sme s if ll the chge wee concentted t the cente E = nd = E (38 N/C)( m) = = C N m /C Since the field is diected inwd, the chge must e negtive The potentil of point chge, tking s zeo, is V = = ( N m /C )( C) = 76 V t the sufce of the m sphee Since the chge ll esides on the sufce of conducto, the field inside the sphee due to this symmeticl distiution is zeo No wok is theefoe done in moving test chge fom just inside the sufce to the cente, nd the potentil t the cente must lso e 76 V EVALUATE: Inside the sphee the electic field is zeo nd the potentil is constnt 34 Sufces éuipotentielles L nlogie des coues de contou (Fig 33) ide à voi une compéhension intuitive P exemples, des coues ppochées coespondent à une pente plus ide; dns le contexte électiue, celà signifie E plus élevé
7 Lie pidement l section, ui est plutôt de ntue conceptuelle 35 Chmp électiue comme gdient du potentiel Si V est connu, los E (3) donne E Si V (et E) est dil, los on utilise E (33) Lie les deux exemples Autes exemples: 347 IDENTIFY nd SET UP: Use E(319) to clculte the components of E () E x = V x V = Axy Bx + Cy = Ay + Bx Ey = V y = Ax C E z = V z = () E = euies tht E x = E y = E z = E z = eveywhee E y = t x = C/A And E x is lso eul zeo fo this x, ny vlue of z, nd y = Bx/A = (B/A)( C/A) = BC/A EVALUATE: 348 IDENTIFY: Apply E(119) V doesn t depend on z so E z = eveywhee SET UP: E(17) sys E = 1 Similly, E y = kqy 3 () E x = V x = x () Fom pt (), E = kq EVALUATE: nd E z = kqz 3 ˆ is the electic field due to point chge kq x + y + z = kqx (x + y + z ) = kqx 3 3 xî + yĵ + z ˆk = kq ˆ, which gees with Eution (17) V is scl E is vecto nd hs components 349 IDENTIFY nd SET UP: Fo solid metl sphee o fo spheicl shell, V = k outside the sphee nd V = k R t ll points inside the sphee, whee R is the dius of the sphee When the electic field is dil, E = V () (i) < : This egion is inside oth spheesv = k k (ii) < < : This egion is outside the inne shell nd inside the oute shell V = k k = k 1 1 = k 1 1 (iii) > : This egion is outside oth sphees nd V = since outside
8 sphee the potentil is the sme s fo point chge Theefoe the potentil is the sme s fo two oppositely chged point chges t the sme loction These potentils cncel () V = 1 ndv =, sov = (c) Between the sphees < < ndv = k 1 1 E = V = 1 1 = + 1 = V (d) Fom Eution (33): E =, since V is constnt (zeo) outside the sphees (e) If the oute chge is diffeent, then outside the oute sphee the potentil is no longe zeo ut is V = 1 1 Q = 1 ( Q) All potentils inside the oute shell e just shifted y n mount V = 1 Q Theefoe eltive potentils within the shells e not ffected Thus () nd (c) do not chnge Howeve, now tht the potentil does vy outside the sphees, thee is n electic field thee: E = V = k + kq = k 1 Q = k ( Q) EVALUATE: In pt () the potentil is gete thn zeo fo ll <
U>, and is negative. Electric Potential Energy
Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When
More informationElectric Potential. and Equipotentials
Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil
More informationr = (0.250 m) + (0.250 m) r = m = = ( N m / C )
ELECTIC POTENTIAL IDENTIFY: Apply Eq() to clculte the wok The electic potentil enegy of pi of point chges is given y Eq(9) SET UP: Let the initil position of q e point nd the finl position e point, s shown
More informationLecture 11: Potential Gradient and Capacitor Review:
Lectue 11: Potentil Gdient nd Cpcito Review: Two wys to find t ny point in spce: Sum o Integte ove chges: q 1 1 q 2 2 3 P i 1 q i i dq q 3 P 1 dq xmple of integting ove distiution: line of chge ing of
More informationElectricity & Magnetism Lecture 6: Electric Potential
Electicity & Mgnetism Lectue 6: Electic Potentil Tody s Concept: Electic Potenl (Defined in tems of Pth Integl of Electic Field) Electicity & Mgnesm Lectue 6, Slide Stuff you sked bout:! Explin moe why
More informationAnswers to test yourself questions
Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E
More information(A) 6.32 (B) 9.49 (C) (D) (E) 18.97
Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10
More informationPhysics 604 Problem Set 1 Due Sept 16, 2010
Physics 64 Polem et 1 Due ept 16 1 1) ) Inside good conducto the electic field is eo (electons in the conducto ecuse they e fee to move move in wy to cncel ny electic field impessed on the conducto inside
More informationELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy:
LCTROSTATICS. Quntiztion of Chge: Any chged body, big o smll, hs totl chge which is n integl multile of e, i.e. = ± ne, whee n is n intege hving vlues,, etc, e is the chge of electon which is eul to.6
More informationCHAPTER 18: ELECTRIC CHARGE AND ELECTRIC FIELD
ollege Physics Student s Mnul hpte 8 HAPTR 8: LTRI HARG AD LTRI ILD 8. STATI LTRIITY AD HARG: OSRVATIO O HARG. ommon sttic electicity involves chges nging fom nnocoulombs to micocoulombs. () How mny electons
More informationElectric Field F E. q Q R Q. ˆ 4 r r - - Electric field intensity depends on the medium! origin
1 1 Electic Field + + q F Q R oigin E 0 0 F E ˆ E 4 4 R q Q R Q - - Electic field intensity depends on the medium! Electic Flux Density We intoduce new vecto field D independent of medium. D E So, electic
More informationChapter 25 Electric Potential
Chpte 5 lectic Potentil consevtive foces -> potentil enegy - Wht is consevtive foce? lectic potentil = U / : the potentil enegy U pe unit chge is function of the position in spce Gol:. estblish the eltionship
More informationGeneral Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface
Genel Physics II Chpte 3: Guss w We now wnt to quickly discuss one of the moe useful tools fo clculting the electic field, nmely Guss lw. In ode to undestnd Guss s lw, it seems we need to know the concept
More informationCHAPTER 25 ELECTRIC POTENTIAL
CHPTE 5 ELECTIC POTENTIL Potential Diffeence and Electic Potential Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic foce on the paticle given by F=E. When
More information10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =
Chpte 1 nivesl Gvittion 11 *P1. () The un-th distnce is 1.4 nd the th-moon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon
More informationThis chapter is about energy associated with electrical interactions. Every
23 ELECTRIC PTENTIAL whee d l is n infinitesiml displcement long the pticle s pth nd f is the ngle etween F nd d l t ech point long the pth. econd, if the foce F is consevtive, s we defined the tem in
More informationWork, Potential Energy, Conservation of Energy. the electric forces are conservative: ur r
Wok, Potentil Enegy, Consevtion of Enegy the electic foces e consevtive: u Fd = Wok, Potentil Enegy, Consevtion of Enegy b b W = u b b Fdl = F()[ d + $ $ dl ] = F() d u Fdl = the electic foces e consevtive
More informationPhysics 1502: Lecture 2 Today s Agenda
1 Lectue 1 Phsics 1502: Lectue 2 Tod s Agend Announcements: Lectues posted on: www.phs.uconn.edu/~cote/ HW ssignments, solutions etc. Homewok #1: On Mstephsics this Fid Homewoks posted on Msteingphsics
More informationChapter 23 Electrical Potential
hpte Electicl Potentil onceptul Polems [SSM] A poton is moved to the left in unifom electic field tht points to the ight. Is the poton moving in the diection of incesing o decesing electic potentil? Is
More informationFI 2201 Electromagnetism
FI 1 Electomgnetism Alexnde A. Isknd, Ph.D. Physics of Mgnetism nd Photonics Resech Goup Electosttics ELECTRIC PTENTIALS 1 Recll tht we e inteested to clculte the electic field of some chge distiution.
More informationSolutions to Midterm Physics 201
Solutions to Midtem Physics. We cn conside this sitution s supeposition of unifomly chged sphee of chge density ρ nd dius R, nd second unifomly chged sphee of chge density ρ nd dius R t the position of
More informationExample 2: ( ) 2. $ s ' 9.11" 10 *31 kg ( )( 1" 10 *10 m) ( e)
Emple 1: Two point chge e locted on the i, q 1 = e t = 0 nd q 2 = e t =.. Find the wok tht mut be done b n etenl foce to bing thid point chge q 3 = e fom infinit to = 2. b. Find the totl potentil eneg
More informationGeneral Physics (PHY 2140)
Genel Physics (PHY 40) Lightning Review Lectue 3 Electosttics Lst lectue:. Flux. Guss s s lw. simplifies computtion of electic fields Q Φ net Ecosθ ε o Electicl enegy potentil diffeence nd electic potentil
More informationChapter 21: Electric Charge and Electric Field
Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme
More informationPHYS 2421 Fields and Waves
PHYS 242 Felds nd Wves Instucto: Joge A. López Offce: PSCI 29 A, Phone: 747-7528 Textook: Unvesty Physcs e, Young nd Feedmn 23. Electc potentl enegy 23.2 Electc potentl 23.3 Clcultng electc potentl 23.4
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 3 Due on Sep. 14, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 4 Due on Sep. 1, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
More informationELECTRO - MAGNETIC INDUCTION
NTRODUCTON LCTRO - MAGNTC NDUCTON Whenee mgnetic flu linked with cicuit chnges, n e.m.f. is induced in the cicuit. f the cicuit is closed, cuent is lso induced in it. The e.m.f. nd cuent poduced lsts s
More informationRadial geodesics in Schwarzschild spacetime
Rdil geodesics in Schwzschild spcetime Spheiclly symmetic solutions to the Einstein eqution tke the fom ds dt d dθ sin θdϕ whee is constnt. We lso hve the connection components, which now tke the fom using
More informationπ,π is the angle FROM a! TO b
Mth 151: 1.2 The Dot Poduct We hve scled vectos (o, multiplied vectos y el nume clled scl) nd dded vectos (in ectngul component fom). Cn we multiply vectos togethe? The nswe is YES! In fct, thee e two
More informationPhysics 11b Lecture #11
Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge
More informationPX3008 Problem Sheet 1
PX38 Poblem Sheet 1 1) A sphee of dius (m) contins chge of unifom density ρ (Cm -3 ). Using Guss' theoem, obtin expessions fo the mgnitude of the electic field (t distnce fom the cente of the sphee) in
More informationChapter 28 Sources of Magnetic Field
Chpte 8 Souces of Mgnetic Field - Mgnetic Field of Moving Chge - Mgnetic Field of Cuent Element - Mgnetic Field of Stight Cuent-Cying Conducto - Foce Between Pllel Conductos - Mgnetic Field of Cicul Cuent
More informationElectric Potential Energy
Electic Ptentil Enegy Ty Cnsevtive Fces n Enegy Cnsevtin Ttl enegy is cnstnt n is sum f kinetic n ptentil Electic Ptentil Enegy Electic Ptentil Cnsevtin f Enegy f pticle fm Phys 7 Kinetic Enegy (K) nn-eltivistic
More information( ) ( ) ( ) ( ) ( ) # B x ( ˆ i ) ( ) # B y ( ˆ j ) ( ) # B y ("ˆ ( ) ( ) ( (( ) # ("ˆ ( ) ( ) ( ) # B ˆ z ( k )
Emple 1: A positie chge with elocit is moing though unifom mgnetic field s shown in the figues below. Use the ight-hnd ule to detemine the diection of the mgnetic foce on the chge. Emple 1 ˆ i = ˆ ˆ i
More informationDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3
DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl
More information6. Gravitation. 6.1 Newton's law of Gravitation
Gvittion / 1 6.1 Newton's lw of Gvittion 6. Gvittion Newton's lw of gvittion sttes tht evey body in this univese ttcts evey othe body with foce, which is diectly popotionl to the poduct of thei msses nd
More informationCh 26 - Capacitance! What s Next! Review! Lab this week!
Ch 26 - Cpcitnce! Wht s Next! Cpcitnce" One week unit tht hs oth theoeticl n pcticl pplictions! Cuent & Resistnce" Moving chges, finlly!! Diect Cuent Cicuits! Pcticl pplictions of ll the stuff tht we ve
More informationThis immediately suggests an inverse-square law for a "piece" of current along the line.
Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line
More informationEinstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,
PE ELECTOSTATICS C Popeties of chges : (i) (ii) (iii) (iv) (v) (vi) Two kinds of chges eist in ntue, positive nd negtive with the popety tht unlike chges ttct ech othe nd like chges epel ech othe. Ecess
More informationCHAPTER 2 ELECTROSTATIC POTENTIAL
1 CHAPTER ELECTROSTATIC POTENTIAL 1 Intoduction Imgine tht some egion of spce, such s the oom you e sitting in, is pemeted by n electic field (Pehps thee e ll sots of electiclly chged bodies outside the
More informationFluids & Bernoulli s Equation. Group Problems 9
Goup Poblems 9 Fluids & Benoulli s Eqution Nme This is moe tutoil-like thn poblem nd leds you though conceptul development of Benoulli s eqution using the ides of Newton s 2 nd lw nd enegy. You e going
More informationSPA7010U/SPA7010P: THE GALAXY. Solutions for Coursework 1. Questions distributed on: 25 January 2018.
SPA7U/SPA7P: THE GALAXY Solutions fo Cousewok Questions distibuted on: 25 Jnuy 28. Solution. Assessed question] We e told tht this is fint glxy, so essentilly we hve to ty to clssify it bsed on its spectl
More information2 mv2 qv (0) = 0 v = 2qV (0)/m. Express q. . Substitute for V (0) and simplify to obtain: v = q
Pof Anchodoui Polems set # Physics 69 Mch 3, 5 (i) Eight eul chges e locted t cones of cue of side s, s shown in Fig Find electic potentil t one cone, tking zeo potentil to e infinitely f wy (ii) Fou point
More informationPhysics 505 Fall 2005 Midterm Solutions. This midterm is a two hour open book, open notes exam. Do all three problems.
Physics 55 Fll 5 Midtem Solutions This midtem is two hou open ook, open notes exm. Do ll thee polems. [35 pts] 1. A ectngul ox hs sides of lengths, nd c z x c [1] ) Fo the Diichlet polem in the inteio
More information3.1 Magnetic Fields. Oersted and Ampere
3.1 Mgnetic Fields Oested nd Ampee The definition of mgnetic induction, B Fields of smll loop (dipole) Mgnetic fields in mtte: ) feomgnetism ) mgnetiztion, (M ) c) mgnetic susceptiility, m d) mgnetic field,
More information$ i. !((( dv vol. Physics 8.02 Quiz One Equations Fall q 1 q 2 r 2 C = 2 C! V 2 = Q 2 2C F = 4!" or. r ˆ = points from source q to observer
Physics 8.0 Quiz One Equations Fall 006 F = 1 4" o q 1 q = q q ˆ 3 4" o = E 4" o ˆ = points fom souce q to obseve 1 dq E = # ˆ 4" 0 V "## E "d A = Q inside closed suface o d A points fom inside to V =
More information10 Statistical Distributions Solutions
Communictions Engineeing MSc - Peliminy Reding 1 Sttisticl Distiutions Solutions 1) Pove tht the vince of unifom distiution with minimum vlue nd mximum vlue ( is ) 1. The vince is the men of the sques
More informationELECTROSTATICS. Syllabus : Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road PE 1
PE ELECTOSTATICS Syllbus : Electic chges : Consevtion of chge, Coulumb s lw-foces between two point chges, foces between multiple chges; supeposition pinciple nd continuous chge distibution. Electic field
More informationChapter 4. Energy and Potential
Chpte 4. Enegy nd Ptentil Hyt; 0/5/009; 4-4. Enegy Expended in Mving Pint Chge in n Electic Field The electic field intensity is defined s the fce n unit test chge. The fce exeted y the electic field n
More informationChapter 2: Electric Field
P 6 Genel Phsics II Lectue Outline. The Definition of lectic ield. lectic ield Lines 3. The lectic ield Due to Point Chges 4. The lectic ield Due to Continuous Chge Distibutions 5. The oce on Chges in
More informationChapter 25: Current, Resistance and Electromotive Force. ~10-4 m/s Typical speeds ~ 10 6 m/s
Chpte 5: Cuent, esistnce nd lectomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m q ndomizing Collisions (momentum, enegy) >esulting Motion http://phys3p.sl.psu.edu/phys_nim/m/ndom_wlk.vi
More informationPhys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1
Monday, Mach 5, 019 Page: 1 Q1. Figue 1 shows thee pais of identical conducting sphees that ae to be touched togethe and then sepaated. The initial chages on them befoe the touch ae indicated. Rank the
More informationHomework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is:
. Homewok 3 MAE 8C Poblems, 5, 7, 0, 4, 5, 8, 3, 30, 3 fom Chpte 5, msh & Btt Point souces emit nuetons/sec t points,,, n 3 fin the flux cuent hlf wy between one sie of the tingle (blck ot). The flux fo
More informationdx was area under f ( x ) if ( ) 0
13. Line Integls Line integls e simil to single integl, f ( x) dx ws e unde f ( x ) if ( ) 0 Insted of integting ove n intevl [, ] (, ) f xy ds f x., we integte ove cuve, (in the xy-plne). **Figue - get
More informationChapter 25: Current, Resistance and Electromotive Force. Charge carrier motion in a conductor in two parts
Chpte 5: Cuent, esistnce nd Electomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m qe ndomizing Collisions (momentum, enegy) =>esulting Motion Avege motion = Dift elocity = v d
More informationELECTROSTATICS. JEE-Physics ELECTRIC CHARGE
J-Physics LCTIC CHAG LCTOSTATICS Chge is the popety ssocited with mtte due to which it poduces nd epeiences electicl nd mgnetic effects. The ecess o deficiency of electons in body gives the concept of
More informationChapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s:
Chpte 7 Kleene s Theoem 7.1 Kleene s Theoem The following theoem is the most impotnt nd fundmentl esult in the theoy of FA s: Theoem 6 Any lnguge tht cn e defined y eithe egul expession, o finite utomt,
More informationPotential Energy. The change U in the potential energy. is defined to equal to the negative of the work. done by a conservative force
Potential negy The change U in the potential enegy is defined to equal to the negative of the wok done by a consevative foce duing the shift fom an initial to a final state. U = U U = W F c = F c d Potential
More informationProblem Set 3 SOLUTIONS
Univesity of Albm Deptment of Physics nd Astonomy PH 10- / LeCli Sping 008 Poblem Set 3 SOLUTIONS 1. 10 points. Remembe #7 on lst week s homewok? Clculte the potentil enegy of tht system of thee chges,
More information17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other
Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.1 Electic Potential Enegy Electic foce is a consevative foce and so we can assign an electic potential enegy (PE) to the system
More informationFriedmannien equations
..6 Fiedmnnien equtions FLRW metic is : ds c The metic intevl is: dt ( t) d ( ) hee f ( ) is function which detemines globl geometic l popety of D spce. f d sin d One cn put it in the Einstein equtions
More informationElectrostatics. 3) positive object: lack of electrons negative object: excess of electrons
Electostatics IB 12 1) electic chage: 2 types of electic chage: positive and negative 2) chaging by fiction: tansfe of electons fom one object to anothe 3) positive object: lack of electons negative object:
More informationHomework: Study 6.2 #1, 3, 5, 7, 11, 15, 55, 57
Gols: 1. Undestnd volume s the sum of the es of n infinite nume of sufces. 2. Be le to identify: the ounded egion the efeence ectngle the sufce tht esults fom evolution of the ectngle ound n xis o foms
More information(a) Counter-Clockwise (b) Clockwise ()N (c) No rotation (d) Not enough information
m m m00 kg dult, m0 kg bby. he seesw stts fom est. Which diection will it ottes? ( Counte-Clockwise (b Clockwise ( (c o ottion ti (d ot enough infomtion Effect of Constnt et oque.3 A constnt non-zeo toque
More information(1) It increases the break down potential of the surrounding medium so that more potential can be applied and hence more charge can be stored.
Cpcito Cpcito: Cpcito ( o conense ) is evice fo stoing chge. It essentilly consists of two conucting sufces such s two pltes o two spheicl shell o two cylines etc. kept exctly pllel to ech othe septe y
More informationChapter 24. Gauss s Law
Chpte 24 Guss s Lw CHAPTR OUTLIN 24.1 lectic Flux 24.2 Guss s Lw 24.3 Appliction of Guss s Lw to Vious Chge Distibutions 24.4 Conductos in lectosttic uilibium 24.5 Foml Deivtion of Guss s Lw In tble-top
More informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chpte The lectic Field II: Continuous Chge Distibutions Conceptul Poblems [SSM] Figue -7 shows n L-shped object tht hs sides which e equl in length. Positive chge is distibuted unifomly long the length
More information(Sample 3) Exam 1 - Physics Patel SPRING 1998 FORM CODE - A (solution key at end of exam)
(Sample 3) Exam 1 - Physics 202 - Patel SPRING 1998 FORM CODE - A (solution key at end of exam) Be sue to fill in you student numbe and FORM lette (A, B, C) on you answe sheet. If you foget to include
More informationContinuous Charge Distributions
Continuous Chge Distibutions Review Wht if we hve distibution of chge? ˆ Q chge of distibution. Q dq element of chge. d contibution to due to dq. Cn wite dq = ρ dv; ρ is the chge density. = 1 4πε 0 qi
More informationEnergy Dissipation Gravitational Potential Energy Power
Lectue 4 Chpte 8 Physics I 0.8.03 negy Dissiption Gvittionl Potentil negy Powe Couse wesite: http://fculty.uml.edu/andiy_dnylov/teching/physicsi Lectue Cptue: http://echo360.uml.edu/dnylov03/physicsfll.html
More informationClass Summary. be functions and f( D) , we define the composition of f with g, denoted g f by
Clss Summy.5 Eponentil Functions.6 Invese Functions nd Logithms A function f is ule tht ssigns to ech element D ectly one element, clled f( ), in. Fo emple : function not function Given functions f, g:
More informationWeek 8. Topic 2 Properties of Logarithms
Week 8 Topic 2 Popeties of Logithms 1 Week 8 Topic 2 Popeties of Logithms Intoduction Since the esult of ithm is n eponent, we hve mny popeties of ithms tht e elted to the popeties of eponents. They e
More informationCHAPTER 29 ELECTRIC FIELD AND POTENTIAL EXERCISES
HPTER ELETRI FIELD ND POTENTIL EXERISES. oulob Newton l M L T 4 k F.. istnce between k so, foce k ( F ( The weight of boy 4 N 4 N wt of boy So,. foce between chges 4 So, foce between chges.6 weight of
More informationPHYS 1444 Lecture #5
Shot eview Chapte 24 PHYS 1444 Lectue #5 Tuesday June 19, 212 D. Andew Bandt Capacitos and Capacitance 1 Coulom s Law The Fomula QQ Q Q F 1 2 1 2 Fomula 2 2 F k A vecto quantity. Newtons Diection of electic
More informationHomework Assignment 3 Solution Set
Homework Assignment 3 Solution Set PHYCS 44 6 Ferury, 4 Prolem 1 (Griffiths.5(c The potentil due to ny continuous chrge distriution is the sum of the contriutions from ech infinitesiml chrge in the distriution.
More informationCHAPTER? 29 ELECTRIC FIELD AND POTENTIAL EXERCISES = 2, N = (5.6) 1 = = = = = Newton
Downloe fo HPTER? ELETRI FIELD ND POTENTIL EXERISES. oulob Newton l M L T 4 k F.. istnce between k so, foce k ( F ( The weight of boy 4 N 4 N wt of boy.5 So, foce between chges 4 So, foce between chges
More informationAlgebra Based Physics. Gravitational Force. PSI Honors universal gravitation presentation Update Fall 2016.notebookNovember 10, 2016
Newton's Lw of Univesl Gvittion Gvittionl Foce lick on the topic to go to tht section Gvittionl Field lgeb sed Physics Newton's Lw of Univesl Gvittion Sufce Gvity Gvittionl Field in Spce Keple's Thid Lw
More informationSection 35 SHM and Circular Motion
Section 35 SHM nd Cicul Motion Phsics 204A Clss Notes Wht do objects do? nd Wh do the do it? Objects sometimes oscillte in simple hmonic motion. In the lst section we looed t mss ibting t the end of sping.
More information1 Using Integration to Find Arc Lengths and Surface Areas
Novembe 9, 8 MAT86 Week Justin Ko Using Integtion to Find Ac Lengths nd Sufce Aes. Ac Length Fomul: If f () is continuous on [, b], then the c length of the cuve = f() on the intevl [, b] is given b s
More informationIntroduction: Vectors and Integrals
Intoduction: Vectos and Integals Vectos a Vectos ae chaacteized by two paametes: length (magnitude) diection a These vectos ae the same Sum of the vectos: a b a a b b a b a b a Vectos Sum of the vectos:
More informationGauss Law. Physics 231 Lecture 2-1
Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationThe Area of a Triangle
The e of Tingle tkhlid June 1, 015 1 Intodution In this tile we will e disussing the vious methods used fo detemining the e of tingle. Let [X] denote the e of X. Using se nd Height To stt off, the simplest
More informationEECE 260 Electrical Circuits Prof. Mark Fowler
EECE 60 Electicl Cicuits Pof. Mk Fowle Complex Numbe Review /6 Complex Numbes Complex numbes ise s oots of polynomils. Definition of imginy # nd some esulting popeties: ( ( )( ) )( ) Recll tht the solution
More informationMAGNETIC EFFECT OF CURRENT & MAGNETISM
TODUCTO MAGETC EFFECT OF CUET & MAGETM The molecul theo of mgnetism ws given b Webe nd modified lte b Ewing. Oested, in 18 obseved tht mgnetic field is ssocited with n electic cuent. ince, cuent is due
More informationOn the Eötvös effect
On the Eötvös effect Mugu B. Răuţ The im of this ppe is to popose new theoy bout the Eötvös effect. We develop mthemticl model which loud us bette undestnding of this effect. Fom the eqution of motion
More information1. The sphere P travels in a straight line with speed
1. The sphee P tels in stight line with speed = 10 m/s. Fo the instnt depicted, detemine the coesponding lues of,,,,, s mesued eltie to the fixed Oxy coodinte system. (/134) + 38.66 1.34 51.34 10sin 3.639
More informationGet Solution of These Packages & Learn by Video Tutorials on EXERCISE-1
FEE Downlod Study Pckge fom website: www.tekoclsses.com & www.mthsbysuhg.com Get Solution of These Pckges & Len by Video Tutoils on www.mthsbysuhg.com EXECISE- * MAK IS MOE THAN ONE COECT QUESTIONS. SECTION
More informationPhysics 1502: Lecture 4 Today s Agenda
1 Physics 1502: Today s genda nnouncements: Lectues posted on: www.phys.uconn.edu/~cote/ HW assignments, solutions etc. Homewok #1: On Mastephysics today: due next Fiday Go to masteingphysics.com and egiste
More informationProf. Anchordoqui Problems set # 12 Physics 169 May 12, 2015
Pof. Anchodoqui Poblems set # 12 Physics 169 My 12, 2015 1. Two concentic conducting sphees of inne nd oute dii nd b, espectively, cy chges ±Q. The empty spce between the sphees is hlf-filled by hemispheicl
More information2 E. on each of these two surfaces. r r r r. Q E E ε. 2 2 Qencl encl right left 0
Ch : 4, 9,, 9,,, 4, 9,, 4, 8 4 (a) Fom the diagam in the textbook, we see that the flux outwad though the hemispheical suface is the same as the flux inwad though the cicula suface base of the hemisphee
More informationCollection of Formulas
Collection of Fomuls Electomgnetic Fields EITF8 Deptment of Electicl nd Infomtion Technology Lund Univesity, Sweden August 8 / ELECTOSTATICS field point '' ' Oigin ' Souce point Coulomb s Lw The foce F
More information2.2 This is the Nearest One Head (Optional) Experimental Verification of Gauss s Law and Coulomb s Law
2.2 This is the Neest One Hed 743 P U Z Z L R Some ilwy compnies e plnning to cot the windows of thei commute tins with vey thin lye of metl. (The coting is so thin you cn see though it.) They e doing
More informationLecture 4. Electric Potential
Lectue 4 Electic Ptentil In this lectue yu will len: Electic Scl Ptentil Lplce s n Pissn s Eutin Ptentil f Sme Simple Chge Distibutins ECE 0 Fll 006 Fhn Rn Cnell Univesity Cnsevtive Ittinl Fiels Ittinl
More informationObjects usually are charged up through the transfer of electrons from one object to the other.
1 Pat 1: Electic Foce 1.1: Review of Vectos Review you vectos! You should know how to convet fom pola fom to component fom and vice vesa add and subtact vectos multiply vectos by scalas Find the esultant
More informationPhysics 2212 GH Quiz #2 Solutions Spring 2016
Physics 2212 GH Quiz #2 Solutions Sping 216 I. 17 points) Thee point chages, each caying a chage Q = +6. nc, ae placed on an equilateal tiangle of side length = 3. mm. An additional point chage, caying
More informationEELE 3331 Electromagnetic I Chapter 4. Electrostatic fields. Islamic University of Gaza Electrical Engineering Department Dr.
EELE 3331 Electomagnetic I Chapte 4 Electostatic fields Islamic Univesity of Gaza Electical Engineeing Depatment D. Talal Skaik 212 1 Electic Potential The Gavitational Analogy Moving an object upwad against
More informationChapter 21 The Electric Field I: Discrete Charge Distributions
Chpte The lectic ield I: Discete Chge Distibutions Conceptul oblems Objects e composed of toms which e composed of chged pticles (potons nd electons); howeve, we el obseve the effects of the electosttic
More informationObjectives: After finishing this unit you should be able to:
lectic Field 7 Objectives: Afte finishing this unit you should be able to: Define the electic field and explain what detemines its magnitude and diection. Wite and apply fomulas fo the electic field intensity
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 10-1 DESCRIBING FIELDS Essential Idea: Electic chages and masses each influence the space aound them and that influence can be epesented
More information