Module 12: Current and Resistance 1
|
|
- Malcolm Gardner
- 5 years ago
- Views:
Transcription
1 Module 12: Cuent and Resistance 1 Table of Contents 6.1 Electic Cuent Cuent Density Ohm s Law Electical Enegy and Powe Summay Solved Poblems Resistivity of a Cable Chage at a Junction Dift Velocity Resistance of a Tuncated Cone Resistance of a Hollow Cylinde Conceptual Questions Additional Poblems Cuent and Cuent Density Powe Loss and Ohm s Law Resistance of a Cone Cuent Density and Dift Speed Cuent Sheet Resistance and Resistivity Powe, Cuent, and Voltage Chage Accumulation at the Inteface These notes ae excepted Intoduction to Electicity and Magnetism by Sen-Ben Liao, Pete Doumashkin, and John Belche, Copyight 2004, ISBN
2 Cuent and Resistance 6.1 Electic Cuent Electic cuents ae flows of electic chage. Suppose a collection of chages is moving pependicula to a suface of aea A, as shown in Figue Figue Chages moving though a coss section. The electic cuent is defined to be the ate at which chages flow acoss any cosssectional aea. If an amount of chage ΔQ passes though a suface in a time inteval Δt, then the aveage cuent I avg is given by I avg = ΔQ (6.1.1) Δt The SI unit of cuent is the ampee (A), with 1 A = 1 coulomb/sec. Common cuents ange fom mega-ampees in lightning to nano-ampees in you neves. In the limit Δt 0, the instantaneous cuent I may be defined as I = dq (6.1.2) dt Since flow has a diection, we have implicitly intoduced a convention that the diection of cuent coesponds to the diection in which positive chages ae flowing. The flowing chages inside wies ae negatively chaged electons that move in the opposite diection of the cuent. Electic cuents flow in conductos: solids (metals, semiconductos), liquids (electolytes, ionized) and gases (ionized), but the flow is impeded in nonconductos o insulatos Cuent Density To elate cuent, a macoscopic quantity, to the micoscopic motion of the chages, let s examine a conducto of coss-sectional aea A, as shown in Figue
3 Figue A micoscopic pictue of cuent flowing in a conducto. Let the total cuent though a suface be witten as I = J da (6.1.3) whee J is the cuent density (the SI unit of cuent density ae A/m 2 ). If q is the chage of each caie, and n is the numbe of chage caies pe unit volume, the total amount of chage in this section is then Δ Q= q( na Δx). Suppose that the chage caies move with a speed v d ; then the displacement in a time inteval Δt will be Δ x = vd Δ t, which implies I = ΔQ avg = nqv d A (6.1.4) Δt The speed v d at which the chage caies ae moving is known as the dift speed. Physically, v d is the aveage speed of the chage caies inside a conducto when an extenal electic field is applied. Actually an electon inside the conducto does not tavel in a staight line; instead, its path is athe eatic, as shown in Figue Figue Motion of an electon in a conducto. Fom the above equations, the cuent density J can be witten as J =nqv d (6.1.5) Thus, we see that J and v d point in the same diection fo positive chage caies, in opposite diections fo negative chage caies. 6-3
4 To find the dift velocity of the electons, we fist note that an electon in the conducto expeiences an electic foce F e = ee which gives an acceleation F e ee a = = (6.1.6) m m e Let the velocity of a given electon immediate afte a collision be v i. The velocity of the electon immediately befoe the next collision is then given by e ee v f = v i + at = v i t (6.1.7) m e whee t is the time taveled. The aveage of v f ove all time intevals is ee v f = v i t (6.1.8) m e which is equal to the dift velocity v d. Since in the absence of electic field, the velocity of the electon is completely andom, it follows that v i = 0. If τ = t is the aveage chaacteistic time between successive collisions (the mean fee time), we have The cuent density in Eq. (6.1.5) becomes ee v d = = τ (6.1.9) v f m e ee ne 2 τ J = nev d = ne τ = E (6.1.10) m e m e Note that J and E will be in the same diection fo eithe negative o positive chage caies. 6.2 Ohm s Law In many mateials, the cuent density is linealy dependent on the extenal electic field E. Thei elation is usually expessed as J = σ E (6.2.1) 6-4
5 whee σ is called the conductivity of the mateial. The above equation is known as the (micoscopic) Ohm s law. A mateial that obeys this elation is said to be ohmic; othewise, the mateial is non-ohmic. Compaing Eq. (6.2.1) with Eq. (6.1.10), we see that the conductivity can be expessed as ne 2 τ σ = (6.2.2) m e To obtain a moe useful fom of Ohm s law fo pactical applications, conside a segment of staight wie of length l and coss-sectional aea A, as shown in Figue Figue A unifom conducto of length l and potential diffeence Δ V = V b V a. Suppose a potential diffeence Δ V = V b V a is applied between the ends of the wie, ceating an electic field E and a cuent I. Assuming E to be unifom, we then have The cuent density can then be witten as V V b V a = b Δ = E d s = El (6.2.3) a With J whee = I / A, the potential diffeence becomes is the esistance of the conducto. The equation J = σ E = σ ΔV (6.2.4) l Δ l V = l J = σ σ A I = RI (6.2.5) ΔV l R = = (6.2.6) I σ A 6-5
6 Δ V = IR (6.2.7) is the macoscopic vesion of the Ohm s law. The SI unit of R is the ohm (Ω, Geek lette Omega), whee 1V 1 Ω (6.2.8) 1A Once again, a mateial that obeys the above elation is ohmic, and non-ohmic if the elation is not obeyed. Most metals, with good conductivity and low esistivity, ae ohmic. We shall focus mainly on ohmic mateials. Figue Ohmic vs. Non-ohmic behavio. The esistivity ρ of a mateial is defined as the ecipocal of conductivity, 1 m ρ = = e (6.2.9) σ ne 2 τ Fom the above equations, we see that ρ can be elated to the esistance R of an object by o E ΔV / l RA ρ = = = J I / A l ρl R = (6.2.10) A The esistivity of a mateial actually vaies with tempeatue T. Fo metals, the vaiation is linea ove a lage ange of T: ρ = ρ [1+α( T T ) 0 0 ] (6.2.11) whee α is the tempeatue coefficient of esistivity. Typical values of ρ, σ and α (at 20 C) fo diffeent types of mateials ae given in the Table below. 6-6
7 Mateial Elements Silve Resistivity ρ ( Ω m ) Conductivity σ ( Ω m) 1 Tempeatue Coefficient α (C) Coppe Aluminum Tungsten Ion Platinum Alloys Bass Manganin Nichome Semiconductos Cabon (gaphite) Gemanium (pue) Silicon (pue) Insulatos Glass Sulfu Quatz (fused) Electical Enegy and Powe Conside a cicuit consisting of a battey and a esisto with esistance R (Figue 6.3.1). Let the potential diffeence between two points a and b be Δ V = V b Va > 0. If a chage Δq is moved fom a though the battey, its electic potential enegy is inceased by Δ U =ΔqΔ V. On the othe hand, as the chage moves acoss the esisto, the potential enegy is deceased due to collisions with atoms in the esisto. If we neglect the intenal esistance of the battey and the connecting wies, upon etuning to a the potential enegy of Δq emains unchanged. Figue A cicuit consisting of a battey and a esisto of esistance R. 6-7
8 Thus, the ate of enegy loss though the esisto is given by P = Δ U Δ t = Δq V I V (6.3.1) Δ t Δ = Δ This is pecisely the powe supplied by the battey. Using Δ V = IR, one may ewite the above equation as (ΔV ) 2 2 P= I R = (6.3.2) R 6.4 Summay The electic cuent is defined as: dq I = dt The aveage cuent in a conducto is I avg = nqv A d whee n is the numbe density of the chage caies, q is the chage each caie has, v d is the dift speed, and A is the coss-sectional aea. The cuent density J though the coss sectional aea of the wie is J = nqv Micoscopic Ohm s law: the cuent density is popotional to the electic field, and the constant of popotionality is called conductivity σ : d J = σ E The ecipocal of conductivity σ is called esistivity ρ : 1 ρ = σ Macoscopic Ohm s law: The esistance R of a conducto is the atio of the potential diffeence ΔV between the two ends of the conducto and the cuent I: 6-8
9 Resistance is elated to esistivity by ΔV R = I ρl R = A whee l is the length and A is the coss-sectional aea of the conducto. The dift velocity of an electon in the conducto is ee v d = τ m e whee m e is the mass of an electon, and τ is the aveage time between successive collisions. The esistivity of a metal is elated to τ by e ρ = 1 = m 2 σ ne τ The tempeatue vaiation of esistivity of a conducto is ρ = ρ0 1+α (T T 0 ) whee α is the tempeatue coefficient of esistivity. Powe, o ate at which enegy is deliveed to the esisto is 6.5 Solved Poblems P= IΔ V = I R = 2 ( ΔV ) 2 R Resistivity of a Cable A 3000-km long cable consists of seven coppe wies, each of diamete 0.73 mm, bundled togethe and suounded by an insulating sheath. Calculate the esistance of the cable. Use Ω cm fo the esistivity of the coppe. 6-9
10 Solution: The esistance R of a conducto is elated to the esistivity ρ by R = ρl/ A, whee l and A ae the length of the conducto and the coss-sectional aea, espectively. Since the cable consists of N = 7 coppe wies, the total coss sectional aea is 2 A N = N π d 2 = 7 π (0.073cm) 2 = π 4 4 The esistance then becomes 6 8 )( ) ρl (3 10 Ω cm 3 10 cm 4 R = = = Ω A 7π (0.073cm) 2 / Chage at a Junction Show that the total amount of chage at the junction of the two mateials in Figue is ε 0 I(σ 2 σ 1 ), whee I is the cuent flowing though the junction, andσ 1 and σ 2 ae the conductivities fo the two mateials. Solution: Figue Chage at a junction. In a steady state of cuent flow, the nomal component of the cuent density J must be the same on both sides of the junction. Since J = σ E, we have σ E = σ E o E 2 = σ 1 E 1 σ 2 Let the chage on the inteface be q in, we have, fom the Gauss s law: o d = (E E ) A = q in E A 2 1 S ε
11 q in E 2 E 1 = A ε Substituting the expession fo E 2 fom above then yields Since the cuent is I = JA = (σ E σ q in = ε 0 AE 1 1 = ε 0 Aσ 1 E 1 σ 2 σ 2 σ ) 0 A, the amount of chage on the inteface becomes 1 1 q in = ε 0 I σ 2 σ Dift Velocity The esistivity of seawate is about 25 Ω cm. The chage caies ae chiefly Na + and Cl ions, and of each thee ae about / cm. If we fill a plastic tube 2 metes long with seawate and connect a 12-volt battey to the electodes at each end, what is the esulting aveage dift velocity of the ions, in cm/s? Solution: The cuent in a conducto of coss sectional aea A is elated to the dift speed v d of the chage caies by I = enav d whee n is the numbe of chages pe unit volume. We can then ewite the Ohm s law as which yields V = IR = (neav d ) ρl = nev d ρl A V v d = neρl Substituting the values, we have 12V 5 V cm 5 cm v = d (6 10 /cm )( C)(25Ω cm )( 200cm ) = C Ω = s 6-11
12 In conveting the units we have used V V 1 A 1 = = = s Ω C Ω C C Resistance of a Tuncated Cone Conside a mateial of esistivity ρ in a shape of a tuncated cone of altitude h, and adii a and b, fo the ight and the left ends, espectively, as shown in the Figue Figue A tuncated Cone. Assuming that the cuent is distibuted unifomly thoughout the coss-section of the cone, what is the esistance between the two ends? Solution: Conside a thin disk of adius at a distance x fom the left end. Fom the figue shown on the ight, we have b b a = x h o = (a b) x + b h Since esistance R is elated to esistivity ρ by R = ρl/ A, whee l is the length of the conducto and A is the coss section, the contibution to the esistance fom the disk having a thickness dy is ρ dx ρ dx dr = = π 2 π[b + (a b) x / h ]
13 Staightfowad integation then yields h ρ dx ρh R = = 0 2 π[b + (a b) x / h ] π ab whee we have used du 1 = (αu + β ) 2 α( α u + β ) Note that if b= a, Eq. (6.2.9) is epoduced Resistance of a Hollow Cylinde Conside a hollow cylinde of length L and inne adius a and oute adius b, as shown in Figue The mateial has esistivity ρ. Figue A hollow cylinde. (a) Suppose a potential diffeence is applied between the ends of the cylinde and poduces a cuent flowing paallel to the axis. What is the esistance measued? (b) If instead the potential diffeence is applied between the inne and oute sufaces so that cuent flows adially outwad, what is the esistance measued? Solution: (a) When a potential diffeence is applied between the ends of the cylinde, cuent flows paallel to the axis. In this case, the coss-sectional aea is A = π (b 2 a 2 ), and the esistance is given by ρl ρl R = = 2 2 A π (b a ) 6-13
14 (b) Conside a diffeential element which is made up of a thin cylinde of inne adius and oute adius + d and length L. Its contibution to the esistance of the system is given by ρ dl ρ d dr = = A 2π L whee A = 2π L is the aea nomal to the diection of cuent flow. The total esistance of the system becomes b ρ d ρ b R = = ln a 2π L 2π L a 6.6 Conceptual Questions 1. Two wies A and B of cicula coss-section ae made of the same metal and have equal lengths, but the esistance of wie A is fou times geate than that of wie B. Find the atio of thei coss-sectional aeas. 2. Fom the point of view of atomic theoy, explain why the esistance of a mateial inceases as its tempeatue inceases. 3. Two conductos A and B of the same length and adius ae connected acoss the same potential diffeence. The esistance of conducto A is twice that of B. To which conducto is moe powe deliveed? 6.7 Additional Poblems Cuent and Cuent Density A sphee of adius 10 mm that caies a chage of 8 nc = C is whiled in a cicle at the end of an insulated sting. The otation fequency is 100π ad/s. (a) What is the basic definition of cuent in tems of chage? (b) What aveage cuent does this otating chage epesent? (c) What is the aveage cuent density ove the aea tavesed by the sphee? Powe Loss and Ohm s Law A 1500 W adiant heate is constucted to opeate at 115 V. 6-14
15 (a) What will be the cuent in the heate? [Ans. ~10 A] (b) What is the esistance of the heating coil? [Ans. ~10 Ω] (c) How many kilocaloies ae geneated in one hou by the heate? (1 Caloie = 4.18 J) Resistance of a Cone A coppe esisto of esistivity ρ is in the shape of a cylinde of adius b and length L 1 appended to a tuncated ight cicula cone of length L 2 and end adii b and a as shown in Figue Figue (a) What is the esistance of the cylindical potion of the esisto? (b) What is the esistance of the entie esisto? (Hint: Fo the tapeed potion, it is necessay to wite down the incemental esistance dr of a small slice, dx, of the esisto at an abitay position, x, and then to sum the slices by integation. If the tape is small, one may assume that the cuent density is unifom acoss any coss section.) (c) Show that you answe educes to the expected expession if a = b. (d) If L 1 = 100 mm, L 2 = 50 mm, a = 0.5 mm, b = 1.0 mm, what is the esistance? Cuent Density and Dift Speed (a) A goup of chages, each with chage q, moves with velocity v. The numbe of paticles pe unit volume is n. What is the cuent density J of these chages, in magnitude and diection? Make sue that you answe has units of A/m 2. (b) We want to calculate how long it takes an electon to get fom a ca battey to the state moto afte the ignition switch is tuned. Assume that the cuent flowing is115 A, 2 and that the electons tavel though coppe wie with coss-sectional aea 31.2 mm and length 85.5 cm. What is the cuent density in the wie? The numbe density of the conduction electons in coppe is /m 3. Given this numbe density and the cuent density, what is the dift speed of the electons? How long does it take fo an 6-15
16 electon stating at the battey to each the state moto? [Ans: A/m 2, m/s,52.5 min.] Cuent Sheet A cuent sheet, as the name implies, is a plane containing cuents flowing in one diection in that plane. One way to constuct a sheet of cuent is by unning many paallel wies in a plane, say the yz -plane, as shown in Figue 6.7.2(a). Each of these wies caies cuent I out of the page, in the ĵ diection, with n wies pe unit length in the z-diection, as shown in Figue 6.7.2(b). Then the cuent pe unit length in the z diection is ni. We will use the symbol K to signify cuent pe unit length, so that K = nl hee. Figue A cuent sheet. Anothe way to constuct a cuent sheet is to take a non-conducting sheet of chage with fixed chage pe unit aea σ and move it with some speed in the diection you want cuent to flow. Fo example, in the sketch to the left, we have a sheet of chage moving out of the page with speed v. The diection of cuent flow is out of the page. (a) Show that the magnitude of the cuent pe unit length in the z diection, K, is given by σ v. Check that this quantity has the pope dimensions of cuent pe length. This is in fact a vecto elation, K (t) = σ v ( t ), since the sense of the cuent flow is in the same diection as the velocity of the positive chages. (b) A belt tansfeing chage to the high-potential inne shell of a Van de Gaaff acceleato at the ate of 2.83 mc/s. If the width of the belt caying the chage is 50 cm and the belt tavels at a speed of 30 m/s, what is the suface chage density on the belt? [Ans: 189 μc/m 2 ] Resistance and Resistivity A wie with a esistance of 6.0 Ω is dawn out though a die so that its new length is thee times its oiginal length. Find the esistance of the longe wie, assuming that the 6-16
17 esistivity and density of the mateial ae not changed duing the dawing pocess. [Ans: 54 Ω] Powe, Cuent, and Voltage A 100-W light bulb is plugged into a standad 120-V outlet. (a) How much does it cost pe month (31 days) to leave the light tuned on? Assume electicity costs 6 cents pe kw h. (b) What is the esistance of the bulb? (c) What is the cuent in the bulb? [Ans: (a) $4.46; (b) 144 Ω; (c) A] Chage Accumulation at the Inteface Figue shows a thee-laye sandwich made of two esistive mateials with esistivities ρ 1 and ρ 2. Fom left to ight, we have a laye of mateial with esistivity ρ 1 of width d /3, followed by a laye of mateial with esistivity ρ 2, also of width d /3, followed by anothe laye of the fist mateial with esistivity ρ 1, again of width d /3. Figue Chage accumulation at inteface. The coss-sectional aea of all of these mateials is A. The esistive sandwich is bounded on eithe side by metallic conductos (black egions). Using a battey (not shown), we maintain a potential diffeence V acoss the entie sandwich, between the metallic conductos. The left side of the sandwich is at the highe potential (i.e., the electic fields point fom left to ight). Thee ae fou intefaces between the vaious mateials and the conductos, which we label a though d, as indicated on the sketch. A steady cuent I flows though this sandwich fom left to ight, coesponding to a cuent density J = I / A. (a) What ae the electic fields E 1 and E 2 in the two diffeent dielectic mateials? To obtain these fields, assume that the cuent density is the same in evey laye. Why must this be tue? [Ans: All fields point to the ight, E 1 = ρ 1 I / A, E 2 = ρ 2 I / A ; the cuent densities must be the same in a steady state, othewise thee would be a continuous buildup of chage at the intefaces to unlimited values.] 6-17
18 (b) What is the total esistance R of this sandwich? Show that you expession educes to the expected esult if ρ 1 = ρ 2 = ρ. [Ans: R = d (2 ρ 1 + ρ 2 )/3 A ; if ρ 1 = ρ 2 = ρ, then R = d ρ / A, as expected.] (c) As we move fom ight to left, what ae the changes in potential acoss the thee layes, in tems of V and the esistivities? [Ans: V ρ 1 / 2 V ρ 1 /( 2ρ 1 + ρ 2 ), summing to a total potential dop of V, as equied]. ( ρ 1 + ρ 2 ),V ρ 2 /( 2ρ 1 + ρ 2 ), (d) What ae the chages pe unit aea, σ a though σ d, at the intefaces? Use Gauss's Law and assume that the electic field in the conducting caps is zeo. [Ans: σ a = σ d = 3ε 0 V ρ 1 / d (2 ρ 1 + ρ 2 ), σ b = σ c = 3ε 0 V (ρ 2 ρ 1 )/ d (2 ρ 1 + ρ 2 ).] (e) Conside the limit ρ 2 ρ 1. What do you answes above educe to in this limit? 6-18
19 MIT OpenCouseWae SC Physics II: Electicity and Magnetism Fall 2010 Fo infomation about citing these mateials o ou Tems of Use, visit:
6 Chapter. Current and Resistance
6 Chapter Current and Resistance 6.1 Electric Current... 6-2 6.1.1 Current Density... 6-2 6.2 Ohm s Law... 6-5 6.3 Summary... 6-8 6.4 Solved Problems... 6-9 6.4.1 Resistivity of a Cable... 6-9 6.4.2 Charge
More informationCurrent, Resistance and
Cuent, Resistance and Electomotive Foce Chapte 25 Octobe 2, 2012 Octobe 2, 2012 Physics 208 1 Leaning Goals The meaning of electic cuent, and how chages move in a conducto. What is meant by esistivity
More informationEM-2. 1 Coulomb s law, electric field, potential field, superposition q. Electric field of a point charge (1)
EM- Coulomb s law, electic field, potential field, supeposition q ' Electic field of a point chage ( ') E( ) kq, whee k / 4 () ' Foce of q on a test chage e at position is ee( ) Electic potential O kq
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 informationELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.
ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic
More informationFlux. Area Vector. Flux of Electric Field. Gauss s Law
Gauss s Law Flux Flux in Physics is used to two distinct ways. The fist meaning is the ate of flow, such as the amount of wate flowing in a ive, i.e. volume pe unit aea pe unit time. O, fo light, it is
More informationExam 3, vers Physics Spring, 2003
1 of 9 Exam 3, ves. 0001 - Physics 1120 - Sping, 2003 NAME Signatue Student ID # TA s Name(Cicle one): Michael Scheffestein, Chis Kelle, Paisa Seelungsawat Stating time of you Tues ecitation (wite time
More informationev dm e evd 2 m e 1 2 ev2 B) e 2 0 dm e D) m e
. A paallel-plate capacito has sepaation d. The potential diffeence between the plates is V. If an electon with chage e and mass m e is eleased fom est fom the negative plate, its speed when it eaches
More informationPhys 222 Sp 2009 Exam 1, Wed 18 Feb, 8-9:30pm Closed Book, Calculators allowed Each question is worth one point, answer all questions
Phys Sp 9 Exam, Wed 8 Feb, 8-9:3pm Closed Book, Calculatos allowed Each question is woth one point, answe all questions Fill in you Last Name, Middle initial, Fist Name You ID is the middle 9 digits on
More informationPY208 Matter & Interactions Final Exam S2005
PY Matte & Inteactions Final Exam S2005 Name (pint) Please cicle you lectue section below: 003 (Ramakishnan 11:20 AM) 004 (Clake 1:30 PM) 005 (Chabay 2:35 PM) When you tun in the test, including the fomula
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 informationPhys-272 Lecture 17. Motional Electromotive Force (emf) Induced Electric Fields Displacement Currents Maxwell s Equations
Phys-7 Lectue 17 Motional Electomotive Foce (emf) Induced Electic Fields Displacement Cuents Maxwell s Equations Fom Faaday's Law to Displacement Cuent AC geneato Magnetic Levitation Tain Review of Souces
More informationFields and Waves I Spring 2005 Homework 8. Due: 3 May 2005
Fields and Waves I Sping 005 Homewok 8 Tansmission Lines Due: 3 May 005. Multiple Choice (6) a) The SWR (standing wave atio): a) is a measue of the match between the souce impedance and line impedance
More informationChapter 23: GAUSS LAW 343
Chapte 23: GAUSS LAW 1 A total chage of 63 10 8 C is distibuted unifomly thoughout a 27-cm adius sphee The volume chage density is: A 37 10 7 C/m 3 B 69 10 6 C/m 3 C 69 10 6 C/m 2 D 25 10 4 C/m 3 76 10
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 informationAlgebra-based Physics II
lgebabased Physics II Chapte 19 Electic potential enegy & The Electic potential Why enegy is stoed in an electic field? How to descibe an field fom enegetic point of view? Class Website: Natual way of
More informationHopefully Helpful Hints for Gauss s Law
Hopefully Helpful Hints fo Gauss s Law As befoe, thee ae things you need to know about Gauss s Law. In no paticula ode, they ae: a.) In the context of Gauss s Law, at a diffeential level, the electic flux
More informationElectrostatics (Electric Charges and Field) #2 2010
Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when
More informationMAGNETIC FIELD INTRODUCTION
MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),
More informationFI 2201 Electromagnetism
FI 2201 Electomagnetism Alexande A. Iskanda, Ph.D. Physics of Magnetism and Photonics Reseach Goup Electodynamics ELETROMOTIVE FORE AND FARADAY S LAW 1 Ohm s Law To make a cuent flow, we have to push the
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 informationA moving charged particle creates a magnetic field vector at every point in space except at its position.
1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units
More informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chapte The lectic Field II: Continuous Chage Distibutions A ing of adius a has a chage distibution on it that vaies as l(q) l sin q, as shown in Figue -9. (a) What is the diection of the electic field
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 informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electical and Compute Engineeing, Conell Univesity ECE 303: Electomagnetic Fields and Waves Fall 007 Homewok 8 Due on Oct. 19, 007 by 5:00 PM Reading Assignments: i) Review the lectue notes.
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 informationA new force Magnetic force. Today. Force Fields: A disturbance of space. The correspondence of a loop of current and magnet.
Today A new foce Magnetic foce Announcements HW#6 and HW#7 ae both due Wednesday Mach 18th. Thanks to my being WAY behind schedule, you 2nd exam will be a take-home exam! Stay tuned fo details Even if
More informationSAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70
SAMPL PAPR I Time Allowed : 3 hous Maximum Maks : 70 Note : Attempt All questions. Maks allotted to each question ae indicated against it. 1. The magnetic field lines fom closed cuves. Why? 1 2. What is
More informationCHAPTER 10 ELECTRIC POTENTIAL AND CAPACITANCE
CHAPTER 0 ELECTRIC POTENTIAL AND CAPACITANCE ELECTRIC POTENTIAL AND CAPACITANCE 7 0. ELECTRIC POTENTIAL ENERGY Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic
More information11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.
Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings
More information1 2 U CV. K dq I dt J nqv d J V IR P VI
o 5 o T C T F 9 T K T o C 7.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC dt L pv nt Kt nt CV ideal monatomic gas 5 CV ideal diatomic gas w/o vibation V W pdv V U Q W W Q e Q Q e Canot H C T T S C
More information16.1 Permanent magnets
Unit 16 Magnetism 161 Pemanent magnets 16 The magnetic foce on moving chage 163 The motion of chaged paticles in a magnetic field 164 The magnetic foce exeted on a cuent-caying wie 165 Cuent loops and
More information2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum
2. Electostatics D. Rakhesh Singh Kshetimayum 1 2.1 Intoduction In this chapte, we will study how to find the electostatic fields fo vaious cases? fo symmetic known chage distibution fo un-symmetic known
More informationPHYS 1444 Section 501 Lecture #7
PHYS 1444 Section 51 Lectue #7 Wednesday, Feb. 8, 26 Equi-potential Lines and Sufaces Electic Potential Due to Electic Dipole E detemined fom V Electostatic Potential Enegy of a System of Chages Capacitos
More informationUnit 7: Sources of magnetic field
Unit 7: Souces of magnetic field Oested s expeiment. iot and Savat s law. Magnetic field ceated by a cicula loop Ampèe s law (A.L.). Applications of A.L. Magnetic field ceated by a: Staight cuent-caying
More informationUniversity of Illinois at Chicago Department of Physics. Electricity & Magnetism Qualifying Examination
E&M poblems Univesity of Illinois at Chicago Depatment of Physics Electicity & Magnetism Qualifying Examination Januay 3, 6 9. am : pm Full cedit can be achieved fom completely coect answes to 4 questions.
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 informationCalculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m
MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3
More informationUniversity Physics (PHY 2326)
Chapte Univesity Physics (PHY 6) Lectue lectostatics lectic field (cont.) Conductos in electostatic euilibium The oscilloscope lectic flux and Gauss s law /6/5 Discuss a techniue intoduced by Kal F. Gauss
More information( ) Make-up Tests. From Last Time. Electric Field Flux. o The Electric Field Flux through a bit of area is
Mon., 3/23 Wed., 3/25 Thus., 3/26 Fi., 3/27 Mon., 3/30 Tues., 3/31 21.4-6 Using Gauss s & nto to Ampee s 21.7-9 Maxwell s, Gauss s, and Ampee s Quiz Ch 21, Lab 9 Ampee s Law (wite up) 22.1-2,10 nto to
More informationChapter 21: Gauss s Law
Chapte : Gauss s Law Gauss s law : intoduction The total electic flux though a closed suface is equal to the total (net) electic chage inside the suface divided by ε Gauss s law is equivalent to Coulomb
More informationCh 30 - Sources of Magnetic Field! The Biot-Savart Law! = k m. r 2. Example 1! Example 2!
Ch 30 - Souces of Magnetic Field 1.) Example 1 Detemine the magnitude and diection of the magnetic field at the point O in the diagam. (Cuent flows fom top to bottom, adius of cuvatue.) Fo staight segments,
More information! E da = 4πkQ enc, has E under the integral sign, so it is not ordinarily an
Physics 142 Electostatics 2 Page 1 Electostatics 2 Electicity is just oganized lightning. Geoge Calin A tick that sometimes woks: calculating E fom Gauss s law Gauss s law,! E da = 4πkQ enc, has E unde
More information18.1 Origin of Electricity 18.2 Charged Objects and Electric Force
1 18.1 Oigin of lecticity 18. Chaged Objects and lectic Foce Thee ae two kinds of electic chage: positive and negative. The SI unit of electic chage is the coulomb (C). The magnitude of the chage on an
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 informationPrepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -
Pepaed by: M. S. KumaSwamy, TGT(Maths) Page - - ELECTROSTATICS MARKS WEIGHTAGE 8 maks QUICK REVISION (Impotant Concepts & Fomulas) Chage Quantization: Chage is always in the fom of an integal multiple
More informationPhysics 107 TUTORIAL ASSIGNMENT #8
Physics 07 TUTORIAL ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapte 8: Poblems 5,, 3, 39, 76 Chapte 9: Poblems 9, 0, 4, 5, 6 Chapte 8 5 Inteactive Solution 8.5 povides a model fo solving this type
More informationReview of Potential Energy. The Electric Potential. Plotting Fields and Potentials. Electric Potential of a Point Charge
eview of Potential negy Potential enegy U() can be used to descibe a consevative foce. efeence point (U) can be chosen fo convenience. Wok done by F : W F d s F d (1D) Change in P.. : U U f U i W Foce
More informationPhysics 313 Practice Test Page 1. University Physics III Practice Test II
Physics 313 Pactice Test Page 1 Univesity Physics III Pactice Test II This pactice test should give you a ough idea of the fomat and oveall level of the Physics 313 exams. The actual exams will have diffeent
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 informationPHYS 2135 Exam I February 13, 2018
Exam Total /200 PHYS 2135 Exam I Febuay 13, 2018 Name: Recitation Section: Five multiple choice questions, 8 points each Choose the best o most nealy coect answe Fo questions 6-9, solutions must begin
More informationPage 1 of 6 Physics II Exam 1 155 points Name Discussion day/time Pat I. Questions 110. 8 points each. Multiple choice: Fo full cedit, cicle only the coect answe. Fo half cedit, cicle the coect answe and
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
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 informationMagnetic fields (origins) CHAPTER 27 SOURCES OF MAGNETIC FIELD. Permanent magnets. Electric currents. Magnetic field due to a moving charge.
Magnetic fields (oigins) CHAPTER 27 SOURCES OF MAGNETC FELD Magnetic field due to a moving chage. Electic cuents Pemanent magnets Magnetic field due to electic cuents Staight wies Cicula coil Solenoid
More information3. Magnetostatic fields
3. Magnetostatic fields D. Rakhesh Singh Kshetimayum 1 Electomagnetic Field Theoy by R. S. Kshetimayum 3.1 Intoduction to electic cuents Electic cuents Ohm s law Kichoff s law Joule s law Bounday conditions
More informationOn the Sun s Electric-Field
On the Sun s Electic-Field D. E. Scott, Ph.D. (EE) Intoduction Most investigatos who ae sympathetic to the Electic Sun Model have come to agee that the Sun is a body that acts much like a esisto with a
More informationFaraday s Law (continued)
Faaday s Law (continued) What causes cuent to flow in wie? Answe: an field in the wie. A changing magnetic flux not only causes an MF aound a loop but an induced electic field. Can wite Faaday s Law: ε
More informationB. Spherical Wave Propagation
11/8/007 Spheical Wave Popagation notes 1/1 B. Spheical Wave Popagation Evey antenna launches a spheical wave, thus its powe density educes as a function of 1, whee is the distance fom the antenna. We
More informationModule 05: Gauss s s Law a
Module 05: Gauss s s Law a 1 Gauss s Law The fist Maxwell Equation! And a vey useful computational technique to find the electic field E when the souce has enough symmety. 2 Gauss s Law The Idea The total
More informatione = 1.60 x 10 ε 0 = 8.85 x C 2 / Nm 2 V i...) F a = m Power =
Equations: 1 1 Constants: q q v v F = k F = qe e = 1.6 x 1-19 C q 1 q 1 9 E = k = k = = 9 1 Nm / C 4πε 4 πε Φ = E da Φ V Total v v q = E da = = V f V i = W q enclosed ε = E ds U e V = q q V V V V = k E
More informationGauss s Law Simulation Activities
Gauss s Law Simulation Activities Name: Backgound: The electic field aound a point chage is found by: = kq/ 2 If thee ae multiple chages, the net field at any point is the vecto sum of the fields. Fo a
More informationReview: Electrostatics and Magnetostatics
Review: Electostatics and Magnetostatics In the static egime, electomagnetic quantities do not vay as a function of time. We have two main cases: ELECTROSTATICS The electic chages do not change postion
More informationConventional Paper-I (a) Explain the concept of gradient. Determine the gradient of the given field: ( )
EE-Conventional Pape-I IES-013 www.gatefoum.com Conventional Pape-I-013 1. (a) Eplain the concept of gadient. Detemine the gadient of the given field: V ρzsin φ+ z cos φ+ρ What is polaization? In a dielectic
More information15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.
Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a)
More informationPHY 213. General Physics II Test 2.
Univesity of Kentucky Depatment of Physics an Astonomy PHY 3. Geneal Physics Test. Date: July, 6 Time: 9:-: Answe all questions. Name: Signatue: Section: Do not flip this page until you ae tol to o so.
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 informationWelcome to Physics 272
Welcome to Physics 7 Bob Mose mose@phys.hawaii.edu http://www.phys.hawaii.edu/~mose/physics7.html To do: Sign into Masteing Physics phys-7 webpage Registe i-clickes (you i-clicke ID to you name on class-list)
More informationPhysics 122, Fall October 2012
Today in Physics 1: electostatics eview David Blaine takes the pactical potion of his electostatics midtem (Gawke). 11 Octobe 01 Physics 1, Fall 01 1 Electostatics As you have pobably noticed, electostatics
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 informationElectromagnetism Physics 15b
lectomagnetism Physics 15b Lectue #20 Dielectics lectic Dipoles Pucell 10.1 10.6 What We Did Last Time Plane wave solutions of Maxwell s equations = 0 sin(k ωt) B = B 0 sin(k ωt) ω = kc, 0 = B, 0 ˆk =
More information13. The electric field can be calculated by Eq. 21-4a, and that can be solved for the magnitude of the charge N C m 8.
CHAPTR : Gauss s Law Solutions to Assigned Poblems Use -b fo the electic flux of a unifom field Note that the suface aea vecto points adially outwad, and the electic field vecto points adially inwad Thus
More informationCapacitors and Capacitance
Capacitos and Capacitance Capacitos ae devices that can stoe a chage Q at some voltage V. The geate the capacitance, the moe chage that can be stoed. The equation fo capacitance, C, is vey simple: C Q
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 informationPhys 1215, First Test. September 20, minutes Name:
Phys 115, Fist Test. Septembe 0, 011 50 minutes Name: Show all wok fo maximum cedit. Each poblem is woth 10 points. k =.0 x 10 N m / C ε 0 = 8.85 x 10-1 C / N m e = 1.60 x 10-1 C ρ = 1.68 x 10-8 Ω m fo
More informationFaraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law
Faaday s Law Faaday s Epeiments Chapte 3 Law of nduction (emf( emf) Faaday s Law Magnetic Flu Lenz s Law Geneatos nduced Electic fields Michael Faaday discoeed induction in 83 Moing the magnet induces
More information20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241
Chapte 0 Electicity 41 0-9 ELECTRIC IELD LINES Goals Illustate the concept of electic field lines. Content The electic field can be symbolized by lines of foce thoughout space. The electic field is stonge
More information21 MAGNETIC FORCES AND MAGNETIC FIELDS
CHAPTER 1 MAGNETIC ORCES AND MAGNETIC IELDS ANSWERS TO OCUS ON CONCEPTS QUESTIONS 1. (d) Right-Hand Rule No. 1 gives the diection of the magnetic foce as x fo both dawings A and. In dawing C, the velocity
More informationPhysics 2A Chapter 10 - Moment of Inertia Fall 2018
Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.
More information4. Electrodynamic fields
4. Electodynamic fields D. Rakhesh Singh Kshetimayum 1 4.1 Intoduction Electodynamics Faaday s law Maxwell s equations Wave equations Lenz s law Integal fom Diffeential fom Phaso fom Bounday conditions
More informationPhysics 2B Chapter 22 Notes - Magnetic Field Spring 2018
Physics B Chapte Notes - Magnetic Field Sping 018 Magnetic Field fom a Long Staight Cuent-Caying Wie In Chapte 11 we looked at Isaac Newton s Law of Gavitation, which established that a gavitational field
More informationTarget Boards, JEE Main & Advanced (IIT), NEET Physics Gauss Law. H. O. D. Physics, Concept Bokaro Centre P. K. Bharti
Page 1 CONCPT: JB-, Nea Jitenda Cinema, City Cente, Bokao www.vidyadishti.og Gauss Law Autho: Panjal K. Bhati (IIT Khaagpu) Mb: 74884484 Taget Boads, J Main & Advanced (IIT), NT 15 Physics Gauss Law Autho:
More informationChapter 7-8 Rotational Motion
Chapte 7-8 Rotational Motion What is a Rigid Body? Rotational Kinematics Angula Velocity ω and Acceleation α Unifom Rotational Motion: Kinematics Unifom Cicula Motion: Kinematics and Dynamics The Toque,
More informationLecture 8 - Gauss s Law
Lectue 8 - Gauss s Law A Puzzle... Example Calculate the potential enegy, pe ion, fo an infinite 1D ionic cystal with sepaation a; that is, a ow of equally spaced chages of magnitude e and altenating sign.
More informationPhysics 2020, Spring 2005 Lab 5 page 1 of 8. Lab 5. Magnetism
Physics 2020, Sping 2005 Lab 5 page 1 of 8 Lab 5. Magnetism PART I: INTRODUCTION TO MAGNETS This week we will begin wok with magnets and the foces that they poduce. By now you ae an expet on setting up
More informationPHY2061 Enriched Physics 2 Lecture Notes. Gauss Law
PHY61 Eniched Physics Lectue Notes Law Disclaime: These lectue notes ae not meant to eplace the couse textbook. The content may be incomplete. ome topics may be unclea. These notes ae only meant to be
More informationMagnetic Dipoles Challenge Problem Solutions
Magnetic Dipoles Challenge Poblem Solutions Poblem 1: Cicle the coect answe. Conside a tiangula loop of wie with sides a and b. The loop caies a cuent I in the diection shown, and is placed in a unifom
More informationChapter Sixteen: Electric Charge and Electric Fields
Chapte Sixteen: Electic Chage and Electic Fields Key Tems Chage Conducto The fundamental electical popety to which the mutual attactions o epulsions between electons and potons ae attibuted. Any mateial
More informationF (-4.32x x10 k) Newtons a = (-4.742x x10 )m/s 9.11x10 kg
P Physics d Quate Test Review KEY k 8.99 x 9 Nm /C 8.85 x - C /Nm e.6 x -9 C milli - mico -6 nano -9 pico - Mega 6 Electostatics. Chage, Field, and Potential a. poton is placed in a unifom electic field
More informationGauss s Law: Circuits
Gauss s Law: Cicuits Can we have excess chage inside in steady state? E suface nˆ A q inside E nˆ A E nˆ A left _ suface ight _ suface q inside 1 Gauss s Law: Junction Between two Wies n 2
More informationThe geometric construction of Ewald sphere and Bragg condition:
The geometic constuction of Ewald sphee and Bagg condition: The constuction of Ewald sphee must be done such that the Bagg condition is satisfied. This can be done as follows: i) Daw a wave vecto k in
More information? this lecture. ? next lecture. What we have learned so far. a Q E F = q E a. F = q v B a. a Q in motion B. db/dt E. de/dt B.
PHY 249 Lectue Notes Chapte 32: Page 1 of 12 What we have leaned so fa a a F q a a in motion F q v a a d/ Ae thee othe "static" chages that can make -field? this lectue d/? next lectue da dl Cuve Cuve
More informationASTR415: Problem Set #6
ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal
More informationToday s Plan. Electric Dipoles. More on Gauss Law. Comment on PDF copies of Lectures. Final iclicker roll-call
Today s Plan lectic Dipoles Moe on Gauss Law Comment on PDF copies of Lectues Final iclicke oll-call lectic Dipoles A positive (q) and negative chage (-q) sepaated by a small distance d. lectic dipole
More informationAP Physics C: Electricity and Magnetism 2003 Scoring Guidelines
AP Physics C: Electicity and Magnetism 3 Scoing Guidelines The mateials included in these files ae intended fo use by AP teaches fo couse and exam pepaation; pemission fo any othe use must be sought fom
More informationForce and Work: Reminder
Electic Potential Foce and Wok: Reminde Displacement d a: initial point b: final point Reminde fom Mechanics: Foce F if thee is a foce acting on an object (e.g. electic foce), this foce may do some wok
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 informationKinetic energy, work, and potential energy. Work, the transfer of energy: force acting through distance: or or
ENERGETICS So fa we have been studying electic foces and fields acting on chages. This is the dynamics of electicity. But now we will tun to the enegetics of electicity, gaining new insights and new methods
More informationTHE MAGNETIC FIELD. This handout covers: The magnetic force between two moving charges. The magnetic field, B, and magnetic field lines
EM 005 Handout 7: The Magnetic ield 1 This handout coes: THE MAGNETIC IELD The magnetic foce between two moing chages The magnetic field,, and magnetic field lines Magnetic flux and Gauss s Law fo Motion
More informationHW #5 Hints. Today. HW #5 Hints. HW #5 Hints. Announcements:
Today HW #5 Hints Announcements: HW and Exta cedit #3 due 2/25 HW hints + Recap the 2nd law of themodynamics Electic and Magnetic Foces and thei unification the Foce Field concept -1-1) The speed at D
More information