Electromagnetism Zhu Jiongming Department of Physics Shanghai Teachers University

Electromagnetism Chapter 1 Electric Field Chapter 2 Conductors Chapter 3 Dielectrics Chapter 4 Direct-Current CircuitsDirect-Current Circuits Chapter 5 Magnetic Field Chapter 6 Electromagnetic Induction Chapter 7 Magnetic Materials Chapter 8 Alternating Current Chapter 9 Electromagnetic Waves

Chapter 4 Direct-Current Circuits §1. Electric Current, Direct-CurrentElectric Current, Direct-Current §2. Direct-Current CircuitsDirect-Current Circuits §3. Ohm’s Law Joule’s LawOhm’s Law Joule’s Law §4. Resistors in Series or ParallelResistors in Series or Parallel §5. Measurement of Current, Voltage and ResistanceMeasurement of Current, Voltage and Resistance §6. Source and Electromotive Force ( emf )Source and Electromotive Force ( emf ) §7. Kirchhoff’s RulesKirchhoff’s Rules §8. Network Circuit with Two endsNetwork Circuit with Two ends

§1. Electric Current, Direct-Current 1. Current 、 Current Intensity 、 Current DensityCurrent 、 Current Intensity 、 Current Density  Electric Current  Current Intensity  Current Density Current Density 2. Conservation of Electric ChargeConservation of Electric Charge 3. Direct-Current and Electric FieldDirect-Current and Electric Field

F Current Intensity —— charge flowing through the area per unit time Unit ： A （ Ampere ）, mA （ A ）,  A （ A ） F Current Density —— Vector  Direction ： positive charge at that point  Magnitude ： I per unit area perpendicular 1. Current and Current Density F Current —— motion of charged particles  Not random motion  Direction ： same as positive charges I （ whole cross section ） （ a point on cross section ）

Current Density Same I in a wire ， not at every point ：  Direction at A 、 B  Velocity at S 1 、 S 2 ∵ S 1 > S 2 ∴ I / S 1 < I / S 2 F Current density ： describe every point in a conductor （ vector function of points ） S1S1 S2S2 A B ( I is the flux of j ) n  j dSdS dSdS

2. Conservation of Electric Charge （ outside conductors j = 0 ） S2S2 S1S1  Left ： the charge flowing out of S per unit time  Right ： decreasing rate of charge within S —— Expression of Conservation of Electric Charge （ Compare with ： ） （ S : any closed surface ）

 at first: U A  U B E  0 j  0  at last: U A = U B E = 0 j = 0 Condition ：  、  not changing with time ，即 3. Direct-Current and Electric Field F Current density ： j ( x, y, z; t ) F Steady current ： j not changing with time t j  E  charge distribution  、  not changing Ex. ： conducting spheres A 、 B connected with a wire A q0q0 B q = 0 （ S : any closed surface ） Caution ： q not changing ， but j  0 j –line is closed

Electric Field of a Direct-Current F Identity ： distribution of q and E not changing F Difference ：  Electrostatic Field —— charges not moving  Field of Steady Current —— charges moving Both of them have the same electrical properties. Gauss’s Law 、 Closed Path Law ( of Electrostatic Fields ) are also valid in the fields of steady currents.

Exercises p.167 /

§2. Direct-Current Circuits 1. Electric CircuitsElectric Circuits 2. Direct-Current CircuitsDirect-Current Circuits

 path ： elements in series  junction ： connecting 3 or more paths 1. Electric Circuits F Circuit ： path of charge wire elements source loads Single loop no junctions 3 paths 2 junctions B A

2. Direct-Current Circuits F Steady current —— Direct-Current Circuits  Same current in a path I S1S1 S2S2 net current outnet current in I1I1 I3I3 I2I2 I4I4 I5I5 Kirchhoff’s Junction Rule  Algebraic sum of the currents into any junction is zero

§3. Ohm’s Law Joule’s Law 1. Ohm’s Law 、 ResistanceOhm’s Law 、 Resistance 2. ResistivityResistivity 3. Joule’s LawJoule’s Law 4. Electrical PowerElectrical Power 5. ExamplesExamples 6. Theory of Metallic ConductionTheory of Metallic Conduction

Caution ： (1) Current-Voltage relation curve (2) Only for a resistor obeying Ohm’s Law Units ： 1  = 1 Simens = 1. Ohm’s Law 、 Resistance F Experiments show ： I  U write I = G U G Conductance or I = U / RR Resistance U （伏） I （安）

 0,  constants ，（ see table on p.191 ） F Supper conductor ： T < T c 时， R  0 F Metallic conductors ：  t =  0 ( 1 +  t ) t     2. Resistivity F Resistivity  ( of a conductor )  Uniform cylinder ： （ ion vibration weaker ） （ ion vibration stronger ）  Different cross-section ： F Conductivity  r dldl

3. Joule’s Law F Heat flows out as a current passing through the conductor : Q = I 2 R t F In the conductor ：  The field accelerates electrons  The electrons collide with ions  The ions vibrate strongly  Temperature increases and heat goes out F Energy ： work A done by E A  Kinetic energy of electrons  Heat energy of ions  heat = qU = I tU= I t I R= I 2 R t = Q

F Heat effect of current  Application ： electric heater 、 light bulb  Harmful ： overheated and damaged F 额定 current （额定 voltage 、 power rating ）  Resistor ： 4 k , 1 W — 4. Electrical Power F Electrical Power —— energy output per unit time energy output = work done by field A = I U t  Bulb ： 220 V, 40 W ——

5. Example F （略）

6. Theory of Metallic Conduction F Free-electron Gas  Temperature, random motion v  Electric field, drift motion u （ derivative form of Ohm’s Law ） （ integral form: U = IR ）

Exercises p.168 / , 3, 4, 5, 7

§4. Source and Electromotive Force 1. Non-electrostatic Force  No Steady Current with only Electrostatic ForceNo Steady Current with only Electrostatic Force  Non-electrostatic ForceNon-electrostatic Force  Source in an ‘Open Circuit’Source in an ‘Open Circuit’  Closed CircuitClosed Circuit  Non-electrostatic FieldsNon-electrostatic Fields 2. Electromotive Force andElectromotive Force and Ohm’s Law for a Complete Circuit with a Source 3. ExamplesExamples

No Steady Current without a Source F 2 points in a closed path ： A 、 B F assuming an electric field ： E F force exerting on a charge ： F = qE F Moving q as a current ： I F If I ： A  B then U A > U B F Closed path Law ： BA I The current can not flow from B to A. There will be no steady current with only electrostatic forces —— must add a source between A and B. 电源

F Circuit opened  F n makes q move B  A  - q at B ， +q at A  E 、 F （ electrostatic field, force ） Source in an ‘Open Circuit’ F Inside a source, q moves ： B  A F A non-electrostatic force F n directed B  A is needed （ chemical or electromagnetic etc. ） source BA q F非F非 F  F n retains ， F   until F = F n ， q stop moving  terminal A ， high potential ， positive terminal B ， low potential ， negative

Closed Circuit, Non-electrostatic Fields F Closed circuit —— source of emf + external circuit  external circuit ： electrostatic force F ， +q ： A  B  inside source ： F < F n ， +q ： B  A —— keep in a balance F Non-electrostatic field E n ：  external circuit ： j =  E ( A  B )  inside source ： j =  ( E + E n ) ( B  A )

2. Emf and Ohm’s Law In source j /  = E + E n Integral ： B  A ( U BA = - U AB terminal voltage ) ( Electromotive force ) （ r internal resistance ） ( Ohm’s Law in a complete circuit )

Example （ p.136 /[ Ex. 2 ] ） Eight same sources of emf are connected. Find the terminal voltage between A and B. Sol. ： assume  、 r symmetry ， the terminal voltage for every source is the same A B

Exercises p.169 / , 3, 5, 7

§5. Kirchhoff’s Rules Simple Circuits and Complicated Circuits 1. Kirchhoff’s Junction RuleKirchhoff’s Junction Rule 2. Kirchhoff’s Loop RuleKirchhoff’s Loop Rule 3. Problem-Solving StrategyProblem-Solving Strategy 4. ExamplesExamples

Simple and Complicated Circuits F Simple Circuits ： series-parallel combinations  reduced  calculate with Ohm’s Law F Complicated Circuits ： can not be reduced ， Ex. ： (1) “ Bridge ” circuit ： 5 resistors (2) 2 or more branches in parallel contain sources (2) (1)

1. Kirchhoff’s Junction Rule Junction Rule—— currents in = currents out  n junctions ， n - 1 independent equations F Assume a direction for every unknown current ， solution  positive ， actual direction is same  negative ， opposite to the assumed A I2I2 I3I3 I1I1 I 1 + I 3 - I 2 = 0 F Mark the assumed direction on diagram F Equations using +/- for in/ out a junction respectively ( Suppose there are n junctions )

2. Kirchhoff’s Loop Rule Loop Rule —— algebraic sum of potential differences = 0  n junctions ， p paths ， p -n + 1 independent loops Ex.Ex. F Assume a direction for an independent loop sign of source 、 current : + for same direction, - for opposite direction ( Direction of a source ： negative  positive ) +  - F Closed path Law ： expressed as ： （ Set a Loop Equation for every loop ）Loop Equation

Independent Loops n junctions ， p paths ， p -n + 1 independent loops （ independent loop includes at least a new path ） Ex. ： 6 loops, 3 independent 3 junctions n = 3 5 paths p = 5 m independent loops m = p - n + 1 = = 3 2 junction equs.+ 3 loop equs. = 5 independent equs. determine the unknown currents of 5 paths ( n - 1) + ( p -n + 1 ) = p BACK

Loop Rule Closed path Law ： I1I1 I2I2 I3I3 A C B B 11 22 R1R1 R2R2 R3R3 B’ A’

3. Problem-Solving Strategy (1) Assume direction for current on every branch path, and mark it on diagram (2) For n junctions ， set n - 1 junction equations (3) For p paths ， chose m = p - n+1 independent loops (4) Assume direction for every loop ， and mark it (5) Set m loop equations (6) Solve the p equations (7) Determine the actual direction for every path according to its sign ( + or - )

Example （ p.142 /[ Ex.1 ] ） Known ：  1 = 32 V,  2 = 24 V, R 1 = 5 , R 2 = 6 , R 3 = 54  Find ： I 1, I 2, I 3 Sol. ： n = 2, m = 2 11 22 R1R1 R2R2 R3R3 I1I1 I2I2 I3I3 I 1 + I 2 - I 3 = 0 ① 5I 1 - 6I 2 = 8 ② 6I I 3 = 24 ③ I 1 = 1A  I 2 = - 0.5A  I 3 = 0.5A  I 1 + I 2 - I 3 = 0  1 -  2 = I 1 R 1 - I 2 R 2  2 = I 2 R 2 + I 3 R 3 ①  54+ ③： 54I I 2 = 24 ④ ②  10+ ④： 104I 1 = 104

Exercises p.171 / , 3

§8. Network Circuit with Two ends