# Electrical polarization. Figure 19-5 [1]

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1 Electrical polarization Figure 19-5 [1]

2 Properties of Charge Two types: positive and negative Like charges repel, opposite charges attract Charge is conserved Fundamental particles with charge: electron (negative) and proton (positive) Magnitude of charge on electron: e=1.60 x C (SI unit coulomb, C) Charge is quantized: ±ne, where n=0,1,2,3 (what about quarks?)

3 Coulomb s Law (I) Any two charges exert a force on each other whose magnitude is directly proportional to the product of the magnitude their charges and inversely proportional to the square of the distance between them. Fig 19-7 [1]

4 Coulomb s Law (II) F 4 1 πε 0 q q = (for charges at rest in a vacuum) r Permittivity constant (of vacuum/free space): ε 0 =8.85 x C 2 / (N m 2 ) Principle of superposition applies (vector addition of forces) Compare with Newton s law of gravitation: similar form, but gravity is always attractive

5 Figure 19-9 [1] Electrostatic force field Magnitude of force is proportional to test charge q 0 Define electric field as force per unit charge

6 Summary Charge (properties) Conductors and Insulators Coulomb s law (electrostatic forces) Electric field (force per unit charge)

7 Electric Field Lines Figure [1] Field is not zero here Field is zero at midpoint Figure [1]

8 Field lines for a conductor Figure [1]

9 Electric flux Φ=EAcosθ Units: N m 2 /C Φ= E A A is a vector normal to surface; magnitude is area of surface A More generally, Φ= E d A Figure [1]

10 Gauss s Law If a net charge q is enclosed by an arbitrary surface, the net electric flux Φ through the surface is Φ= q ε 0 Use this to calculate electric field. Most useful when system has some symmetry: Sphere, plane, cylinder Figure 23-8 [2]

11 Summary Electric field: point charges Electric field lines Conductors (properties) Electric flux Gauss s Law: calculate electric fields

12 Electric Potential and Electric Potential Energy Figure 20-2 [1]

13 Electron Microscope Electrons accelerated by electric field Taken from

14 Summary Electric Potential: V Electric Potential Energy: U=qV Electric Field: E= - V/ s (cf. F=qE) For a point charge q: For two point charges q 1 and q 2 : V q q =, E = 4πε r πε r 0 U qq 1 2 qq 1 2 =, F = 4πε r 4πε r 0 0 2

15 Positive point charge placed at origin Electric potential Equipotential surfaces Figures 20-5a and 20-6 [1]

16 Charged spherical shell: radius 1m, charge on surface 1.0 µc V q q =, E = 4πε r 4πε r Figure [2]

17 Conductors of arbitrary shape Thin conducting wire; connects two conducting spheres of radii R and r (with R > r) Model real conductor in (b) as simplified system in (a) Adapted from figure [1]

18 Parallel-Plate Capacitor Connected to battery (not shown) which applies voltage difference V between plates Q C V ε 0 A C= d = general parallel-plate capacitor

19 Dielectrics E E = κ κε 0 A C= d Figure [1] κ ( kappa ) is the dielectric constant; κ=1 in a vacuum, very close to 1 for air, about 80 for water

20 Summary Equipotential surfaces and conductors Capacitors and dielectrics Parallel-Plate Capacitor Electrical energy storage (in electric field)

21 Summary Current Direct-Current (DC) Circuits Resistance: Ohm s Law Energy and Power in Electric Circuits

22 Resistors in series R = R + R + R eq More generally, equivalent resistance is sum of individual resistances Figure 21-6 [1]

23 Resistors in parallel = + + R R R R eq Figure 21-8 [1]

24 Kirchhoff s Rules C E Figure [1] D F Junction rule: algebraic sum of all currents at any junction must be zero. Loop rule: algebraic sum of all potential differences around any closed loop must be zero.

25 RC circuits Figures 21-18, 19, 20 [1]

26 Summary Resistors in series (sum) Resistors in parallel (harmonic mean) Kirchhoff s rules Capacitors in circuits: series, parallel, RC ([RC]=[time])

27 Magnetic Force on Moving Charges F = q v B Figures 22-7 and 22-8 [1]

28 Lorentz Force Law Figure [1] F = q (E+ v B)

29 Bubble Chamber: electron-positron shower images/pow/1998/ jpg Can deduce charge (sign) and mass of particle

30 Mass spectrometer (electrospray): Can calculate mass of protein to within 0.02%

31 Hall effect Velocity selector

32 Magnetic Force on Current-Carrying Wire F = I L B L is in the direction of the current Figure [1]

33 Summary Magnetic field: properties Magnetic force on moving charges: different types of motion Magnetic force due to currents

34 Magnetic Torque Top view Figures and [1] Side view

35 B l =µ 0Ienc Ampère s Law More generally, B d l =µ I 0 enc l is a vector along the closed path μ 0 is the permeability of free space. Its value is 4π x10-7 Units: T m/a Figure [1]

36 Forces between current-carrying wires d L Parallel wires attract; Opposite currents repel F = I LB 2 µ I µ II = IL 2 = 2πd 2πd L Figure [1]

37 Current Loop B(center) = µ I 0 2R R is radius of loop Figure [1]

38 Solenoid B(inside) = µ ni 0 Figure and [1] n=number of turns/unit length

39 Summary Loops of current and torque Ampère s Law Current Loops and Solenoids You should be able to derive magnetic field for simple cases using Ampère s Law

40 Magnetic Flux (I) Φ=BAcosθ Units: T m 2 = 1 weber (wb) Φ= B A A is a vector normal to surface; magnitude is area of surface compare with electric flux Figure 23-3 [1]

41 Magnetic Flux (II) Conceptual Checkpoint 23-1 [1] Which loop has a magnetic flux that changes with time?

42 Faraday s Law of Induction: Electric Guitar pickups Cost: \$2,449 Figure 23-5 [1]

43 Lenz s Law An induced current always flows in a direction so as to oppose the change that caused it. Example: rod in frictionless contact with two vertical wires Figure [1]

44 Summary Faraday s Law of Induction: E dφ = N dt E = induced electromotive force N = number of (tightly wound) turns Φ = magnetic flux minus sign from Lenz s Law

45 Direct current generator (DC dynamo) brushes are fixed in space; commutator rings move with wire From Ordinary Level Physics 4 th ed., A.F. Abbott p

46 Alternating current generator brushes are fixed in space; slip ring always in contact with same brush From Ordinary Level Physics 4 th ed., A.F. Abbott p. 495

47 Inductance and Induced EMF E di = L dt Figure [2]

48 RL circuits Figures and 20 [1] compare RC circuits: charge and τ =RC τ = L R

49 Transformers Figure from the text V V s p = N N s p

50 Summary Inductance RL Circuit ([L/R]=time) Energy Stored in a Magnetic Field Transformers, Motors, Generators

51 Alternating Current (I) V = V ωt max sin I = I ωt max sin Figures 24-1 and 2 [1]

52 Alternating Current (II) Power dissipated in a resistor: P = VI = I R = I Rsin ωt max P = I R< sin t > 2 2 ω av max av I = I 2 rms max Figure 24-4 [1] 2 Imax 2 Pav = R= IrmsR 2

53 Alternating Current: Power Figure [1] P av =< VI > av P = I R av 2 rms P av = 0 e.g. resistor e.g. capacitor, inductor

54 Electricity in the world (I) Some countries have issues: e.g. Brazil (110 V, 115 V, 127 V, 130 V, 220 V or 240 V) e.g. Japan (East: 50Hz; West 60Hz) from

55 Electricity in the world (II) from A B C G M

56 Figure 31-1 [2] LC circuits Oscillations with angular frequency: ω = 1 LC

57 Figure 31-5 [2] RLC circuits Figure [1] Start with charge on capacitor: damped harmonic oscillator Resistor is source of damping (can be underdamped, overdamped or critically damped) Drive oscillations with ac power supply Resonance occurs when the frequency of the power supply is same as the natural frequency of circuit (1/ LC)

58 Summary Alternating voltage and current Root mean square values Power in ac circuits LC and RLC circuits (oscillations and resonance)

59 D = ρ Maxwell s Equations (I) Gauss s Law B= 0 No magnetic monopoles B E= t Faraday and Lenz s Laws D H=J+ Ampère s Law (modified) t

60 Maxwell s Equations (II)---Genesis 1:

61 The Electromagnetic Spectrum c = fλ Figure 25-8 [1] from

62 References [1] J. S. Walker, Physics, 2 nd ed (Pearson/Prentice Hall, Upper Saddle River, 2004). [2]: D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics, 7 th ed; extended (Wiley, New York, 2005).

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