Electrical polarization

Figure 19-5 [1]

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 10-19 C (SI unit coulomb, C) • Charge is quantized: ±ne, where n=0,1,2,3… (what about quarks?)

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.

Coulomb’s Law (I)

Fig 19-7 [1]

Coulomb’s Law (II)

1 22

0

14

q qF

rπε= (for charges at rest

in a vacuum)

•Permittivity constant (of vacuum/free space): ε0=8.85 x 10-12 C2/ (N m2)

•Principle of superposition applies (vector addition of forces) •Compare with Newton’s law of gravitation: similar form, but gravity is always attractive

Electrostatic force field

Figure 19-9 [1]

Magnitude of force is proportional to test charge q0

Define electric field as force per unit charge

Summary

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

Figure 19-14 [1]

Figure 19-17 [1]

Field is zero at midpoint

Field is not zero here

Electric Field Lines

Field lines for a conductor

Figure 19-20 [1]

Figure 19-23 [1]

Electric flux

cosEA θΦ =Units: N m2/C

Φ = ⋅E A

dΦ = ⋅∫ E A

More generally, A

A is a vector normal to surface; magnitude is area of surface

Gauss’s Law

If a net charge q is enclosed by an arbitrary surface, the net electric flux Φ through the surface is

0

qε

Φ =

Use this to calculate electric field. Most useful when system has some symmetry: Sphere, plane, cylinder

Figure 23-8 [2]

Summary

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

Electric Potential and Electric Potential Energy

Figure 20-2 [1]

Electron Microscope

Taken from http://www-outreach.phy.cam.ac.uk/paw2004/exhibitor/microscope_facility.htm

Electrons accelerated by electric field

Summary

• Electric Potential: V • Electric Potential Energy: U=qV (cf. F=qE) • Electric Field: E= -∆V/∆s

, 24 40 0

q qV Er rπε πε

= =

For a point charge q: For two point charges q1 and q2:

1 2 1 22

0 0

, 4 4q q q qU F

r rπε πε= =

Figures 20-5a and 20-6 [1]

Electric potential

Positive point charge placed at origin

Equipotential surfaces

Charged spherical shell: radius 1m, charge on surface 1.0 µC

Figure 24-18 [2]

20 0

, 4 4

q qV Er rπε πε

= =

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 20-10 [1]

Parallel-Plate Capacitor

Connected to battery (not shown) which applies voltage difference V between plates

0

=

QCV

ACd

ε

= general

parallel-plate capacitor

Dielectrics

Figure 20-15 [1]

0

=

EE

ACd

κκε

=

κ (“kappa”) is the dielectric constant; κ=1 in a vacuum, very close to 1 for air, about 80 for water

Summary

• Equipotential surfaces and conductors

• Capacitors and dielectrics

• Parallel-Plate Capacitor

• Electrical energy storage (in electric field)

Summary

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

Resistors in series

1 2 3eqR R R R= + +

Figure 21-6 [1]

More generally, equivalent resistance is sum of individual resistances

Resistors in parallel

Figure 21-8 [1]

1 2 3

1 1 1 1

eqR R R R= + +

Kirchhoff’s Rules

C

D

E

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.

Figure 21-14 [1]

RC circuits

Figures 21-18, 19, 20 [1]

Summary

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

Magnetic Force on Moving Charges

F = q v × B

Figures 22-7 and 22-8 [1]

Lorentz Force Law

F = q (E+ v × B)

Figure 22-10 [1]

http://hepweb.rl.ac.uk/ppUKpics/ images/POW/1998/980318.jpg

Bubble Chamber: electron-positron shower

Can deduce charge (sign) and mass of particle

Mass spectrometer (electrospray):

Can calculate mass of protein to within 0.02%

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/

Hall effect

Velocity selector

Magnetic Force on Current-Carrying Wire

F = I L × B

L is in the direction of the current

Figure 22-15 [1]

Summary

• Magnetic field: properties • Magnetic force on moving charges:

different types of motion • Magnetic force due to currents

Top view

Side view

Magnetic Torque

Figures 22-16 and 22-17 [1]

Ampère’s Law

μ0 is the permeability of free space. Its value is 4π x10-7 Units: T m/A

0 encd Iµ⋅ =∫ B l

More generally,

l is a vector along the closed path

0 encB l Iµ∆ =∑

Figure 22-22 [1]

Figure 22-24 [1]

Forces between current-carrying wires

Parallel wires attract; Opposite currents repel

d

L

2

0 1 0 1 22

2 2

F I LBI I II L Ld d

µ µπ π

=

= =

Current Loop

0 (center)2

IBR

µ=

R is radius of loop

Figure 22-25 [1]

Solenoid

0 (inside)B nIµ=

n=number of turns/unit length Figure 22-27 and 22-28 [1]

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

cosBA θΦ =Units: T m2 = 1 weber (wb)

Φ = ⋅B A

compare with electric flux

A is a vector normal to surface; magnitude is area of surface

Figure 23-3 [1]

Magnetic Flux (I)

Magnetic Flux (II)

Which loop has a magnetic flux that changes with time?

Conceptual Checkpoint 23-1 [1]

Faraday’s Law of Induction: Electric Guitar

pickups

Cost: $2,449

http://www.gibsoncustom.com; Figure 23-5 [1]

Lenz’s Law

An induced current always flows in a direction so as to oppose the change that caused it.

Figure 23-11 [1]

Example: rod in frictionless contact with two vertical wires

Summary

• Faraday’s Law of Induction:

dNdtΦ

= −E

E = induced electromotive force N = number of (tightly wound) turns Φ = magnetic flux minus sign from Lenz’s Law

Direct current generator (DC dynamo)

brushes are fixed in space; commutator rings move with wire

From “Ordinary Level Physics” 4th ed., A.F. Abbott p. 496-497

Alternating current generator

brushes are fixed in space; slip ring always in contact with same brush From “Ordinary Level Physics”

4th ed., A.F. Abbott p. 495

Inductance and Induced EMF

Figure 30-17 [2]

dILdt

= −E

RL circuits Figures 23-19 and 20 [1]

LR

τ =compare RC circuits: charge and τ =RC

Transformers

Figure 23-22 from the text

s s

p p

V NV N

=

Summary

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

Alternating Current (I)

Figures 24-1 and 2 [1]

max sinV V tω=

max sinI I tω=

rms max 2I I=

Alternating Current (II)

2 2 2max

2 2av max av

22max

av rms

sin

sin

2

P VI I R I R t

P I R t

IP R I R

ω

ω

= = =

= < >

= =

Power dissipated in a resistor:

Figure 24-4 [1]

Alternating Current: Power

e.g. resistor e.g. capacitor, inductor

av 0P =2av rmsP I R=

av avP VI=< >Figure 24-12 [1]

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 http://en.wikipedia.org

Electricity in the world (II)

A

B

C G M

from http://en.wikipedia.org

LC circuits

Oscillations with angular frequency: 1LC

ω =

Figure 31-1 [2]

RLC circuits Figure 24-20 [1] Figure 31-5 [2]

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)

Summary

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

Maxwell’s Equations (I)

ρ0

t

t

∇ ⋅ =∇ ⋅

∂∇× −

∂∂

∇×∂

DB =

BE =

DH = J +

Gauss’s Law

No magnetic monopoles

Faraday and Lenz’s Laws

Ampère’s Law (modified)

Maxwell’s Equations (II)---Genesis 1: 3

http://www.cafepress.com/; http://www.thegiftedchildlearning.com/ http://www.gaftee.com/

The Electromagnetic Spectrum

Figure 25-8 [1] c f λ=

from http://www.pa.msu.edu/courses/2000spring/PHY232/lectures/emwaves/visible.html

References

• [1] J. S. Walker, Physics, 2nd ed (Pearson/Prentice Hall, Upper Saddle River, 2004).

• [2]: D. Halliday, R. Resnick and J. Walker, Fundamentals

of Physics, 7th ed; extended (Wiley, New York, 2005).