Electricity, Magnetism and Light PHYSICS 208, Instructor: Olga Kocharovskaya

Lectures 1,2 (Ch.21)Electric Charge and Electric Field

1. Introduction• How to solve the problems? • Four types of interactions

2. Electric Properties of the matter Two types of electric charge Conductors and Insulators Coulomb’s Law

3. Electric field

How to solve problems?• Solve many before this one• Solve it yourself• Ask for hints but not for solution• Discuss it with your friends• Think about it before you go to sleep (you may find a solution in your

dream)

• Use symmetry of the problem• Use superposition principle• Do not surrender!• Forget it (not for exam!), then try again• Enjoy the solution!!!

How to make sure your answer is correct?• Get a general (algebraic) solution• Check the units of the answer, make sure you have

units consistency• Check limiting cases • Check an order of magnitude, is it REASONABLE?

(the speed should not be greater then than that of the light in vacuum, a charge should not be smaller than that of electron, a distance is unlikely to be smaller than 10-15 m in our course, etc.)

• Check the answer in the textbook

Four types of interactions

1.Gravity (between massive bodies)

F

g

Gm1m

2

r 2

Planetary systems, Galaxies,Space trajectories

Earth

Weight:F=mg

gF

2. Electromagnetic Interactions ( ELECTRICALLY CHARGED BODIES) Structure of ATOMS

e

e

Positive and negative Ions

Structure of the Molecules

e e

H2 Na+Cl-

ee

Chemical reactions and biological processes

Water is an excellent solvent due to the dipole character of its molecule

Modern Technologies: internet, telecommunications, nanotechnolgies, CD, DVD,

lasers, cell phones,…

Large Hadron Collider (LHC) Counter propagating proton beams accelerated to 7x1012 eVIn search for a dark matter

27 km ring

4.Weak InteractionsHadrons (proton, neutron,…),

colour charge

3.Strong InteractionsLeptons (electron, muon, tau-

lepton, neitrinos)

lepton charge Interactions between elementary particles, using modern EM technologies

Electric Properties of the matter1. Two types of charges: + and – (Ben Franklin,1740)

glass

plastic

silk

fur

2. Quatization of chargeQ=ne, n=1,2,3,…

e is the minimum value of charge

Particle mass charge electron 9.11×10-31kg -1.60×10-19 C (-e)proton 1.672×10-27kg +1.60×10-19C (+e)neutron 1.674×10-27kg 0

SI : [Q]=1C

3. Conservation of Charge:

e e

Na Cl Na+Cl-

ee

N

ii constq

1

Na+ q1=e Cl- q2=-e

q1=0 q2=0 q1+q2=0

4. Three types of materials1. Conductors (free electrons)Metalls, alloys, plasmas

Induction2. Insulators=Dielectrics (bounded electrons)Glass, plastic, paper

Polarization3. Semiconductors (number of free electrons stronglydepends on external conditions such as temperature, electric

field , pressure; under the usual conditions number of electrons is small)

5. Amber effect: Charged and neutral object always attract each other

6. Charging of neutral objects1.By friction: q1=0, q2=0 q1=Q q2=-Q

2. By contactq1=Q q2=0 q1+q2=Q q1=Q/2 q2=Q/2

3. By induction

Coulomb’s Law, 1786

Coulomb’s Law

For an ensemble of charges use a Superposition Principle:

oe rr

kQqF

2

r

rr testsource

0

2

29

0

100.94

1

C

Nmk

2

212

0 10854.8Nm

C

qr

rkQF

N

i i

iitotal

1

0

0r

0r

0r

0r

kgm

kgm

Ce

mGm

ke

F

F

p

e

epg

e

27

31

19

362

1067.1

109

106.1

!10

oe rr

kQqF

2

Example1. Compare the electric and gravity forcesbetween an electron and a proton.

02r

r

GMmFg

Electric Field,

“That one body may act upon another at a distance … is to me so great an absurdity…” I. Newton

Michael Faraday (1791-1867) Two steps:1.Q creates electric field,

2. produces the force on q

oe rr

kQqF

2

02

rr

GMmFg

Coulomb’s Law Newton’s Law

r r

)(rE

)(rEQ

q

FE Qq

Q

orq

FE Qonq

Q

lim

)(rEQ

QQq EqF

QE

0r

0r

Q Mq m

Two steps in more details: the source and test charges

QSource

Q produces electric field at point P indepententely on the presence of charge q at this point:

0202r

r

kQr

r

kQq

q

FE Qq

)(rEQ

produces a force on a test charge q:

1.

2.

02r

r

kqQEqF QQq

SI units of E:[E]=[F]/[q]=N/C

of a point charge)(rE

0202r

r

kQr

r

kQq

q

FE qQ

For charged bodies of finite size atr

02r

r

kQE

∞

E of a dipole: along x axis

-q +q

x0-a

p

22222222 )(

2

)(

4]

)(

1

)(

1[

ax

kpx

ax

axkq

axaxkqEEEtotal

x-aa

x+a

3

2

x

kpE

ax

aqp 2E

E

tE

E of a dipole: along y axis

q -q

-a a

y E

E

tE

3

2/3222/322 )()(

22

y

kpE

ay

ya

kp

ya

kqaEE

total

xtotal

22

22 )(

ya

aCos

CosEE

ya

kQE

x

• Field of a line of charge (along the line)

2)( rz

kdqdE

dza

Qdq

)(]

11[

)(02 arr

kQ

arra

kQ

rz

dz

a

kQE

a

dq

z

x

k

ax

kQE

xa

2222/322

1

)( yx

y

xyx

dy

2x

kQE

ax

22

)( 22

yx

xCos

dECosdE

dE

x

yx

kdQ

E of a half of the ring of charge

dq

dE

2

2/

02

22

22

a

kQdSin

a

kQE

dESindE

Qd

a

k

a

kdqdE

Qd

a

Qaddl

a

Qdq

total

y

Etot

dEy dE

Rx

x

kQ

x

R

x

RE

Rx

x

220

2

0 4])(

2

111[

2

2

(near the disc it looks like an infinite plane)

2

2

R

Q

rdrQ

EdE

ring

ringx

Two infinite planes

0

Electric field lines 1.Tangent is in direction of E

2.Density of lines is proportional to |E|3. Originate on “+” and terminate on “-” charges4. Crossing of E lines is impossible5. Closed lines are impossible in ES

NB: in the general case (i)|E| is not const along E lines(ii)Not the trajectories of the charged particles

2

2

1~|~|

rS

NE

rS

constN

02r

r

kQE

E

E

A positive vs. negative point charge

of a dipoleE

Infinite line of charge

rrl

N

S

NE

1~

2~

Two infinite planes

0

Uniform E : the same direction and magnitude at each pointN=const, S=const, E=const

Motion in a uniform E

-

+v0

e E

Data: electron, , L,v0

Find: 1.trajectory; 2.vf

02

0

20

2

0

20

22

0

0

00tan

,

,

22.2

.1

m

q

v

L

vvv

m

q

m

qEaaTv

v

axaty

TvL

tvx

vaT

v

v

fyf

fy

fy

Fvf

parabola

Electric dipole in a uniform E

EpU

Ep

pESinqdESin

Sind

qE

Fr

tot

tot

2

1.Stable equilibrium

2.Unstable equilibrium

pEU 0

pEU 0