1

2

PHYSICS 632 SUMMER 20109:00 – 10:50 Room 203Electricity, Magnetism

and Light

Richard A. Lindgren, Office Room 302/22

Text: Halliday, Resnick, and Walker, 7’th edition, Extended Version, Starting with Chapter 21 on Charge.

3

Your Goals and Interest• Get a Masters degree• Crossover teaching• Fill in knowledge gaps• Review, learn new teaching ideas• Peer learning• Modeling• Inquiry learning• Group learning• New experiments and demos• Computer technology• Solidify concepts• Learn how to do problems - practice - practice - practice.

4

Assignments and Exams• See syllabus for daily homework assignments using

WebAssign.– Graded Problems on webassign –assignments are up– Ungraded Problems - not on WebAssign– Warm up Problems - also ungraded

• Work on problems in recitation after lecture. • Polling questions in class.• Discuss with TA’s and others in the apartments at night. Due

at 8:00 am next day. • How do you improve problem-solving skills. Lots of practice

and more practice. • Quizzes on second two Wednesdays and one Thursday• There will also be 4 homework assignments due in August

and September. • Final exam at the beginning of September on WebAssign.

Grading

• Homework Problems – 25%• Polling in Class questions – 5%• Quizzes (3) – 2 hours each – 35%• Final exam - 3 hours – 35%

5

6

Class Organization

• Cartoon• Lecture and discussion• Demonstrations• Hand-worked problems on Elmo• Clicker / Polling / Conceptual problems

7

References and other Texts

• Check out Appendices and and back of covers of your text.• Physics for Scientists and Engineers,

– Serway, Jewett• Physics for Scientists and Engineers,

– Fishbane, Gasiorowicz, Thornton• Physics for Scientists & Engineers,

– Giancoli

• Principals of Electricity – Page, Adams

• Calculus-Based Physics II (download)– Schnick– http://www.anselm.edu/internet/physics/cbphysics/downloadsII.html

8

Lecture 1 Charge Ch. 21• Electrostatics: study of electricity when the charges are not in motion• Math Review and Tooling up•Topics

–What is electric charge? –Methods of charging objects. –Electrostatic kit–Instruments to measure charge–Quantization of charge and conservation of charge–Coulombs Law and examples–Principle of superposition and examples

• Demos• Elmo Some Examples• Polling

9

• “In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself more valuable than 20 formulae.” Albert Einstein

Student charged up to 300,000 Volts

10

Charge• What is charge?• How do we visualize it.• We only know charge exists because in experiments electric forces cause objects to move. • Charge is analogous to mass in mechanics. We know how it behaves, but we don’t know what it really is. The same is true for charge..• Need some experiments to get the point across

11

3 protons, 3 neutrons

12

Properties of Elementary Particles.• Electron: charge -1.6 x 10 -19 Coulombs (SI units) mass me= 9.11 x 10 - 31 kg radius < 10 – 18 m • Proton: charge = +1.6 x 10 -19 Coulombs mp= 1.67 x 10-27 kg radius = 0.805 +/-0.011 x 10-15 m • Neutron: charge = 0 • Pions: Three types: charge = + , - , 0 radius = 0.66 +/- 0.01 x 10-15 m

• Quarks: Point objects. Confined to the proton and neutron,– Not free– Proton (uud) charge = 2/3e + 2/3e -1/3e = +e– Neutron (udd) charge = 2/3e -1/3e -1/3e = 0

13

• Normally atoms are in the lowest energy state. This means that the material is electrically neutral. You have the same number of electrons as protons in the material.

• How do we change this?

• How do we add more electrons than protons or remove electrons?

• There are several different ways.

How do materials get a net charge?

14

3

15

Charging using the UVa Electrostatic Kit

16

- - - - - -

- - -- - -

Two teflon rods on spinner

17

Detect Charge using UVa Electroscope

18

Summary Comments

•Silk(+) on teflon(-)– Leads to Conservation of Charge

•Charged objects always attract neutral objects– Leads to electric dipoles

•Show Triboelectric series–In air everything gets more negative

• Not only chemical composition important, structure of surface is important - monolayer of molecules involved, quantum effect.(nanotechnology)

19

Triboelectric serieshttp://www.sciencejoywagon.com/physicszone/lesson/07elecst/static/triboele.htm

Positive (Lose electrons easily)AirHuman HandsAsbestosRabbit FurGlassMicaAcrylicHuman HairNylonWoolFurLeadSilkAluminumPaperCotton

SteelWoodAmberSealing WaxHard RubberNickel, CopperBrass, SilverGold, PlatinumSulfurAcetate, RayonPolyesterStyreneOrlonSaranBalloonPolyurethanePolypropyleneVinyl (PVC)SiliconTeflonNegative (Gains electrons easily)

20

More on our Model of electricity

1cm long and a radius of 0,005 cm1cm long and a radius of 0,005 cm

Copper atom:Copper atom:

Z=29(protons), N= 34(neutrons),Z=29(protons), N= 34(neutrons),

29 Electrons29 Electrons

Carbon or diamond - poor conductor

Copper (Face Centered Cube) - good conductor

Consider solid material like a piece of copper wire. The proton core is fixed in position in a lattice like structure. In a conductor, the valence electrons are free to move about. How many electrons are free to move about?

21

Electrostatics is based on 4 four empirical facts

• Conservation of charge

• Quantization of charge (Lets get more quantitative)

• Coulombs Law

• The principle of superposition

22

Conservation of charge

• Rubbing does not create charge, it is transferred from object to another

• Teflon negative - silk positive• Acrylic positive - silk negative Demo: Show electronic electroscope with cage: gives magnitude and sign of charge. Use teflon and silk to show + and -.

• Electromagnetic reactions p++e- = p++pi0 + e-

• Radioactive decay 238U92 = 234Th90 + 4He2

• High energy particle reactions p+ + n0 = d+ + γ0

23

What is meant by quantization of charge?

• Discovered in 1911 by Robert A. Millikan in the oil drop experiment.He determined that the difference in charges on different oil drops was always a multiple of

• The unit of charge is so tiny that we will never notice it comes in indivisible lumps. The elementary unit is defined as

• Electron charge is - e• Proton charge is + e

• Example: Suppose in a typical experiment we charge an object up with a nanoCoulomb of charge (Q = 10-9 C). How many elementary units, N, of charge is this?

N=

Qe=

10−9C+1.6 ×10−19C

=0.625 ×1010 =6.25 ×109

1.602 ×10−19C

e =+1.602 ×10−19C

24

Coulombs Law

In 1785 Charles Augustin Coulomb reported in the Royal Academy Memoires using a torsion balance two charged mulberry pithballs repelled each other with a force that is inversely proportional to the distance .

q2q1 r

Lab ExperimentLab Experiment

Spheres same as pointsSpheres same as points

F = kq1q2

r2 where k = 8.99 ×109Nm 2 /C2

Point chargesPoint charges

Also k= 1

4πe0

where e0= 8.85 ×10-12 C2 / N. m 2

Electrical Permittivity of Vacuum

F=Gm1m2

r2

Coulomb constant

25

Coulombs Law

q2q1 r

RepulsionRepulsion

RepulsionRepulsion

AttractionAttraction

F=kq1q2

r2 where k = 8.99 ×109Nm 2 /C2

++ ++

++

-- --

--

Charges can be positive or negative

In solving problems you have to take account of whether the force is attractive or repulsive

26

Coulombs Law Two Positive Charges

F=kq1q2

r2

+1 nC+1 nC 1 cmq2q1 r

• What is the magnitude of the force between two positive charges, each 1 nanoCoulomb, and 1cm apart in a typical demo?

RepulsionRepulsion

F =8.99 ×109 Nm 2

C2( ) 10−9c( )2

10−2m( )2 =9 ×10−5N

• What is the direction of the force?+1 nC+1 nC 1 cm

What is the direction of the force F1 on charge q1 and F2 on charge q2

in unit vector notation in rectangular coordinates?

27

F =8.99 ×109 Nm 2

C2( ) 10−9c( )2

10−2m( )2 =9 ×10−5N

1 nC1 nC 1 cm

What is the direction of the force F1 on charge q1 and F2 on charge q2 in unit vector notation rectangular coordinates?

x

y

j

i

F1 =−9 ×10−5N i

1 2

F2 =+9 ×10−5N i

28

F=kq2

(r)2

F≈kq2

(r+2R)2

Demo: Show uniformity of charge around sphere using electrometer.

Demo: Show charging spheres by induction using electrometer

29

Show induction using two conducting spheres and Electrometer

30

31

Use Principle of SuperpositionAssume you can use the Coulomb Laws for each pair of charges and add up the results algebraically. This is true for any number of charges. Coulombs Law does not change when you add a 3rd charge near the first two charges.

Consider the following example.Three charges lie on the x axis: q1=+25 nC at the origin, q2= -12 nC at x = 2m, q3=+18 nC at x=3 m. What is the net force on q1 and the direction of the force?

Method 1We simply compute the magnitude of the force for each charge and put in the sign according to the direction of the force using common sense and add them up algebraically. Choose some direction to be positive. Solve without using unit vector notation.

1 2x

3

q1=+25 nC q3=+18 nCq2= -12 nC

Principle of Superposition

32

=+6.74 × 10−7 N - 4.49 ×10−7 N

=+2.25 × 10−7N (Directed to the right in the positive x direction)

rF12 = 8.99 ×109 Nm 2

C2( )(25 ×10−9C)(12 ×10−9C)

(2m )2=6.74 ×10−7N

rF1,net

Attraction positive x direction

Repulsion negative x direction

1 2x

3

q1=+25 nC q3=+18 nCq2= -12 nC

is the magnitude of the force acting on particle 1 by particle 2. rF12

rF13 = 8.99 ×109 Nm 2

C2( )(25 ×10−9C)(18 ×10−9C)

(3m )2=4.49 ×10−7N

rF13 is the magnitude of the force acting on particle 1 by particle 3.

rF1,net =

rF1,2 +

rF1,3

33

Some texts use the following notation. Thornton et al.

vF12 =k

q1 q2

r2 r12

where: 12Fv is the force acting on particle 1 by particle 2, r12 is a unit vector and k, q1, and q2 are defined as before (the Coulomb constant, the charge on particle 1, and the

charge on particle 2 respectively).

rF12 =

8.99 ×109 Nm 2

C2( ) 10−9c( ) 10−9c( )

10−2m( )2 r12 =+9 ×10−5N r12

The positive sign means the force on q2 is in the same direction as the unit vector

.q1 .q2

r

r12

rF12

34

Method 2: Now use unit vector notation. Same problem of three charges in a line. What is the net force on q1 and the direction of the force? When you have more than one charge, it is customary to use a different notation. This also allows you to generalize when the charges are not all in a line.

=−6.74 ×10−7 N r + 4.49 × 10−7 N r

(Directed to the right)

rF1,net =

rF12 +

rF13

rF1,net =k

q1 q2

r122 r12 + k

q1 q3

r132 r13

= 8.99 ×109 Nm2

C2( )(25 × 10−9C)(−12 ×10−9C)

(2m)2 r + 8.99 ×109 Nm2

C2( )(25 × 10−9C)(18 ×10−9C)

(3m)2 r

r =r12 =r13

1 2x

3

r12 r13

=−2.25 ×10−7N r rF1,net

Note put in sign of charge

35

Force on one charge q1 due to many charges lying in a plane

- q3

+q2+q1

r13

r12

r12

r13

-q3

+q2+q1

rF13

rF12

rFnet

rFnet =

rF12 +

rF13

rF12 =

kq1q2

(r12 )2 r12

rF13 =

kq1q3

(r13)2 r13

rFnet =

rF1i

i=2

N

∑

rFnet

rF13

rF12

36

q1= + 1 nC q2= + 1 nC

+y

+x

5 cm2 cm

1 cm

q3= - 2 nC

Example Consider three point charges in a plane. What is the magnitude of the net force on q1 and in what direction?

37

Find magnitude of and the angle relative to x axis.

Method 3: Find x and y components of force on q1 due to q2 and q3 and add them up.

rF13

rFnet

rF12

rFnet

q1= + 1 nC q2= + 1 nC

+y

+x

5 cm2 cm

1 cm

q3= - 2 nC

38

Magnitude of Force due to q3

F13y

F13x

q€

x and y Components of force due to q3

rF13 =8.99 ×109 Nm 2

C2

(2 ×10−9C)(1×10−9C)( 5 ×10−2m )2

=0.36 ×10−4N

deg 43.63)(tan value axis-xvalue axis-ytan 1

21- ==q⇒=q

F13x =rF13 cosq =(0.36 ×10−4N)(cos63.43)=0.161×10−4N

F13y =rF13 sinq =(0.36 ×10−4N)(sin63.43)=0.322 ×10−4N

Find x and y Components of force due to q2

F12x =−8.99 ×109 Nm 2

C2

(10−9C)2

(10−2m )2=−9 ×10−5N

0F y12 =

Example Cont

q1= + 1 nC q2= + 1 nC

+y

+x

5 cm2 cm

1 cm

q3= - 2 nC

q rF13

rF13

rF12

negative x direction

39

Fnet = Fxnet2 + Fynet

2 = ((0.739)2 + (0.322)2 )× (10−4 )2N

Example Cont. Total force along the x-axis

Fxnet =F12x + F13x =(−0.9 ×10−4 + 0.161×10−4 )N =−0.739 ×10−4N

Total force along the y-axis

Fynet =F12y+ F13y =(0 + 0.322 ×10−4 )N =0.322 ×10−4N

tanq1 =Fynet

Fxnet

q1 =tan−1 Fynet

Fxnet

⎛⎝⎜

⎞⎠⎟

q1 = tan−1 0.322 × 10−4N−0.739 × 10−4N

⎛⎝⎜

⎞⎠⎟

q1 = −23.5° from the -x axis

rF net =+0.806 ×10-4Nq1

q1= + 1 nC

+y

+x

5 cm

1 cm

q3= - 2 nC

q

q2= + 1 nC

rF13

rF12

rFnet

Magnitude

Direction

40

Example Two Pennies without electrons

What is the force between two 3 gm pennies one meter apart if we remove all the electrons from the copper atoms? Can we neglect the gravitational force between the pennies?

41

In an atom can we neglect the gravitational force between the electrons and protons? What is the ratio of Coulomb’s electric force to Newton’s gravity force for 2 electrons separated by a

distance r ?

Fc

Fg

=ke2

Gm2

qq r mm r

Fg =Gmm

r2Fc =keer2

Fc

Fg

=8.99 ×109 Nm 2

C2( ) 1.6 ×10−19C( )2

6.67 ×10−11 Nm 2

kg2( ) 9.1×10−31kg( )2

=4.2 ×1042

Huge number - pure number - no units

42

Why are neutral objects always attracted to positive or negative charged objects.

For example:•Rubbed balloon is attracted to wall•Comb is attracted to small bits of paper•Clothes in the dryer stick together.

Demo: Put 2 x 4 on glass and move it using charged teflon rod.

What is the explanation of all of these phenomena?

43

Explanation: The neutral objects atoms and molecules orientthemselves in the following way so that the Coulomb forces due to attraction are greater than those due to repulsion because the latter are further away. (Inverse square Law)

++++++

Acrylic Rod Wooden block

++++++

------

++++++

Acrylic Rod Wooden block

AttractionRepulsion

Attractive forces >> Repulsive Forces

221

rqkqF =

44

Demonstration: Hanging charged pith ball– First attraction by induction, – Then contact, then conduction of charge, then repulsion–Two equally charged pith balls

Problem for Recitation: Two equally charged hanging pith balls •Two equally charged pith balls mass 0.2 mg are in equilibrium as shown below. If d=2.0 cm and L= 20 cm, what is the charge q on each ball?

L

d

45

Force on a charge due to an infinitely long wire.Charge Q is uniformly distributed on the infinite wire with charge density . We choose the Y-axis through the line charge and the X-axis through the point charge. Now, because the line charge is infinite and straight (on Y-axis), we can assume the X-axis is the mid-point of the infinite wire.

Then by Coulomb’s law for the small line segment dy

d

rF =

kqdQr2

r but dQ =dy ⇒ drF=

kqdyr2

r

Resolving the forces into its components:

∫∫∫∫ =+== 0dFsymmetry by but dFjdFidFF yyx

As it is can be seen that the y-component of the force exerted by the top half of the infinite wire will cancel the y-component force exerted by the bottom half of the infinite wire.

+L

-L

0 xdF

dFydF

x

yr

dy

r

46

Force on a charge due to an infinitely long wire cont.

r cos)yx(

dykqFL

L22∫

+

−

q+=

r So, F = dFx∫ = cosqdF∫

222 yxr also +=

)yx(xcos

22 +=q

∫+

− +=

L

L22 2

3

)yx(dyxkqF

xkq2F ,So =

You can also use polar coordinates for this integration.

-L

0 xdF

dFydF

x

yr

dy

+L

€

Now, dy

(y 2 + x 2)32

−L

+L

∫ =2L

x 2 L2 + x 2

222 xLxLxkq2F ,So+

=

∞→L wire,infinite an for ,Now

€

So, F = 2kqλx

1

1+ x 2

L2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

Integration

47€

Now, dy

(y 2 + x 2)32

−L

+L

∫ =2L

x 2 L2 + x 2

L=0.1 mx=.05 m Area under the curve

xy

48

Am J. Phys. 65,846(1977)

0 1 2 3 4 5

Charge in

nanocouombs/volt/cm

How is charge distributed along a conducting rod?No such thing as a uniformly charged metal rod.

Click on C1_21_Charge

49

+++

+++

+++

+++

mg

Fc = kq2/r2

Fc = kq2/r2

q

q

q

q

Pivotpoint

How Does the Electroscope Work?

Consist of two electrically connected conductors with pivot point above cm.

50

Charged Hair Van de Graaff Demo

• How does the Van de Graaff produce the spark?• What upward forces are keeping your hair up?• How are these forces produced?• Why do the hair strands spread out from each other?• Why do they spread out radially from the head?• Is hair a conductor or insulator? How can we find out? Does

it depend if is wet or dry.

• Need a female teacher to come forward.

51

I-clickers and Polling