The study of electric chargesElectrostatics

Introduction• Did you ever run a comb through your hair? What do

you notice.• What causes the paper holes to jump onto the comb?• There are electrical forces that are in place due to the

presence of charge on the comb.

The Atom• An atom consists of

various charged and uncharged particles.

• The central region is called the nucleus.

• Protons (+) and neutrons make up the nucleus.

• Electrons (-) move around the nucleus in an orbital path.

Nucleus

NeutronsProtons (+)

Electrons (-)

The Significance of Charge• As mentioned before, protons

are positive and electrons are negative.

• An atom with balanced charges is considered neutral.

• The overall charge can be changed by adding or removing electrons. This makes the atom an ion.

Overall Charge:

(Neutral Atom)(Positive Ion)(Negative Ion)

Add e- Take e-

01 1

Sample Problem (Atomic Charge)• An helium atom has a net electric charge of -

8.0x10-19C.• Is it neutral or an ion?• Are there extra electrons or a shortage of them?• How many extra electrons are there?

– Charge Per e-: -1.60*10-19C

# Net

e

qeq

19

19

8.0 10#1.6 10

CeC

# 5e

Sample Problem• How many excess electrons are on a ball that

has a charge of q = -4x10-17C?

# Net

e

qeq

17

19

4.0 10#1.6 10

CeC

# 250e

Sample Problem (Atomic Charge)

• An atom has a net electric charge of 4.8x10-19C.• Are there extra electrons or a shortage of them?• How many electrons short is this atom?• Draw this atom given it is Boron.

Electrostatic Demo’s• Tape• Electroscope• Pith Balls

Electric Forces• Charges exert a force on other charges

Like Charges Repel

Opposites Attract

Actual Charge of Protons/Electrons• Recall, charge is measured in Coulombs (C).• Even though protons and electrons are very

small, they still have charge.• Let us use q as a variable for charge.

Electron Proton

191.60 10electronq C 191.60 10protonq C

How do atoms get charged?

• Work can remove electrons from the atom.– Results in a positively charged atom

• The free Electron can be transferred to another atom.– Results in negatively charged atoms

Separating Charge• Charges are balanced in neutral objects.• Work must be done to separate charge (free electrons).• Once charge is separated, it can be used in

experiments.

Separation of Charge• Bring a charge rod near a neutral conductor

• Like charges are repelled• Un-like charges are attracted

Charge by conduction• A charge rod touches a neutral conductor• Like charges are repelled and uniformly distribute

Charge by InductionA charge object is placed near neutral conductors

A BA BA BA B

Separation of charge takes placeContact between the conducting sphere is brokenThe charge object is removedThe charges on the spheres redistribute to maximum separationResult: Two spheres charged by induction

Charging by Polarization• Certain substances, such as the one below, have polar

molecules. These molecules have opposite charges at each end.

• Charging by polarization takes place when a charged object is brought near, realigning the molecules in the substance.

Magnification

Conductors and Insulators

• Electrical Conductors are similar to Heat conductors.

• Electrical Conductors allow charge to move easily.

• Electrical Insulators do not allow charge to move easily

Conductors and Insulators• Electrical Conductors all electrons to move

easily.– Metals– Graphite

• Electrical Insulators do not allow electrons to move easily– Glass– Plastic– Rubber

Homework• Ch 16.1-16.5• Page 464

– 1-8– 11-12

Lightning• Charging by induction occurs during

thunderstorms

• The negatively charged cloud induces a positive charge on the ground

• Lightning: An electrical between the clouds and oppositely charged ground.

Outlet

Ground

• The earth stores a seemingly infinite amount of charge, both kinds.

• An object is grounded when it is connected to the earth or another large object.

• Electrical devices often have a “ground,” which prevents unwanted charge buildup.

• Grounding is also the principle behind lightning rods.

Grounding

Lightning• Average Temperature 30,0000C

– (roughly 5x as hot as the sun)

• Typical charge (q) for lightning 10C to 25C

• How many electrons is this?

Lightning is actually a discharge of static electricity. Charge differences are developed from the friction of dust particles within the cloud.

When the concentration of charges becomes too great, an electrical discharge results

The Electroscope• An electroscope is a device that detects

electrical charge in objects brought near.• Its metallic inner contents, which are usually

neutral, have to be separated from surroundings by some type of insulator.

• There are two metal leaves that hang inside.

• When a charged object is brought near, the leaves separate.

• Charge can also be stored in the electroscope by touching it with the rod.

Leaves

Coulomb’s Law• The electrostatic force one charged object exerts

on an other

• The force is related to the amount of charge – i.e more charge – more force

• The force is proportional to 1/d2 – i.e. the further apart the charges, the smaller

the force

Coulomb’s Law

Symbol UnitF Force Nq1 Charge Cq2 Charge Cd Distance mK constant N m2 / C2

1 2

2

Kq qF

d

Ex. Coulomb’s Law WS 20.1 #4Object A has a charge of 6x10-6C. Object B has a charge of 3x10-6C and is 0.03m away. Calculate the force on A.

1 2

2

Kq qF

d

9 2 2 6 6

2

(9.0 10 / )(6 10 )(3 10 )(.03 )

x N m C x C x CFm

180F N

Ex. Coulomb’s Law WS 20.1 #5The distance that separates electrons in a typical atom is 1.5x10-10m. What is the electrostatic force between them?

2

1 2Kq qFd

9 2 2 19 19

10 2

(9.0 10 / )( 1.6 10 )( 1.6 10 )(1.5 10 )

x N m C x C x CFx m

81.024 10F x N

Electro-static ApplicationsElectrostatic filter

Electro-static Applications• Electrostatic painting

Electrostatic filters

• Scan pictures from p.416

Practice Problems

• WS 20.1– #’s 2, 3, 6

Ex. Coulomb’s Law WS 20.2 #1Three charges are aligned as shown. Calculate the force on q2 due to q1.

2

1 2Kq qFd

9 2 2 4 4

12 2

(9.0 10 / )(4.25 10 )(2.5 10 )(.15 )

x N m C x C x CFm

12 42500F N

Electric Charge Positions Scale: 1 Square = 0.05m

q1 q3q2

41

42

43

4.25 10

2.50 10

4.25 10

q x C

q x C

q x C

Ex. Coulomb’s Law WS 20.2 #1Three charges are aligned as shown. Calculate the net force on q2.

2

1 2Kq qFd

9 2 2 4 4

23 2

(9.0 10 / )(2.5 10 )( 4.25 10 )(.3 )

x N m C x C x CFm

23 10625F N

Electric Charge Positions Scale: 1 Square = 0.05m

q1 q3q2

41

42

43

4.25 10

2.50 10

4.25 10

q x C

q x C

q x C

Ex. Coulomb’s Law WS 20.2 #1Three charges are aligned as shown. Calculate the force on q2 due to q3.

42500 10625net right rightF N N

Electric Charge Positions Scale: 1 Square = 0.05m

q1 q3q2

41

42

43

4.25 10

2.5 10

4.25 10

q x C

q x C

q x C

53125net rightF N

Practice Problems

• WS 20.2– #’s 3

FNet

Coulomb’s Law in 2-D• To find Fnet with 3 or more charges• Calculate each Force vector. • It helps to have a grid system on which to work.• Use vector addition to find the resultant Fnet

q2 q3

q4

F13

F12

F14q1

Coulomb’s Law in 2-D (cont.)• Find the net force acting on q1.

• First find the distance between q1 and the others.• Use the Pythagorean Theorem to find these distances.

q2 q3

q1

CA

B

C

BA

2 2 2A B C 2 2C A B 2 22 3C

13C

12 13d

The variable C from each triangle’s hypotenuse is the variable d used in the Coulomb’s Law equation.

2 2C A B 2 22 4C 20C

13 20d

1st Triangle 2nd Triangle

Coulomb’s Law in 2-D (cont.)

q2 q3

q1

Charge (C)q1 3.0 X 10-4

q2 -2.6 X 10-5

q3 7.2 X 10-6

2013

1 212 2

12

kq qFd

2

29 4 5

12 2

9.0 10 3.0 10 2.6 10

13

NmC

C CF

m

12 5.4F N

1 313 2

13

kq qF

d

2

29 4 6

13 2

9.0 10 3.0 10 7.2 10

20

NmC

C CF

m

13 0.972F N

F12

F13

Coulomb’s Law in 2-D Sample• Determine the direction of each of the forces prior to

vector addition.

q2 q3

q1

5.4N

0.972N

hypopp

adj

hyp

adjopp

tan oppadj

1 2tan4

26.6

1 2tan3

33.7

26.6 180

206.6

33.7 180

146.3

Quad II Adjust Quad III Adjust

F12 F13

• The remaining task is to use analytical vector addition.

Coulomb’s Law in 2-D SampleMag Ang X Y Q

F12 5.4N 146.3° -4.49 3.00 II

F13 0.972N 206.6° -0.87 -0.44 III

FNet 5.94N 154.5° -5.36 2.56 II12 12 cosxF F

12 5.4 cos 146.3xF N 12 4.49xF N12 12 sinyF F

12 5.4 sin 146.3yF N 12 3.00yF N13 13 cosxF F

13 0.972 cos 206.6xF N 13 0.87xF N13 13 sinyF F

13 0.972 sin 206.6yF N 13 0.44yF N

2 2Net Tot TotF X Y

2 25.36 2.56NetF N N

5.94NetF N

12 13Tot x xX F F 4.49 0.87TotX N N 5.36TotX N

12 13Tot y yY F F

2.56TotY N

tan Tot

Tot

YX

1tan Tot

Tot

YX

1 2.56tan

5.36NN

25.5

25.5 180 154.5 5.94 @154.5NetF N

Quad II Adjust

Conclusion• Electrostatics, the study of the forces between charges

at rest.

I had a dream…

And in it there’s no lightning

Practice Problems

• WS 20.2– #’s 2

Coulomb’s Law in 2-D Sample

Three charges are aligned as shown. Find the net force on q1.

41

42

43

4.5 10

3.2 10

7.3 10

q x C

q x C

q x C

Electric Charge Positions Scale: 1 Square = 0.5

cm

q1 q3

q2

Mag Ang X Y Q

F12 5.4N 146.3° -4.49 3.00 II

F13 0.972N 20.6° -0.87 -0.44 III

FNet 5.94N 154.5° -5.36 2.56 II

Static Discharge Pic’s

End Ch 20

Example: Charge Distribution• What is the total charge of three conducting spheres with

charges of 6q,-1q, and 0q

6 ( 1 ) 0totalq q q q

A6q

B-1q

C0q

5totalq q

Example: Charge Distribution cont.• What is the final charge distribution if sphere A and B

touch?

C0q

A6q

B-1qB2.5q

A2.5q

Example: Charge Distribution cont.• What is the final charge distribution if sphere B and C

touch?

B2.5q

A2.5q

C0qC1.25q

B1.25q

Example: Charge Distribution cont.• What is the total charge of three conducting spheres

A2.5q

C1.25q

B1.25q

2.5 1.25 1.25totalq q q q

5totalq q

Example: Charge Distribution cont.• Sphere B is twice as large as sphere A, what will be the

charge distribution after they touch?

A5q B

5q

Charge by Conduction• Bring a charge rod near a neutral conductor

• Like charges are repelled• Un-like charges are attracted

A5q

B-1q

C0q

q2

q3

q1

Scale: 1 square =0.1cm

q1 q3q2