Electricity Lecture Series email: [email protected]; [email protected] ...

Electricity Lecture SeriesElectricity Lecture Series

email: email: [email protected]@salam.uitm.edu.my; ; [email protected]@hotmail.comhttp://www3.uitm.edu.my/staff/drjj/http://www3.uitm.edu.my/staff/drjj/

Applied Sciences Education Research Group (ASERG)

Faculty of Applied SciencesUniversiti Teknologi MARA

Charges Electric Charges Electric Fields, Potential Fields, Potential and Capacitorsand Capacitors

Copyright DR JJ,FSG, UiTM 2

Electric ChargesElectric Charges

1. Explain the gravitational forces acting on any object.

2. Mathematically represent the gravitational force and describe its impact on physical events.

3. Describe existence of electrical charges in matter and its quantization property.

4. Sketch and explain the charging by induction and charging by contact

5. Mathematically represent forces acting between electrical charges (Coulomb’s Law)

Objectives:

Objectives:



6. Represent forces acting between charges both pictorially and vectorially.

7. Describe and explain gravitational and electric field.

8. Derive mathematical relations for electric field of point charges, line charges and surface charges and the use of Gaussian surface.

9. Describe and explain capacitors and its purpose.

Objectives:

Objectives:



10.Write mathematical relations for parallel plate capacitors related to capacitance, potential difference, its geometrical dependence, and electric field it can store.

11.Obtain energies stored by capacitors.

12.Explain and pictorially and graphically represent the charging and discharging of capacitors.

Objectives:

Objectives:



13.Describe, draw and obtain resultant capacitances for capacitors connected in parallel and in series respectively.

14.Solve conceptual and numerical problems associated with capacitors.

Objectives:

Objectives:



MatterMatter: made up of atoms and molecules

Charged objectCharged object: imbalance number of electrons & protonsPositively chargedNegatively charged

AtomAtom: made up of nucleus, protons and electrons

ConductorsConductors: charges can move freelyInsulatorsInsulators: charges cannot move freely


18.1 18.1 The Origin of ElectricityThe Origin of ElectricityCutnell & Johnson 7ECutnell & Johnson 7E

The electrical nature of matter is inherentin atomic structure.

kg10673.1 27pm

kg10675.1 27nm

kg1011.9 31em

C1060.1 19e

coulombs



Charge quantizationCharge quantization: charges exist in multiples of an elementary charge, the charge of an electron

,..2, eeNeq where N are the number of electrons & the elementary charge e is e =1.6 x 10-19 CNumber of charges in 1 C?? N=q/e =1 C/1.6 x 10-19 CN = 6.25 x 1018


18.2 18.2 Charged Objects and the Electric ForceCharged Objects and the Electric ForceCutnell & Johnson 7ECutnell & Johnson 7E

LAW OF CONSERVATION OF ELECTRIC CHARGE

During any process, the net electric charge of an isolated system remains constant (is conserved). Total number of negative charges (electrons) and positive charges (protons) must be equal


18.3 18.3 Conductors and InsulatorsConductors and InsulatorsCutnell & Johnson 7ECutnell & Johnson 7E

Not only can electric charge exist on an object, but it can also movethrough and object.

Substances that readily conduct electric charge are called electricalConductors – copper, iron, gold, water, human body

Materials that conduct electric charge poorly are called electricalInsulators – plastic, wood, rubber


18.4 18.4 Charging by ContactCharging by ContactCutnell & Johnson 7ECutnell & Johnson 7E

Charging by contact.


18.4 18.4 Charging by InductionCharging by InductionCutnell & Johnson 7ECutnell & Johnson 7E

Charging by induction.


18.4 18.4 Charging by Contact and by InductionCharging by Contact and by InductionCutnell & Johnson 7ECutnell & Johnson 7E

The negatively charged rod induces a slight positive surface chargeon the plastic.


Electric Forces-Coulomb’s LawElectric Forces-Coulomb’s Law

Gravitational forces (Law of Gravitational forces (Law of Gravitation)Gravitation): Earth pulls on the moon and vice-versa. Any 2 objects will always exert and feel attractive gravitational forces. They exert with same magnitude. Moon feels attraction because it is in the earth’s gravitational field.

2r

MmF earthmoon

earth to due moon

F is inversely proportional to square of separation between masses.

2r

mMF moonearth

moon to due earth

r Fme


Electric Charges-ForcesElectric Charges-ForcesGravitational forcesGravitational forces:

F is inversely proportional to square of separation between masses.

r, m r2, m2 F, N Ratios of F

10 100 F1=Gm1m2/100 F1/F2=4

20 400 F2=Gm1m2/400 F1/F3=9

30 900 F3=Gm1m2/900 F2/F3=9/4

2r

MmGF earthmoon

earth to due moon r F12


18.2 18.2 Charged Objects and the Charged Objects and the Electric ForceElectric Force

Cutnell & Johnson 7ECutnell & Johnson 7E

Like charges repel and unlike charges attract each other.


18.5 18.5 Coulomb’s LawCoulomb’s Law Cutnell & Johnson 7E Cutnell & Johnson 7E


Electric Charges-Coulomb’s LawElectric Charges-Coulomb’s Law

Electric forcesElectric forces: Charged objects exert electric forces on each other. Can be attractive or repulsive. Like charges repel. Unlike charges attract.

221

221

12 r

qqk

r

qqFF 2 to due 1

+

+

r F21

q1=e

q2=2e

20

122

1221 4 r

qq

r

qqkFF 1 to due 2

constant electrick 04

1

0 = permittivity of free space0 = 8.85 x 10-12 C2/Nm2



COULOMB’S LAW

The magnitude of the electrostatic force exerted by one point charge on another point charge is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them.

221

r

qqkF

229 CmN1099.841 ok

2212 mNC1085.8



Example 4 Three Charges on a Line

Determine the magnitude and direction of the net force on q1.


Nm

CCCmN

r

qqkF

22

7.220.0

100.4100.31099.82

669

221

12

Nm

CCCmN

r

qqkF

22

4.815.0

100.7100.31099.82

669

231

13

5.7NN4.8N7.21312 FFF



Electric Point ChargesElectric Point Charges

Electric forcesElectric forces: repulsive forces since both are positively charged.

212

21)2/(r

qqkFF 1 to due 2

4/212

r

qqkF 21

2124

r

qqkF 21

212

21r

qqkFF 1 to due 2

+

+

r F

q1=e

q2=2e

Fset1 Fset2<

+

+

r/2 F

q1=e

q2=2e

SET 2

Is accset1 bigger or smaller than accset2??

down

down



Electric forcesElectric forces: attractive forces since opposite charges

212

r

qqkF 21

2

242

r

ekF 21

2

2

2

422

r

ek

r

eekF 21

-

+

r F

q1=2e

q2=2e

Fset1 Fset2<

-

+

r F

q1=4e

q2=2e

2

28

r

ekF 21

Is accset1 bigger or smaller than accset2??

up

up



Electric forcesElectric forces: Determine forces acting on charge 2

2232 22

r

eek

r

qqkF 23

2

2

2

2

2

2 844

r

ek

r

ek

r

ekFF 3 21 2

2

2

2

422

r

ek

r

eekF 21

-

+

r F

q1=2e

q3=2eWhat is the magnitude and direction of net force acting on q2?

+ q2=2e

r

up

up

up

What is the magnitude and direction of acceleration of q2?




2232 22

r

eek

r

qqkF 23

2

2

2

2

2

2 54

r

ek

r

ek

r

ekFF 3 21 2

2

2

2212

4

4

2

22

r

ek

r

eek

r

qqkF 21

-

+

2r F

q1=2e

q3=2e


+ q2=2e

r

up

up

up



Example 3 A Model of the Hydrogen Atom

In the Bohr model of the hydrogen atom, the electron is in orbit about the nuclear proton at a radius of 5.29x10-11m. Determine the speed of the electron, assuming the orbit to be circular.

221

r

qqkF


18.518.5 Coulomb’s LawCoulomb’s Law Cutnell & Johnson 7E Cutnell & Johnson 7E

N1022.8

m1029.5

C1060.1CmN1099.8 8211

219229

2

21

r

qqkF

sm1018.2

kg109.11

m1029.5N1022.8 631-

118

mFrv

rmvmaF c2

For circular motion & using Newton’s 2nd law of motion




2232 22

r

eek

r

qqkF 23

2

2

2

2

2

2 34

r

ek

r

ek

r

ekFF 3 21 2

2

2

2212

4

4

2

22

r

ek

r

eek

r

qqkF 21

+

+

2r F12

q1=2e

q3=2e


+ q2=2e

r

down

up

up

F21




+

+

2r

q1=2e

q3=2e

-

r

+ q4=2e

q2=e

+ q5=2e

2r

2r

F21

F23

F24

F25

F24

F25

F25sin25

F24sin24

F2

4co

s2

4

F2

5co

s2

5


Electric Point ChargesElectric Point ChargesElectric forcesElectric forces: Determine forces acting on charge 2

2r

2r

Pythagoras theorem: Charge 2 & 4 is separated by the distance:

2

2

2221

12

22

2

r

ek

r

eek

r

qqkF 21

2

2

2223

32 22

r

ek

r

eek

r

qqkF 23

up

down

2

2

2

2

2224

42

48

2

22

2

r

ek

r

ek

r

eek

r

qqkF 24

228)2()2( 22224 rrrrr

Charge 2 & 5 is separated by the distance:

55)2( 22225 rrrrr

2

2

2

2

2225

52

5

2

5

2

5

2

r

ek

r

ek

r

eek

r

qqkF 25

2e 2e

r

2r

2e 2e

-e

r 24 = ??

r25 = ??



2

2

2212

22

2

r

ek

r

eek

r

qqkF 21

2

2

2232 22

r

ek

r

eek

r

qqkF 23

up

down

2

2

2

2

2242

48

2

22

2

r

ek

r

ek

r

eek

r

qqkF 24

2

2

2

2

2252

5

2

5

2

5

2

r

ek

r

ek

r

eek

r

qqkF 25

2

1

22

2cos 24

r

r

2

1

22

2sin 24

r

r

5

1

5cos 25

r

r

5

2

5

2sin 25

r

r

Thenup

r

ekF y24 ;

24 2

2

right r

ekF x24 ;

24 2

2

down r

ekF y25 ;

54 2

2

right r

ekF x25 ;

52 2

2



down r

ekFFFFF yy 25242321y ;

54

1

24

12

2

12

2

right r

ekFFF xx 2524x ;

52

1

24

12

2

22

yx FFF Then,

22

2

2

54

1

24

1

2

3

52

1

24

1

r

ekF Then,

F

Fx

Fy

54

1

24

123

52

1

24

1

naT

Take the arctan of theta to determine the force direction


Elrctric field & forcesElrctric field & forcesAssignment: Due Aug 3Assignment: Due Aug 3rdrd 2006. 2006.

Chap 18Chap 18Exercises from the back of chapter.1,3,5,9, 13, 17,70, 71, 75Submit all

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