Electric Forces & Electric Fields

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Chapter 18

Elec tr ic Forces andElec tr ic Fields

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18.1 The Origin o f Electr ic i ty

The electrical nature of matter is inherent

in atomic structure.

kg10673.1 27pm

kg10675.1 27

nm

kg1011.9 31em

C1060.1 19e

coulombs

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In nature, atoms are normally

found with equal numbers of protonsand electrons, so they are electrically

neutral.

By adding or removing electrons

from matter it will acquire a net

electric charge with magnitude equalto etimes the number of electrons

added or removed, N.

Neq

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Example 1 A Lot of Electrons

How many electrons are there in one coulomb of negative charge?

Neq

18

19-

1025.6C101.60

C00.1

e

qN

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18.2 Charged Objects and the Electr ic Force

It is possible to transfer electric charge from one object to another.

The body that loses electrons has an excess of positive charge, while

the body that gains electrons has an excess of negative charge.

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LAW OF CONSERVATION OF ELECTRIC CHARGE

During any process, the net electric charge of an isolated system remainsconstant (is conserved).

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Like charges repel and unlike

charges attract each other.

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18.3 Conductors and Insulators

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

Substances that readily conduct electric charge are called electr ical

conductors.

Materials that conduct electric charge poorly are called electricalinsulators.

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18.4 Charging b y Contact and by Indu ction

Charging by contact.

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18.4 Charging b y Contact and by Indu ction

Charging by induction.

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18.5 Coulombs Law

COULOMBS 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.

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21

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qqkF

229 CmN1099.841 ok

2212 mNC1085.8

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18.5 Coulombs Law

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.

2

21

r

qqkF

12

C l b L


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18.5 Coulombs Law

N1022.8m1029.5

C1060.1CmN1099.8 8211

219229

2

21

rqqkF

rmvmaF c2

sm1018.2

kg109.11

m1029.5N1022.8 631-

118

mFrv

13

18 C l b L


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18.5 Coulombs Law

Example 4 Three Charges on a Line

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

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18 5 C l b L


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18.5 Coulombs Law

N7.2m20.0

C100.4C100.3CmN1099.82

66229

2

21

12

r

qqkF

N4.8m15.0

C100.7C100.3CmN1099.8

2

66229

2

31

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r

qq

kF

5.7NN4.8N7.21312 FFF

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18 5 C l b L


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18.5 Coulombs Law

Figure (a) shows three point charges that lie in the x, y plane in a vacuum.

Find the magnitude and direction of the net electrostatic force on q1.

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18 6 Th El t i Fi ld


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18.6 The Electr ic Field

The positive charge experiences a force which is the vector sum of the

forces exerted by the charges on the rod and the two spheres.

This test chargeshould have a small magnitude so it doesnt affectthe other charge.

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18 6 The Electr ic Field


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Example 6 A Test Charge

The positive test charge has a magnitude of

3.0x10-8C and experiences a force of 6.0x10-8N.

(a) Find the force per coulombthat the test charge

experiences.

(b) Predict the force that a charge of +12x10-8C

would experience if it replaced the test charge.

CN0.2C100.3

N100.6

8

8

oq

F

(a)

(b) N1024C100.12CN0.2 88 F

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DEFINITION OF ELECRIC FIELD

The electric field that exists at a point is the electrostatic force experienced

by a small test charge placed at that point divided by the charge itself:

oq

FE

SI Units of Electric Field: newton per coulomb (N/C)

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It is the surrounding charges that create the electric field at a given point.

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Example 7 An Electric Field Leads to a Force

The charges on the two metal spheres and the ebonite rod create an electric

field at the spot indicated. The field has a magnitude of 2.0 N/C. Determine

the force on the charges in (a) and (b)

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N1036C100.18CN0.2 88 EqF o(a)

(b) N1048C100.24CN0.2 88 EqF o

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Electric fields from different sourcesadd as vectors.

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Example 10 The Electric Field of a Point Charge

The isolated point charge of q=+15C is

in a vacuum. The test charge is 0.20mto the right and has a charge qo=+0.80C.

Determine the electric field at point P.

oq

FE

2

21

r

qqkF

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N7.2m20.0 C1015C1080.0CmN1099.8 266229

2

r

qqkF o

CN104.3C100.80

N7.2 66-

oq

FE

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2r

qkE

The electric field does not depend on the test charge.

o

o

o qrqqk

qFE 1

2

Point charge q:

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Example 11 The Electric Fields from Separate Charges May Cancel

Two positive point charges, q1=+16C and q2=+4.0C are separated in a

vacuum by a distance of 3.0m. Find the spot on the line between the chargeswhere the net electric field is zero.

2r

qkE

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2

6

2

6

m0.3

C100.4C1016

dk

dk

21

EE 2r

q

kE

22m0.30.4 dd

m0.2d

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8 6 e ect c e d

Conceptual Example 12 Symmetry and the

Electric Field

Point charges are fixed to the corners of a rectangle in twodifferent ways. The charges have the same magnitudes

but different signs.

Consider the net electric field at the center C of the rectangle

in each case. Which field is stronger?

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THE PARALLEL PLATE CAPACITOR

Parallel plate

capacitorooA

qE

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charge density

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18.7 Electric Field Lines


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Elect r ic field l ines or l ines of forc eprovide a map of the electric field

in the space surrounding electric charges.

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Property 2: Electric field lines always begin on a positive charge

and end on a negative charge and do not stop in

Midspace and they are ALWAYS perpendicular to the charges.

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Property 3: The number of lines leaving a positive charge or entering a

negative charge is proportional to the magnitude of the charge.

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Conceptual Example 13 Drawing Electric

Field Lines

There are three things wrong with part (a) ofthe drawing. What are they?

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18.8 The Electr ic Field Inside a Conducto r: Shielding


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At equilibrium under electrostatic conditions, any

excess charge resides on the surface of a conductor.

At equilibrium under electrostatic conditions, the

electric field is zero at any point within a conductingmaterial.

The conductor shields any charge within it fromelectric fields created outside the conductor.

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18.8 The Electr ic Field Inside a Conducto r: Shielding


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The electric field just outside the surface of a conductor is perpendicular to

the surface at equilibrium under electrostatic conditions.

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Electric Forces & Electric Fields

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