Chapter 16 Electric Forces and Electric Fields Phy 2054 Lecture Notes

Chapter 16Electric Forces and

Electric Fields

Phy 2054Lecture Notes

15-01 Properties of Electric Charges

15-02 Insulators and Conductors

15-03 Coulomb’s Law

15-04 The Electric Field

15-05 Electric Field Lines

15-06 Conductors in Electrostatic Equilibrium

15-07 The Millikan Oil-Drop Experiment

Electric Forces and Electric Fields

Sections

15-08 The Van de Graaff Generator

Ch15: Electric Charge and Electric Field (02 of 46)

Properties of Electric Charges

Attraction Repulsion


Chapter 15: Electric Forces and Electric Fields

~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10~M9~M11~M12~M13~M14~M15~M16~M17~M18 ~M20~M19~M21~M22~M23~M24~M25~M26~M27~M28 ~M30~M29~M31~M32~M33~M34~M35~M36~M37~M38 ~M40~M39~M41~M42~M43~M44~M45~M46~M47~M48 ~M50~M49~M51~M52~M53~M54~M55~M56~M57~M58 ~M60~M590% 20% 40% 60% 80% 100%

4

3

2

1

Is it possible for two negative charges to attract each other?

(A) Yes, they always attract.

(B) Yes, they will attract if they are close enough.

(C) Yes, they will attract if one carries a larger charge than the other.

(D) No, they will never attract.


Insulators and Conductors

Charging by Contact


Insulators and Conductors

Charging by Induction

Bring in a charged rod.Connect ground wire to sphere.Remove ground wire.Remove charged rod.A metal sphere.




4

3

2

1

How can a negatively charged rod charge an electroscope positively?

(A) by conduction

(B) by induction

(C) by deduction

(D) It cannot.




4

3

2

1

A neutral atom always has

(A) more neutrons than protons.

(B) more protons than electrons.

(C) the same number of neutrons as protons.

(D) the same number of protons as electrons.




4

3

2

1

A negatively charged rod is brought near one end of an uncharged metal bar. The end of the metal bar farthest from the charged rod will be charged

(A) positive.

(B) negative.

(C) neutral.

(D) none of the given answers


Coulomb’s law:

221

r

QQkF

r1Q 2Q

Charge (Q)Coulombs (C)

1 C = 6.2421 x 1018 e

e = 1.602 x 109 C

Distance (m)

Coulomb’s constant (k)

k = 8.988 x 109 Nm2/C2

Force (N)

12F 21F

2112 FFF

Coulomb’s Law


Coulomb’s law:

221

o r

QQ

πε41

F

r1Q 2Q

oπε41

k

2mN

2C12o 10x 8.85

kπ41

ε

Permittivity of free space

221

r

QQkF

Coulomb’s Law




4

3

2

1

What are the units of the Coulomb constant k, which appears in Coulomb's law?

(A) N∙m/C

(B) N/C

(C) N2∙m/C2

(D) N∙m2/C2

221

r

QQkF

21

2

QQFr

k


The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same.

Coulomb’s Law




4

3

2

1

Two charges are separated by a distance d and exert mutual attractive forces of F on each other. If the charges are separated by a distance of d/3, what are the new mutual forces?

(A) F/9

(B) F/3

(C) 3F

(D) 9F


Vector addition review:

Two forces acting on an object

tail-to-tip method

Parallelogram method

Components method

Coulomb’s Law


Coulomb’s law strictly applies only to point charges.

Superposition: for multiple point charges, the forces on each charge from every other charge can be calculated and then added as vectors.

1Q2Q

3Q

32F

31F

3Q

32F

31F

netF

Net force on Q3

Coulomb’s Law


Two charged dust particles exert a force of 0.032 N on each other. What will be the force if they are moved so they are only one-eighth as far apart?

Coulomb’s law is an inverse square law.

N 048.2N 032.0 64F

Coulomb’s Law (Problem)


What is the magnitude of the electrical force between twopeople 10 m apart if each water molecule in their bodies is

assumed to have a net negative charge of q = 1.6 x 1019 C?Assume each body is 45 kg.

mol 2500kg/mole 0.018

kg 45

molecules10x 5.1 10x 6.02mol 2500 27mole

molucules23

C 10x 4.2molecules/C10x 6.1molecules10x 5.1Q 81927

2

2

r

QkF

228229

m 10

C 10 x 4.2 /CmN 10 x .09 N 10 x .25 24



A person scuffing her feet on a wool rug on a dry day accumulates a net charge of 42 C. How many excess electrons does she get,

By how much does her mass increase?

lectronse 10 x 622.2C 10 x 602.1

electron 1 C 10 x 42 14

196

kg 10 x 389.2e 1

kg 10 x .119e 10 x 622.2 16

3114



Compare the electric force holding the electron in orbit

(r = 0.53 x 10 l0 m) around the proton nucleus of the hydrogen atom, with the gravitational force between the same electron and proton.What is the ratio of these two forces?

21

21

221

221

G

EmGm

QkQ

r

mGmr

QkQ

F

F

kg10 x .671kg10 x .119/kgmN 10 x .676

C 10 x 602.1 /CmN 10 x .988827312211

219229

3910 x 3.2



At each corner of a square of side L there are four point charges. Determine the force on the charge 2Q.

Q2Q

3Q4QL

2

2

2

2o

22x L

kQ 8284.4222

L

kQ45cos

L2

Q4Q2k

L

QQ2kF

2

2

2

2o

22y L

kQ 8284.8226

L

kQ45sin

L2

Q4Q2k

L

Q3Q2kF

2

22y

2xQ2 L

kQ 0625.10 FFF



A +4.75 C and a 3.55 C charge are placed 18.5 cm apart. Where can a third charge be placed so that it experiences no net force?

Q1 Q2

d x

Q

21 FF

22

21

x

QQk

xd

QQk

21

2

QQ

Qdx

C 10 x 5.3C 10 x .74

C 10 x 5.3cm 5.18x

66

6

cm 116



The electric field is defined as the force on a test charge (small positive charge), divided by the charge:

qF

E

E E

F F

qEF qEF

The Electric Field


Electric field of a point charge

+Q

r

q

qF

E qr

Qqk

2

2r

QkE

2r

QqkF

The Electric Field




4

3

2

1

At twice the distance from a point charge, the strength of the electric field

(A) is four times its original value.

(B) is twice its original value.

(C) is one-half its original value.

(D) is one-fourth its original value.


Calculate forces using Coulomb’s law

Add forces vectorially to get result

Draw a diagram; show all charges, with signs, and electric fields and forces with directions

Problem solving in electrostatics:

The Electric Field


A proton is released in a uniform electric field, and it

experiences an electric force of 3.75 x 1014 N toward the south. What are the magnitude and direction of the electric field?

+ south

E

F

qF

E (South) N/C 10x 2.34 C 10x 1.602

N 10x 3.75 591

14

The Electric Field (Problem)


What are the magnitude and direction of the electric field at a point midway between a +7.0 C and a 8.0 C charge 8.0 cm apart? Assume no other charges are nearby.

+ -

d

q1 q2

E1

E2

21 EEE

22

21

2d

kq

2d

kqE

212qq

d

k4E

N x10 8.0N x10 7.0

m 08.0

m/CN x10 8.9884 662

9

N/C x10 8.4E 7



Two point charges, Q and +2Q, are separated by a distance of d = 12 cm. The electric field at point P is zero, where ispoint P and how far is it from Q?

+-Q Q2

d = 12 cm

P

x

E1E2

21 EE

22

21

dx

kQ

x

kQ

12

1

QQ

Qdx

11

1

QQ2

Qdx

12d

x

12

cm 12

cm 29x



A proton (m = 1.67 x 1027 kg) is suspended at rest in a uniform electric field E. Take into account gravity at the Earth's surface, and determine E.

+q

E

GF

EF GE FF

mgqE

qmg

E

C 10x 602.1

m/s 9.80 kg 10x 67.1E

91

227

N/C 10x 02.1E 7



The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.

Electric Field Lines


The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge.

The electric field is stronger where the field lines are closer together.

A

B C

E

E





4

3

2

1

The electric field shown

(A) decreases to the right.

(B) increases down.

(C) increases to the right.

(D) decreases down.

E


Electric field of two charges:



The electric field between two closely spaced, oppositely charged parallel plates is constant.



Field lines indicate the direction of the field; the field is tangent to the line.

The magnitude of the field is proportional to the density of the lines.

Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge.

Summary of field lines:





4

3

2

1

Electric field lines near positive point charges

(A) circle clockwise.

(B) circle counter-clockwise.

(C) radiate inward.

(D) radiate outward.


Conductors in Electrostatic Equilibrium


The electric field is perpendicular to the surface of a conductor

The electric field is zero inside a conductor





4

3

2

1

A cubic block of aluminum rests on a wooden table in a region where a uniform electric field is directed straight upward. What can be said concerning the charge on the block's top surface?

(A) The top surface is charged positively.

(B) The top surface is charged negatively.

(C) The top surface is neutral.

(D) The top surface's charge cannot be determined without further information. E




4

3

2

1

Materials in which the electrons are bound very loosely to the nuclei and can move about freely within the material are referred to as

(A) insulators.

(B) conductors.

(C) semiconductors.

(D) superconductors.




4

3

2

1

A solid block of metal in electrostatic equilibrium is placed in a uniform electric field. Give a statement concerning the electric field in the block's interior.

(A) There is no electric field in the block's interior.

(B) The interior field points in a direction opposite to the exterior field.

(C) The interior field points in a direction that is at right angles to the exterior field.

(D) The interior points in a direction that is parallel to the exterior field.


The Millikan Oil-Drop Experiment


The Van de Graaff Generator



When finger is removed

When charged rod is removed

Electrically neutral

Net positive charge( on outer surface)

Charging by induction:

Electric Charge and Electric Field 16


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Chapter 16 Electric Forces and Electric Fields Phy 2054 Lecture Notes