Chapter 16

Electric Charge and Electric Field

© 2008Giancoli, PHYSICS,6/E © 2004. Electronically reproduced by

permission of Pearson Education, Inc., Upper Saddle River, New Jersey

Ch16 2

Structure of the atom (protons, neutrons and electrons)

• Nucleus contains protons and neutrons

•Protons have positive charge, neutrons are neutral

•Mass of proton ≈ mass of neutron

•Mass of proton (and neutron) 1800x mass of electron

• Electrons have negative charge and are attracted to nucleus

• Charge of electron is equal in magnitude to that of proton

• Normal atom is neutral

• Ion is atom that has gained or lost one or more electrons

Ch16 3

Conductors and Insulators

Conductor: metal atoms in solids have one or more “free” electrons per atom which move freely through the material

Insulator: no free electrons so it will not conduct electricity

Ch16 4

Static Electricity

Static Electricity:• Rubbing certain materials together can separate electrons from their atoms• Removing electrons from a material makes it positive• In solids, it is always the free electrons that move• Electrical charge on the plastic rod induces a separation of charge in scraps of

paper and thus attracts them.

Ch16 5

Induced Charge

(a) If you bring a + charge near a conductor, it will attract electrons to it leaving the other half of the metal positive.

(b) If they touch, then electrons move to the positively charged object, leaving the conductor positively charged.

Ch16 6

Coulomb’s Law

•Forces are equal in magnitude but opposite in direction

•For spherical charges, r is the center to center distance

•This equation gives the magnitude of the force--you have to figure the direction from the signs of the charges

221

r

QQkF

Ch16 7

Coulomb’s Law

•k 9.0 109 N·m2 / C2

•C is Coulomb -- the unit of charge

• e = 1.60x10-19 C electronic charge (positive)

221

r

QQkF

Ch16 8

Coulomb’s Law

Ch16 9

Example 1. Particles of charge Q1 = +5.00 C, Q 2 = -6.0 C and Q3 = +8.0 C are placed in a line separated by 0.40 m between each pair. Calculate the force on Q2.

+

Q1

_

Q2

+

Q321F

23F

221

1221 r

QQkF

2

66

2

29

40.0

100.5100.61000.9

m

CC

C

mN

NF 7.121 This is the magnitude, we get direction from charges.

223

3223 r

QQkF

2

66

2

29

40.0

100.8100.61000.9

m

CC

C

mN

NF 7.223

2123 FFF NNN 0.17.17.2

Force is directed to the right.

Ch16 10

Example 2. Particles of charge Q1 = +5.00 C, Q 2 = -6.00 C and Q3 =

+8.00 C are placed on the corners of a square of side 0.400 m as shown below. Calculate the force on Q2 (Magnitude and direction).

+

Q1

_Q2 + Q3

21F

23F

Note that the charges and distances are the same as in Example 1, so we do not need to use Coulombs Law again.

NF 7.121

NF 7.223

223

221 FFF NNN 2.3)7.2()7.1( 22

F

23

21tanF

F

23

211tanF

F o

N

N32

7.2

7.1tan 1

Ch16 11

The Electric Field•Graphical representation of electrical forces

•Electrical force “acts at a distance” like gravity

•Electric field E surrounds every charge

•We investigate the field with a small positive charge called a “test charge” q

•The field is given by:

q

FE

Ch16 12

The Electric Field

•Units are N/C •E is a vector = direction of force experienced by positive test charge•The magnitude of q is so small that it does not disturb the charges that cause the field•To plot the field, move the test charge around the charges that cause the field•Since q is positive the field points away from a + charge and towards a - charge

q

FE

Ch16 13

Field of a Point Charge Q

qrQq

k

q

FE

2

22

21

r

Qqk

r

QQkF

This is the field created by a point charge or a spherical charge distribution Q

2r

QkE

Ch16 14

Electric Field is a Vector

•Field thus points toward a negative charge and away from a positive charge•Since test charge is positive, the direction of the electric field is the direction of the force felt by a positive charge•If there are two or more charges creating the field then the field at any point is the vector sum of the fields created by each of the charges•The test charge does not contribute to the field and it is too weak to cause any of the charges creating the field to move.

Ch16 15

Example 3A. A +100 C point charge is separated from a -50 C charge by a distance of 0.50 m as shown below. (A) First calculate the electric field at midway between the two charges. (B) Find the force on an electron that is placed at this point and then calculate the acceleration when it is released.

E1 E2+

Q1

_Q2

21

1 r

QkE

22

2 r

QkE

C

Nm

C

C

mN 72

6

2

29 104.1

25.0

10100100.9

C

Nm

C

C

mN 62

6

2

29 102.7

25.0

1050100.9

21 EEE CN

CN

CN 767 101.2102.7104.1

Ch16 16

Example 3B. A +100 C point charge is separated from a -50 C charge by a distance of 0.50 m as shown below. (A) First calculate the electric field at midway between the two charges. (B) Find the force on an electron that is placed at this point and then calculate the acceleration when it is released.

+

Q1

_Q2

E

In part A we found that E = 2.1x107 N/C and is directed to the right.

q

FE

EeEqF

CNCF 719 101.2106.1 N12104.3

amF

( to left )

m

Fa 2

1831

12

107.3101.9

104.3s

mkg

N

( to left )

Ch16 17

Example 4. A +100 C point charge is separated from a -50 C charge by a distance of 0.50 m as shown below. Sketch the electric field at the point x as shown.

1E

2E

E

+

Q1

_Q2

X

Ch16 18

Electric Field Lines

• Graphical way of showing the electric field.

• You have seen graphical representations of the earth’s magnetic field-the electric field maps are similar.

• Sometimes called lines of force.

• Arrow on field line gives direction of force.

• The closer together the lines of force are, the stronger the electric field.

• Electric field lines are directed out from positive charges (a) and in toward negative charges (b).

Ch16 19

Electric Field of Point Charges

Ch16 20

Electric Field of Point Charges

Ch16 21

Electric Field of Parallel Plates

Ch16 22

Electric Fields and Conductors•In the static situation, the field outside the conductor is perpendicular to the surface of the conductor

• if the field had a component parallel to the surface, it would cause the electrons in the conductor to move until there was only a perpendicular component.

Ch16 23

Electric Fields and Conductors

•If a conductor is placed in an electric field, the electrons will rearrange themselves until the field inside the conductor is zero

•The field inside a hollow conductor shell is zero (Fig 16-33)

•This makes a metal car a relatively safe place in an electrical storm.