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CHAPTER 15 ELECTRIC FORCE & FIELDS

We will look at the basic properties of electric charge. • Electric charge comes in discrete units • The total charge in the universe remains constant • The force law that describes the interactions between electric charges • Static Electricity; Electric Charge and Its Conservation • Electric Charge in the Atom • Insulators and Conductors • Induced Charge; the Electroscope • Coulomb’s Law • Solving Problems Involving Coulomb’s Law and Vectors • The Electric Field

Around 700 B.C. the ancient Greeks conducted the earliest known study of electricity. Someone noticed that a fossil material called amber would attract small object after being rubbed with wool.

Static Electricity; Electric Charge and Its Conservation

Objects can be charged by rubbing

Charge comes in two types, positive and negative; like charges repel and opposite charges attract. If they have equal positive and negative are electrically neutral. (+) (-) charges proposed by Benjamin Franklin

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Benjamin Franklin

• 1706 – 1790 • Printer, author, founding father, inventor, diplomat • Physical Scientist

– 1740’s work on electricity changed unrelated observations into coherent science

Static Electricity; Electric Charge and Its Conservation

The law of conservation of electric charge states: The net amount of electric charge produced in any process is zero. If one object acquires a positive charge, then an equal amount of negative charge will be found in neighboring objects.

Properties of Electric Charges

• Two types of charges exist – They are called positive and negative – Named by Benjamin Franklin

• Like charges repel and unlike charges attract one another • Nature’s basic carrier of positive charge is the proton

– Protons do not move from one material to another because they are held firmly in the nucleus

• Nature’s basic carrier of negative charge is the electron – Gaining or losing electrons is how an object becomes charged

• Electric charge is always conserved – Charge is not created, only exchanged – Objects become charged because negative charge is transferred from one object

to another

Electric Charge in the Atom

Atom: Nucleus (small, massive, positive charge) Electron cloud (large, very low density, negative charge) All electrons have same electric charge. Coulomb (C) named for a French physicist

191.60 10 Ce x

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Other terms used when discussing charged objects is saying that an object has a net charge. This means that the object has an excess of either (+) or (-) charges.

Protons are bound in the nucleus and, under most common situations do not leave.

Charles Coulomb

• 1736 – 1806 • Studied electrostatics and magnetism • Investigated strengths of materials

– Identified forces acting on beams

Atom is electrically neutral. Rubbing charges objects by moving electrons from one to the other. When objects are charged by rubbing they hold their charge for a limited time. They “leak off” onto water molecules in air. This is because water molecules are polar – neutral overall, but charge not evenly distributed.

Insulators and Conductors

Conductor: Insulator:

Charge flows freely Almost no charge flows Metals Most other materials

Some materials are semiconductors: silicon and germanium

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Induced Charge; the Electroscope

Metal objects can be charged by conduction:

A neutral metal rod in (a) will acquire a (+) charge if placed in contact (b) with a (+) charged metal object. Electrons move as shown by the red arrow. This is called conduction (“by contact”).

They can also be charged by induction:

Take a grounded object: which can easily accept or give up electrons, is brought near a (-) charged object, free electrons in the metal are repelled and move down the wire to the Earth (ground). Cut the wire, the metal object will have a (+) charge.

Nonconductors won’t become charged by conduction or induction, but will experience charge separation:

Almost no electrons move about freely but the (-) charged electrons, attract to the external (+) charge.

The electroscope can be used for detecting charge: you cannot tell the sign of the charge since (-) charge will cause the leaves to separate just as much as a (+) charge.

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The electroscope can be charged either by conduction or by induction. An electroscope can be used to determine the sign of the charge if it is first charged by conduction (b) or induction (a).

The charged electroscope can then be used to determine the sign of an unknown charge.

Coulomb’s Law

Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

This equation gives the magnitude of the force. This equation looks like the Universal Law of Gravitation but – gravity is always an attractive force – electric can be (+) or (-). Also k instead of G.

The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same. Unit of charge: coulomb, C The proportionality constant in Coulomb’s law is then:

Charges produced by rubbing are typically around a microcoulomb:

Charge on the electron: Electric charge is quantized in units of the electron charge.

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Example 1: Determine the magnitude & direction of the electric force on the electron of a hydrogen atom exerted by the single proton

Example 2. Three charged particles are arranged in a line. Calculate the net electrostatic force on particle 3 due to the other charges. Approach: The net force on particle 3 is the vector sum of the force F31 exerted on 3 by particle 1 and the force F32 exerted on 3 by particle 2.

The magnitude of these two forces are obtained using Coulomb’s Law

The magnitude of the net force is 1.5N, and it points to the left.

Coulomb’s Law

The proportionality constant k can also be written in terms of , the permittivity of free space:

This equation looks more complicated but is the same as the previous one just uses .

100.53 10r x m1 2

2

Q QF k

r

9 2 2 19 19

10 2

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

(0.53 10 )

x N m C x x

x m

88.2 10x N

3 1 3 231 322 2

31 32

Q Q Q Q

F k F kr r

9 6 6

31 2

(9.0 10 )(4.0 10 )(8.0 10 )1.2

(0.50 )

x x C x CF N

m

9 6 6

32 2

(9.0 10 )(4.0 10 )(3.0 10 )2.7

(0.20 )

x x C x CF N

m

32 31 2.7 1.2 1.5F F F N N N

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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.

Example 3: Calculate the net electrostatic force on charge Q3 due to the charges Q1 and Q2. The magnitudes of F31 and F32 are

Resolve F31 into its components along the x and y axis

The force 32 has only a y component. So the net force F on Q3 has components

The magnitude of the net force is

And it acts at an angle of

3 1 3 131 322 2

31 32

Q Q Q Q

F Fr r

9 5 5

31 2

(9.0 10 )(6.5 10 )(8.6 10 )140

(0.60 )

x x C x CF N

m

9 5 5

32 2

(9.0 10 )(6.5 10 )(5.0 10 )330

(0.30 )

x x C xF N

m

31 31

31 31

cos30 (140 )cos30 120

sin 30 (140 )sin 30 70

o o

x

o o

y

F F N N

F F N N

31

32 31

120

330 70 260

x x

y y

F F N

F F F N N N

2 2 2 2(120 ) (260 ) 290x yF F F N N N

260tan 2.2 65

120

ox

y

F N

F N

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The Electric Field

The electric field is the force on a small charge, divided by the charge:

The electric field at any point in space can be measured (a). The force on a (+) charge (b) and the force on a (-) charge at that point (c).

Example 4: Calculate the magnitude and direction of the electric field at a point P which is 30 cm to the right of a point charge

The direction of the electric field is toward the charge Q.

The Electric Field

Problem solving in electrostatics: electric forces and electric fields 1. Draw a diagram; show all charges, with signs, and electric fields and forces with directions 2. Calculate forces using Coulomb’s law 3. Add forces vectorially to get result

Field Lines

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

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2

/F kqQ r QE k

q q r

63.0 10Q x C

9 65

2 2

(9.0 10 )(3.0 10 )3.0 10 /

(0.30 )

Q x x CE k x N C

r m

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Electric dipole: two equal charges, opposite in sign:

Electric field lines for two equal positive charges. For unequal charges.

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

Summary of field lines: 1. Field lines indicate the direction of the field; the field is tangent to the line. 2. The magnitude of the field is proportional to the density of the lines. 3. Field lines start on positive charges and end on negative charges; the number is

proportional to the magnitude of the charge.

Electric Fields and Conductors

The static electric field inside a conductor is zero – if it were not, the charges would move.

The net charge on a conductor is on its surface.

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The electric field is perpendicular to the surface of a conductor – again, if it were not, charges would move.

Gauss’s Law

Electric flux:

Electric flux through an area is proportional to the total number of field lines crossing the area. The net number of field lines through the surface is proportional to the charge enclosed, and also to the flux, giving Gauss’s law:

This can be used to find the electric field in situations with a high degree of symmetry.

Electric Forces in Molecular Biology: DNA Structure and Replication

Molecular biology is the study of the structure and functioning of the living cell at the molecular level. The DNA molecule is a double helix:

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The A-T and G-C nucleotide bases attract each other through electrostatic forces.

Replication: DNA is in a “soup” of A, C, G, and T in the cell. During random collisions, A and T will be attracted to each other, as will G and C; other combinations will not.

Photocopy Machines and Computer Printers Use Electrostatics

Photocopy machine: • drum is charged positively • image is focused on drum • only black areas stay

charged and therefore attract toner particles

• image is transferred to paper and sealed by heat

Laser printer is similar, except a computer controls the laser intensity to form the image on the drum

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CHAPTER 15

ELECTRIC FORCES

CONCEPTS

1. The part of an atom is most likely to be transferred as a body acquires a static electric charge is the electron. 2. If a positively charged rod is brought near the knob of a positively charged electroscope, the leaves of the electroscope will diverge. 3. A negatively charged object is brought is brought near the knob of a negatively charged electroscope. The leaves of the electroscope will move farther apart. 4. Electrostatic force F exists between two point charges with a separation distance d. The graph that best represents the relationship between F and d is C. 5. The coulomb is a unit of electric charge. 6. The diagram to the right shows the electric field in the vicinity of two charged conducting spheres, A and B. The static charge for A is positive and B is negative. 7. Electric field intensity is a vector quantity. 8. A metallic sphere is positively charged. The field at the center of the sphere due to this positive charge is zero. 9. An inflated balloon which has been rubbed against a person’s hair is touched to a neutral wall and remains attached to it. The diagram that best represents the charge distribution on the balloon and wall is C. 10. Doubling the magnitude of one charge will double the force between two point charges.

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11. The graph that best represents the relationship between electric field intensity and distance from a point charge is A. 12. An electron is located between a pair of oppositely charged parallel plates. As the electron approaches the positive plate, the kinetic energy of the electron increases. 13. The diagram to the right that best illustrates the electric field around two unlike charges is B.

14. The Millikan oil drop experiment showed the existence of an elementary charge. 15. If the charge on each of two small spheres a fixed distance apart is doubled, the force of attraction between the spheres will be quadrupled. 16. The diagram below that best represents the charge distribution on a neutral electroscope when a negatively charged rod is held near it is B. 17. The unit “volt per meter” measures the same quantity as Newton’s per Coulomb. 18. Electrostatic force F exists between two point charges with a separation distance d. The graph that best represents the relationship between F and d is C.

19. When an object is brought near the knob of a positively charged electroscope, the leaves of the electroscope initially diverge. The charge on the object must be positive.

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20. An electron beam passes upward between two charged plates a represented by the diagram to the right. The electric beam will be deflected toward the left. 21. The electron volt is a unit of energy. 22. The diagram that best illustrates a neutral electroscope being charged by conduction is D. 23. A negatively charged rod is held near the knob of an uncharged electroscope. The diagram that best represents the distribution of charge on the electroscope is D. 24. The diagram to the right shows the arrangement of three charged hollow spheres A, B, and C. The arrows indicate the direction of the electric forces acting between the spheres. At least two of the spheres are positively charged. The sphere that could be negatively charged is A. 25. As an electron moves between two charged parallel plates from point B to point A, as shown to the right, the force of the electric field on the electron remains the same.