1 coulomb’s law and electric field chapter 24: all chapter 25: all

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Coulomb’s Law and Electric Field

Chapter 24: allChapter 25: all

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Electric charge Able to attract other objects Two kinds

Positive – glass rod rubbed with silk Negative – plastic rod rubbed with fur

Like charges repel Opposite charge attract Charge is not created, it is merely

transferred from one material to another

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Elementary particles Proton – positively charged Electron – negatively charged Neutron – no charge Nucleus – in center of atom,

contains protons and neutrons Quarks – fundamental particles –

make up protons and neutrons, have fractional charge

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ions

Positive ions – have lost one or more electrons

Negative ions – have gained one or more electrons

Only electrons are lost or gained under normal conditions

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Conservation of charge

The algebraic sum of all the electric charges in any closed system is constant.

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Electrical interactions

Responsible for many things The forces that hold molecules and

crystals together Surface tension Adhesives Friction

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Conductors

Permit the movement of charge through them

Electrons can move freely Most metals are good conductors

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Insulators

Do not permit the movement of charge through them

Most nonmetals are good insulators

Electrons cannot move freely

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Charging by induction

See pictures on pages 539-540

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Coulomb’s Law Point charge – has essentially no

volume The electrical force between two

objects gets smaller as they get farther apart.

The electrical force between two objects gets larger as the amount of charge increases

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Coulomb’s Law

221

r

qqkF

r is the distance between the charges q1 and q2 are the magnitudes of the

charges k is a constant

8.99 x 109 N∙m2/C2

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Coulombs

SI unit of charge, abbreviated C Defined in terms of current – we

will talk about this later

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Coulomb’s law constant

k is defined in terms of the speed of light k = 10-7c

k = 1/4

0 is another constant that will be more useful later

0 = 8.85 x 10-12 C2/N∙m2

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The coulomb

Very large amount of charge Charge on 6 x 1018 electrons Most charges we encounter are

between 10-9 and 10-6 C 1 C = 10-6 C

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Examples

See pages 543 - 546

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Electric FieldElectric Field

• A field is a region in space where a A field is a region in space where a force can be experienced.force can be experienced.

• Or: a region in space where a Or: a region in space where a quantity has a definite value at quantity has a definite value at every point.every point.

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• Produced by a charged particle.Produced by a charged particle.• The force felt by another charged The force felt by another charged

particle is caused by the electric particle is caused by the electric field. field.

• We can check for an electric field We can check for an electric field with a test charge, qwith a test charge, qtt. If it . If it experiences a force, there is an experiences a force, there is an electric field.electric field.

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Electric fieldElectric field

• The definite quantity is a ratio of The definite quantity is a ratio of the electric force experienced by a the electric force experienced by a charge to the amount of the charge to the amount of the charge.charge.

• Vector quantity measured in N/C.Vector quantity measured in N/C.

EF tqtq

FE

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Electric fieldElectric field

• To determine the field from a point To determine the field from a point charge, charge, QQ, we place a test charge, , we place a test charge, qqtt, at some position and , at some position and determine the force acting on it.determine the force acting on it.

Q qt

F

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Direction of EDirection of E

• If the test charge is positive, If the test charge is positive, EE has has the same direction as the same direction as FF..

• If the test charge is negative, If the test charge is negative, EE has has the opposite direction as the opposite direction as FF..

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Electric Field - Point Electric Field - Point ChargeCharge

2

Q

4

1

rE

o

tq

FE

2r

Qqk tF

2r

QkE

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• The field is there, independent of a The field is there, independent of a test charge or anything else!test charge or anything else!

• The electric field vector points in The electric field vector points in the direction a positive charge the direction a positive charge would be forced.would be forced.

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Example 1Example 1

• Two charges, QTwo charges, Q11 = +2 x 10 = +2 x 10-8-8 C and C and Q Q22 = +3 x 10 = +3 x 10-8-8 C are 50 mm apart C are 50 mm apart as shown below.as shown below.

• What is the electric field halfway What is the electric field halfway between them?between them?

Q1Q2

50 mm

E1E2

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Example 1Example 1

• At the halfway point, rAt the halfway point, r11 = r = r22 = 25 = 25 mm.mm.

• Magnitudes of fields:Magnitudes of fields:

E1 kQ1

r12

(9 x 109 N • m2

C2

)(2 x 10 8C)

(2.5 x 10 2 m)2

E2 kQ2

r22

(9 x 109 N • m2

C2

)(3 x 10 8 C)

(2.5 x 10 2 m)2

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Example 1Example 1

• EE11 = 2.9 x 10 = 2.9 x 1055 N/C N/C

• EE22 = 4.3 x 10 = 4.3 x 1055 N/C N/C

• EE11 is to the right and E is to the right and E22 is to the left. is to the left.

• EE11 = 2.9 x 10 = 2.9 x 1055 N/C N/C

• EE22 = - 4.3 x 10 = - 4.3 x 1055 N/C N/C

• EE = = EE11 + + EE22 = - 1.4 x 10 = - 1.4 x 1055 N/C N/C

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Example 2Example 2

• For the charges in Example 1, For the charges in Example 1, where is the electric field equal to where is the electric field equal to zero?zero?

• Since the fields are in opposite Since the fields are in opposite directions between the charges, directions between the charges, the point where the field is zero the point where the field is zero must be between them.must be between them.

Q1Q2

E1E2

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Example 2Example 2

E1 E2

kQ1

r12

kQ2

r22

Q1

r12

Q2

r22

r1 + r2 = s, so r2 = s – r1

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Example 2Example 2

Q1

r12

Q2

r22

Q1

r12

Q2

(s r1)2

(s r1 )2

r12

Q2

Q1

s r1

r1

Q2

Q1

r1 s

1 Q2

Q1

r1 23 mm

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Field DiagramsField Diagrams

• To represent an electric field we To represent an electric field we use lines of force or use lines of force or field linesfield lines..

• These represent the sum of the These represent the sum of the electric field vectors.electric field vectors.

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• At any point on the At any point on the field linesfield lines, the , the electric field electric field vectorvector is along a line is along a line tangenttangent to the to the field linefield line..

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• Lines leave positive charges and Lines leave positive charges and enter negative charges.enter negative charges.

• Lines are drawn in the direction of Lines are drawn in the direction of the force on a positive test charge.the force on a positive test charge.

• Lines never cross each other.Lines never cross each other.• The spacing of the lines represents The spacing of the lines represents

the strength or magnitude of the the strength or magnitude of the electric field.electric field.

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Point ChargesPoint Charges

• Lines leave or enter the charges in Lines leave or enter the charges in a symmetric pattern.a symmetric pattern.

• The number of lines around the The number of lines around the charge is proportional to the charge is proportional to the magnitude of the charge.magnitude of the charge.

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Gauss’s LawGauss’s Law

• Electric flux through a closed Electric flux through a closed surface is proportional to the total surface is proportional to the total number of field lines crossing the number of field lines crossing the surface in the outward direction surface in the outward direction minus the number crossing in the minus the number crossing in the inward direction.inward direction.

0Q

EA

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Example 25-9 (see page Example 25-9 (see page 563)563)

Field of a charged sphere is the Field of a charged sphere is the same as if it were a point chargesame as if it were a point charge

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1

r

qE

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Example 25-10 (see page Example 25-10 (see page 564)564)

Field of a infinite line of charge is Field of a infinite line of charge is

rE

02

1

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Other scenarios Other scenarios

• See table on page 567See table on page 567

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Example 3Example 3

• Two parallel metal plates are 2 cm Two parallel metal plates are 2 cm apart.apart.

• An electric field of 500 N/C is placed An electric field of 500 N/C is placed between them.between them.

• An electron is projected at 10An electron is projected at 1077 m/s m/s halfway between the plates and halfway between the plates and parallel to them.parallel to them.

• How far will the electron travel before it How far will the electron travel before it strikes the positive plate?strikes the positive plate?

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Example 3Example 3

• Two charged parallel plates create Two charged parallel plates create a uniform electric field in the space a uniform electric field in the space between them.between them.

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Example 3Example 3

Evo

This is just like a projectile problem except that the acceleration is not a given value.

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Example 3Example 3

a =F

mF = qE = eE

a =eE

m=

(1.6 x 10–19C)(500 N/C)

9.1 x 10–31kg

= 8.8 x 1013 m/s2

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Example 3Example 3

• 8.8 x 108.8 x 101313 m/s m/s22 is the is the vertical vertical accelerationacceleration of the electron. of the electron.

• HorizontallyHorizontally, the acceleration is , the acceleration is zerozero..

• x = vtx = vt• v = 1 x 10v = 1 x 1077 m/s & t = ? m/s & t = ?

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Example 3Example 3

• Back to vertical direction:Back to vertical direction:• y = yy = yoo + v + voot + t + 11//22atat22

• y = y = 11//22atat22

a

2yt

2(0.01 m)8.8x1013 m / s2

= 1.5 x 10-8 s

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Example 3Example 3

• Back to horizontal direction:Back to horizontal direction:• x = vtx = vt• x = (1 x 10x = (1 x 1077 m/s)(1.5 x 10 m/s)(1.5 x 10–8–8 s) s)

• x = 0.15 m = 15 cmx = 0.15 m = 15 cm

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DipolesDipoles

• A pair of charges with equal and A pair of charges with equal and opposite sign.opposite sign.

• Induced dipoles, molecular dipoles, Induced dipoles, molecular dipoles, etc.…etc.…

1 coulomb’s law and electric field chapter 24: all chapter 25: all

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