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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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Electric FieldElectric Field
• 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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Electric FieldElectric Field
• 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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Field DiagramsField Diagrams
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Field DiagramsField Diagrams
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Field DiagramsField Diagrams
• 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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Field DiagramsField Diagrams
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Field DiagramsField Diagrams
• 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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Point ChargesPoint Charges
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Point ChargesPoint Charges
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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
204
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.…