electricity and magnetism phy 220 chapter1: electric fields
TRANSCRIPT
ELECTRICITY AND MAGNETISMPhy 220
Chapter1 :ELECTRIC FIELDS
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IntroductionIntroduction
Knowledge of electricity dates back to Greek antiquity Knowledge of electricity dates back to Greek antiquity (700 BC).(700 BC).
Began with the realization that amber (fossil) when Began with the realization that amber (fossil) when rubbed with wool, attracts small objects.rubbed with wool, attracts small objects.
This phenomenon is not restricted to amber/wool but may This phenomenon is not restricted to amber/wool but may occur whenever two non-conducting substances are occur whenever two non-conducting substances are rubbed together.rubbed together.
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1.1 Properties of Electric Charges1.1 Properties of Electric Charges
Observation of “Static Electricity”Observation of “Static Electricity” A comb passed though hair attracts small pieces of paper.A comb passed though hair attracts small pieces of paper. An inflated balloon rubbed with wool.An inflated balloon rubbed with wool.
Two kinds of chargesTwo kinds of charges Named by Benjamin Franklin (1706-1790) as Named by Benjamin Franklin (1706-1790) as positivepositive and and
negativenegative..
Like charges repel one another and unlike charges Like charges repel one another and unlike charges attract one anotherattract one another..
Electric charge is however always Electric charge is however always conservedconserved.. Charge is Charge is neither created nor disappearedneither created nor disappeared.. Usually, Usually, negative chargenegative charge (electron) is transferred from one (electron) is transferred from one
object to the other.object to the other.
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Robert Millikan found, in 1909, that charged objects may only have Robert Millikan found, in 1909, that charged objects may only have an integer multiple of a fundamental unit of charge.an integer multiple of a fundamental unit of charge.
Charge is Charge is quantizedquantized.. An object may have a charge An object may have a charge e, or e, or 2e, or 2e, or 3e, etc but not 3e, etc but not
say say 1.5e. 1.5e. Proton has a charge Proton has a charge +1e+1e.. Electron has a charge Electron has a charge –1e–1e.. Some particles such a Some particles such a neutronneutron have no (zero) charge. have no (zero) charge. A neutral atom has as many positive and negative charges.A neutral atom has as many positive and negative charges.
UnitsUnits In SI, electrical charge is measured in coulomb ( C).In SI, electrical charge is measured in coulomb ( C). The value of |The value of |e| = 1.602 19 x 10e| = 1.602 19 x 10-19-19 C C..
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1.2 Coulomb’s Law - Observation1.2 Coulomb’s Law - Observation
Charles Coulomb discovered in 1785 the fundamental law of Charles Coulomb discovered in 1785 the fundamental law of electrical force between two stationary charged particles.electrical force between two stationary charged particles.
An electric force has the following properties:An electric force has the following properties: Inversely proportionalInversely proportional to the to the square of the separationsquare of the separation, , rr, between the , between the
particles, and is along a line joining them.particles, and is along a line joining them. Proportional to the product of the magnitudes of the charges Proportional to the product of the magnitudes of the charges |q|q11|| and and |q|q22||
on the two particles. on the two particles. AttractiveAttractive if the charges are of if the charges are of opposite signopposite sign and and repulsiverepulsive if the charges if the charges
have have the same signthe same sign..
q1 q2
r
1.2 Coulomb’s Law – Mathematical Formulation
•ke known as the Coulomb constant.
•Value of ke depends on the choice of units.•SI units
–Force: the Newton (N)–Distance: the meter (m).–Charge: the coulomb ( C).–Current: the ampere (A =1 C/s).
•Experimentally measurement: ke = 8.9875109 Nm2/C2.•Reasonable approximate value: ke = 8.99109 Nm2/C2.
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How do we know the units of ke?
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Example: Fun with unitsExample: Fun with units
Recall that units can be manipulated:
Example
•1e = -1.60 10-19 c•Takes 1/e=6.6 1018 protons to create a total
charge of 1C•Number of free electrons in 1 cm3 copper ~ 1023
•Charge obtained in typical electrostatic experiments with rubber or glass 10-6 C = 1 c
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Charge and Mass of the Electron, Charge and Mass of the Electron, Proton and Neutron.Proton and Neutron.
ParticleParticle Charge ( C)Charge ( C) Mass (kg)Mass (kg)
ElectronElectron -1.60 -1.60 1010-19-19 9.11 9.11 1010-31-31
ProtonProton +1.60 +1.60 1010-19-19 1.67 1.67 1010-27-27
NeutronNeutron 00 1.67 1.67 1010-27-27
1.2 Coulomb’s Law – Remarks•The electrostatic force is often
called Coulomb force.•It is a force (thus, a vector) :
–a magnitude –a direction.
•Second example of action at a distance.
21F
12F
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++
r
q1
q2
+-
r
q1
q212F 21F
Example: Electrical ForceQuestion:
The electron and proton of a hydrogen atom are separated (on the average) by a distance of about 5.3x10-11 m. Find the magnitude of the electric force
that each particle exerts on the other.
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Question:The electron and proton of a hydrogen atom are separated (on the average) by a
distance of about 5.3x10-11 m. Find the magnitude of the electric force that each particle exerts on the other.
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Observations:Observations:
We are interested in finding the magnitude of the force between two We are interested in finding the magnitude of the force between two particles of known charge, and a given distance of each other.particles of known charge, and a given distance of each other.
The magnitude is given by Coulomb’s law.The magnitude is given by Coulomb’s law.
qq11 =-1.60x10 =-1.60x10-19-19 C C
qq22 =1.60x10 =1.60x10-19-19 C C
r = 5.3x10r = 5.3x10-11-11 m m
Question:The electron and proton of a hydrogen atom are separated (on the average) by a distance of
about 5.3x10-11 m. Find the magnitude of the electric force that each particle exerts on the other.
Observations:•We are interested in finding the magnitude of the force between two particles
of known charge, and a given distance of each other.•The magnitude is given by Coulomb’s law.•q1 =-1.60x10-19 C•q2 =1.60x10-19 C•r = 5.3x10-11 m
Solution:
Attractive force with a magnitude of 8.2x10-8 N.
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2
2
22 19
9 822 11
1.6 108.99 10 8.2 10
5.3 10
Nme e C
CeF k N
r m
Superposition Principle
•From observations: one finds that whenever multiple charges are present, the net force on
a given charge is the vector sum of all forces exerted by other charges.
•Electric force obeys a superposition principle.
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Example: Using the Superposition Principle
Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q3 if
q1 = 6.00 x 10-9 C
q2 = -2.00 x 10-9 C
q3 = 5.00 x 10-9 C
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+ x
y
- +q2
q1
3.00 m
4.00 m
q3
F32
F31
37.0o
Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on q3.
Observations:•The superposition principle tells us that the net force on q3 is the vector sum of the
forces F32 and F31.•The magnitude of the forces F32 and F31 can calculated using Coulomb’s law.
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+ x
y
- +q2
q1
3.00 m
4.00 m
q3
F32
F31
37.0o
2
2
2
2
9 9
3 2 9 932 22
9 9
3 1 9 831 22
932 31
931
2 2 9
5.00 10 2.00 108.99 10 5.62 10
4.00
5.00 10 6.00 108.99 10 1.08 10
5.00
cos37.0 3.01 10
sin 37.0 6.50 10
7.16 10
Nme C
Nme C
ox
oy
x y
C Cq qF k N
r m
C Cq qF k N
r m
F F F N
F F N
F F F N
65.2o
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Consider three point charges at the corners of a triangle, as shown Consider three point charges at the corners of a triangle, as shown below. Find the resultant force on qbelow. Find the resultant force on q33..
5.00 m
Solution:Solution:
+ x
y
- +q2
q1
3.00 m
4.00 mq3
F32
F31
37.0o
1.3 Electric Field - Discovery
•Electric forces act through space even in the absence of physical contact.
•Suggests the notion of electrical field (first introduced by Michael Faraday (1791-1867).
•An electric field is said to exist in a region of space surrounding a charged object.
•If another charged object enters a region where an electrical field is present, it will be
subject to an electrical force.
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1.3 Electric Field – Quantitative Definition
•A field : generally changes with position (location)
•A vector quantity : magnitude and direction.
•Magnitude at a given location–Expressed as a function of the force imparted
by the field on a given test charge.
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( / )o
FE N C
q
1.3 Electric Field – Quantitative Definition (2)
•Direction defined as the direction of the electrical force exerted on a small positive charge placed at
that location .
E
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- -- - -
- - - -- - -
- -
+ ++ + +
+ + + ++ + +
+ +
+
+ ++ + + +
+ + ++ +
E
1.3 Electric Field – Electric Field of a Charge “q”
•Given
•One finds
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2o
e
q qF k
r
2e
qE k
r
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+
r
qqo
-
r
qqo
• If q>0, field at a given point is radially outward from q.
• If q<0, field at a given point is radially inward from q.
E
E
Problem-Solving Strategy
•Electric Forces and Fields–Units :
•For calculations that use the Coulomb constant, ke, charges must be in coulombs, and distances in meters.
•Conversion are required if quantities are provided in other units.
–Applying Coulomb’s law to point charges.•It is important to use the superposition principle properly.•Determine the individual forces first.•Determine the vector sum.•Determine the magnitude and/or the direction as needed.
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Example:•An electron moving horizontally passes between
two horizontal planes, the upper plane charged negatively, and the lower positively. A uniform,
upward-directed electric field exists in this region. This field exerts a force on the electron. Describe
the motion of the electron in this region.
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-vo
- - - - - - - - - - - - - - - - - - - - - -
+ + + + + + + + + + + + + + + + + + + + + +
Observations:•Horizontally :
–No electric field –No force–No acceleration–Constant horizontal velocity
0
0
0
x
x
x
x o
o
E
F
a
v v
x v t
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-vo
- - - - - - - - - - - - - - - - - - - - - -
+ + + + + + + + + + + + + + + + + + + + + +
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-vo
- - - - - - - - - - - - - - - - - - - - - -
+ + + + + + + + + + + + + + + + + + + + + +
Observations:Observations:
Vertically: Vertically: Constant electric field Constant electric field Constant forceConstant force Constant accelerationConstant acceleration Vertical velocity increase Vertical velocity increase
linearly with time.linearly with time.2
/
/
1/
2
y o
y o o
y o o o
y o o o
o o o
E E
F q E
a q E m
v q E t m
y q E t m
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-
- - - - - - - - - - - - - - - - - - - - - -
+ + + + + + + + + + + + + + + + + + + + + +
Conclusions:Conclusions:
The charge will follow a parabolic path downward.The charge will follow a parabolic path downward.
Motion similar to motion under gravitational field only except the Motion similar to motion under gravitational field only except the downward acceleration is now larger.downward acceleration is now larger.
Example: Electric Field Due to Two Point Charges
Question :Charge q1=7.00 C is at the origin, and
charge q2=-10.00 C is on the x axis, 0.300 m from the origin. Find the electric
field at point P, which has coordinates (0,0.400) m.
E
1E
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x
y
0.300 mq1 q2
0.40
0 m
PE
2E
Question: Charge q1=7.00 C is at the origin, and charge q2=-10.00 C is on the x axis, 0.300 m from the origin. Find the electric field at point P, which has coordinates (0,0.400) m.
Observations:•First find the field at point P due to charge q1 and q2.•Field E1 at P due to q1 is vertically upward.•Field E2 at due to q2 is directed towards q2.•The net field at point P is the vector sum of E1 and E2.•The magnitude is obtained with
2e
qE k
r
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Question: Charge q1=7.00 C is at the origin, and charge q2=-10.00 C is on the x axis, 0.300 m from the origin. Find the electric field at point P, which has coordinates (0,0.400) m.
Solution:
2
2
2
2
6
1 9 51 22
1
6
2 9 52 22
2
5325
541 2 1 25
2 2 5
7.00 108.99 10 3.93 10 /
0.400
10.00 108.99 10 3.60 10 /
0.500
2.16 10 /
sin 1.05 10 /
2.4 10 /
arctan( / ) 25.9
Nme C
Nme C
x
y
x y
oy x
CqE k N C
r m
CqE k N C
r m
E E N C
E E E E E N C
E E E N C
E E
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1.4 Electric Field Lines•A convenient way to visualize field patterns is to draw
lines in the direction of the electric field.•Such lines are called field lines.•Remarks:
.1Electric field vector, E, is tangent to the electric field lines at each point in space.
.2The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength
of the electric field in a given region.
E is large when the field lines are close together and small when far apart.
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1.4 Electric Field Lines (2)
•Electric field lines of single positive (a) and (b) negative charges.
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+ q
a)
- q
b)
1.4 Electric Field Lines (3)
•Rules for drawing electric field lines for any charge distribution.
.1Lines must begin on positive charges (or at infinity) and must terminate on negative charges
or in the case of excess charge at infinity..2The number of lines drawn leaving a positive
charge or approaching a negative charge is proportional to the magnitude of the charge.
.3No two field lines can cross each other.
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1.4 Electric Field Lines (4)
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Electric field lines of a Electric field lines of a dipoledipole..
+ -
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1.4 Insulators and Conductors –Material 1.4 Insulators and Conductors –Material classificationclassification
Materials/substances may be classified according to their capacity Materials/substances may be classified according to their capacity to carry or to carry or conductconduct electric charge electric charge
ConductorsConductors are material in which electric charges move freely. are material in which electric charges move freely.
Insulator Insulator are materials in which electrical charge do not move freely.are materials in which electrical charge do not move freely. Glass, Rubber are good insulators.Glass, Rubber are good insulators. Copper, aluminum, and silver are good conductors.Copper, aluminum, and silver are good conductors.
Semiconductors are a third class of materials with electrical Semiconductors are a third class of materials with electrical properties somewhere between those of insulators and conductors.properties somewhere between those of insulators and conductors.
Silicon and germanium are semiconductors used widely in the Silicon and germanium are semiconductors used widely in the fabrication of electronic devices.fabrication of electronic devices.
Conductors in Electrostatic Equilibrium
•Good conductors (e.g. copper, gold) contain charges (electron) that are not bound to a
particular atom, and are free to move within the material.
•When no net motion of these electrons occur the conductor is said to be in electro-static
equilibrium.
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