chapter 17 electric charge and electric field. two kinds of charges: positive and negative two...
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Chapter 17
Electric Charge and Electric Field
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Two kinds of charges: positive and negative
• Two charges of the same kind REPEL each other
• Two charges of different kinds
ATTRACT each other
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Coulomb’s Law
• The magnitude F of the force that each of two point charges q1 and q2 exerts on each
other when they are separated by a distance r is directly proportional to the product of the two charges and inversely proportional to the distance squared
F = k |q1q2|/r2
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q1 q2
Additive forces
q3
r12 r23
r13
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ELECTRIC FIELD
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GAUSS’s LAW
The total flux ΦE coming out of any closed surface is proportional to the total electric charge Qencl inside the volume surrounded by this surface.
ΦE = Qencl / ɛo
Ɛo = 8.854x10-12C2/(N.m2)
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Chapter 18
Electric Potential and Capacitance
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ELECTRIC POTENTIAL ENERGYElectric potential energy is between two
charges (q and q’ ) separated by a distance r and is defined as:
PE = kqq’/r
Electric potential energy is a scalar and has units of Joule (J).
When there are more than 2 charges, the total potential energy is the sum of the energy associated with each pair of charges
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• In the gravitational case, the change in the potential energy associated with an object with mass m when moved from the surface to a height h is
mgh
Similarly, the electric potential energy associated with a charge q in a field E is:
qEd
When the charge is moved a distance d along or opposite direction of the field
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ELECTRIC POTENTIAL or VOLTAGE
• A charge Q creates an electric field around it.
Similarly, this charge will create an electric potential V around it, commonly called voltage
It is a scalar and is defined as:
V = kQ/r
The unit for electric potential is the Volt (V).
Consequently, when a charge q is placed at a distance r from Q, the electric potential energy between the two charges would be:
U = qV
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ELECTRIC POTENTIAL and ELECTRIC FIELD
• For parallel plates separated by a distance d
and a potential difference between them V
the field between the plates is then:
E= V/d
Or
V=Ed
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DEFINITION
• The CAPACITANCE C of a capacitor is the ratio of the magnitude of the charge Q on either conductor (plate) to the magnitude of the potential Vab between the conductors (plates):
C =Q/Vab
The SI unit of capacitance is FARAD
(1farad = 1C/1V)
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CAPACITANCE FOR PARALLEL PLATES
• If the capacitor is made of parallel plates with surface area A and a separation d between the plates, the capacitance is:
C = ɛ0A/d
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Capacitors are often joined
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Capacitors are often joined II – Figures 18.22
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Electric Field Energy in a Capacitor
• One of the applications of the capacitor is to store energy (analogous to the potential energy stored in a spring)
Ucapacitor = (1/2) CV2
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Chapter 19
Current, Resistance, and Directed-Current Circuits
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Current defined
Unit: 1coulomb/second = 1 ampere = 1A
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Resistance and Ohm’s Law
• When the potential difference V between the two ends of a conductor is proportional to the current I passing through the conductor, the ratio (V)/(I) is called the resistance of the conductor :
R = V/IThe SI unit for resistance is the ohm and it is
represented by the Greek letter Ω 1Ω = 1V/A
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Resistivity• The resistance is the property of a given conductor and
it depends on its length L and cross- section area A
L
R = ρ L/A
ρ characterizes the conduction properties of the material
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Power in Electric Circuit
The power P is defined as
P = VabI
The unit for power is the watt1W = 1J/s
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Power for a pure resistor:
For a pure (single) resistor, we have:
P=VabI
Since V= RI
P = RI2 or P = V2ab/R
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Connections in series
Req = R1 + R2 + R3
SAME CURRENTDIFFERENT POTENTIAL
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Connections in parallel
1/Req = 1/R1 + 1/R2 + 1/R3
SAME POTENTIALDIFFERENT CURRENT
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Chapter 20
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Charges moving with respect to a field
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Charges moving with respect to a field
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Charges moving with respect to a field
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UNIT FOR MAGNETIC FIELD• The magnetic field B has unit, in SI :
TESLA
1 tesla = 1T=1N/(A.m)
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The effect of the sign of a moving charge
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Magnetism and circular motion
F = |q|vB
If the motion is Circular
F = mv2/R
R = mv/ |q|B
ω = v/R = |q|B/m
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Force on a conductor with current
F = ILB
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The motor and torque
= (IaB)bsinΦ
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Magnetic field of long straight conductor
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Magnetic field of a long, straight wire:
B = μ0I/(2πr)
r is the distance from the wire μ0 is called the permeability of vacuum
μ0 = 4π x 10-7 T.m/A
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Fields in two conductors side-by-side
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2 wires with currents flowing in the same direction attract each other
2 wires with currents flowing in opposite directions repel each other
F = μ0 L(I1 I2)/(2πr)
Force per unit lengthF/L = μ0 (I1 I2)/(2πr)
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Currents in a loop
Magnetic field at the center of a circular loopB = μoI /(2R) For N loops: B = μo NI /(2R)
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Magnetic field of a Solenoid: B = μonIn = number of turns per unit lengthn = N/L
SOLENOID
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Chapter 21
Electromagnetic Induction
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Does the field induce a current or not?
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Magnetic flux at various orientations
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Magnetic flux at various orientations
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Magnetic flux at various orientations
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Magnetic flux at various orientations
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FRADAY’s LAW• When the magnetic flux ΦB changes in
time, there is a an induced emf directly proportional
to the time rate of change of the magnetic flux :
ɛ = |Δ ΦB /Δt |If we have a coil with N identical turns, then
ɛ = N |Δ ΦB /Δt |
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Lenz’s Law
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Lenz’s Law
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Self-inductance
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Transformers
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TRANSFORMERSV2 / V1 = N2 / N1
If energy completely transformed
V1I1 = V2I2
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Energy associated with an induced current.•energy is stored in an electronic device.
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The R-L circuit
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The L-C circuit •
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In this case, the energy is transferred from the electric field (capacitor) to magnetic field (inductor) and vice versa.
The total energy is however conserved:
The back and forth of the energy constitutes an oscillatory behavior with a frequency ω:
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Chapter 22
Alternating Current
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• A coil of wire rotating with constant angular velocity in a magnetic field develops a sinusoidal oscillating current.
• The potemtial will vary from a maximum V at a frequency ω (or, by a factor of 2π, as f in Hz).
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What are phasors?
• Phasors are graphic representations of location. In two dimensions, you can locate a unique point with a radius vector of length L and its angle with respect to zero.
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Resistance and Reactance
VR = RI
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Resistance and Reactance – Figure 22.6
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Resistance and Reactance – Figure 22.6
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An Inductor in a circuit
VL = XLIXL = ωL
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An Inductor in a circuit
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An Inductor in a circuit –
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A capacitor in an AC circuit
VC = XCIXC = 1/ωC
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A capacitor in an AC circuit
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A capacitor in an AC circuit – Figure 22.8
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The series R-L-C circuit
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V=ZI
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Current and voltage may be found
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Current and voltage may be found
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Power in AC Circuits
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Chapter 23
Electromagnetic Waves
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Electromagnetic waves
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The electromagnetic wave
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The electromagnetic wave• The waves are transverse: electric to magnetic and both to the direction of propagation.
•The ratio of electric to magnetic magnitude is E=cB.
•The wave(s) travel in vacuum at c (speed of light in vaccum).
C = 3.00x108 m/s•Unlike other mechanical waves, there is no need for a medium to propagate.
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vwave = λ /T vwave = λ f
for light: c= λ f
Speed of a wave
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S = Ɛ0cE2 S = EB/μo
Sav = (1/2) Ɛ0cE2max
Sav = (EmaxBmax)/(2μ0)
The INTESITY of the wave I :I = Sav
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Reflection and refraction
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Refraction
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Definition of Index of Refraction
• The index of refraction of an optical material is
n = c/vWhere c is the speed of light in vacuum and v
the speed of light in the material
The frequency f of the wave does NOT change when moving from one material to
another
λ =λ0/n
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Relation between angles
• The angle of reflection θr is equal to the angle of incidence θa for al wavelengths and pair of materials.
• For monochromatic light the angle of refraction θb is related to the angle of incidence θa by:
nasin θa = nbsin θb
With the refracted ray being always on opposite sides of the normal
This is Snell’s Law
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To perform calculations, use the data in Table 23.1
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Total internal reflection
Sinθcrit = nb/na
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Chapter 24
Geometric Optics
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Reflections at a plane surfaceReview key terms.
• object
• image
• real
• virtual
• distance to image
• distance to object
• magnification
• upright
• inverted
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Sign rules for images and objects
• The position of the object and the image determine sign convention.
• Object distance:
Object same side of reflecting/refracting surface as incoming light: s is positive
image distance:imaget same side of reflecting/refracting surface as outgoing light: s’ is positive
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Magnification
m = y’/y = -s’/s
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Plane mirrors exhibit left-right reversalHave you ever looked at some emergency service vehicles and
wondered what ECILOP or ECNALUBMA means? (Actually it’s even harder, the letters are reversed in their presentation).
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Spherical mirrors• Reflections from a spherical mirror depend on the
radius of curvature.
1/s + 1/s’ = 2/R
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Concave spherical mirrors
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Concave spherical mirrors
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• Focal length: f
f = R/2
Hence:
1/s + 1/s’ = 1/f
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The principal rays for mirror imaging
m = y’/y = -s’/s
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The convex spherical mirror
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The convex spherical mirror
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Reflection and production of paraxial rays
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Specific ray tracing for mirror analysis
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Specific ray tracing for mirror analysis
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A complete image construction
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A complete image construction
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A complete image construction
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Refraction at spherical surfaces
(na/s) +(nb/s’) = (nb-na)/R
m = y’/y = -(nas’)/(nbs)
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THIN LENSES
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The converging lens –
Converging lensf > 0
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The principal rays for thin lenses
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The converging lens –
Diverging lensf < 0
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Diverging lenses and foci
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Diverging lenses and foci
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The principal rays for thin lenses
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Any lens that is THICKER in the center than the edges is a converging lens with POSITIVE f
Any lens that is THINNER in the center than the edges is a diverging lens with NEGATIVE f
We assume that the index of refraction of the lens is greater than surrounding one.
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Equations for thin lenses
(1/s) + (1/s’) = (n-1)[(1/R1) – (1/R2)]
(1/f) = (n-1)[(1/R1) – (1/R2)]
This is the lensmaker equation
R is positive when it is on the OUTGOING side (by convention light comes from left)
m = y’/y = -s’/s
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Chapter 25
Optical Instruments
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The camera
• The shutter controls the exposure time and this depends on the film (which would be chemistry, the darkening of silver salts on exposure to light).
• The size of the opening provides interesting physics and is calibrated as “f-stops”. See page 838 in your text.
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• The f-number = focal length/aperture diameter
f-number = f/D
The intensity is proportional to the square of the diameter
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The projector
The position of the projector bulb, lens, and screen image actually serve as a “camera in reverse”
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The eyeThe physics of eyeball optics and the chemistry of rhodopsin’s conformational changes to produce sight is a masterpiece of design and function.
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Aging changes the focal point of an eye – Table 25.1
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Hyperoptic correction
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Myopic correction
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• Lenses for correcting vision are described in terms of power which is defined as the inverse of the focal length expressed in meters:
The unit of this “power” is the DIOPTER
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Correction for a farsighted person: use s=25 cmand a converging lens
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Correction for a near-sighted person: use s=∞and a diverging lens
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The magnifier
Angular Magnification M:M = θ’/θ M=25cm/f(cm)
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The microscope
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The microscope
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Microscope
• m1= -s1’/s1
• M=m1M2 = (25cm)s1’/f1f2