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ACADEMIC
PHYSICS
WHAT IS PHYSICS ALL ABOUT?
Physics seeks to understand the natural phenomena |Symbol Unit Other physical quantities are derived from these basic units:
Base Quantity
that occur in our universe; a description
phenomenon uses many speci c terms, de nitions and
of a natural Length ,x Meter - m Pre xes denote fractions or multiples of units; many variable
symbols are Greek letters
Mass m, M Kilogram - kg
mathematical equations Math Skills: Many physical concepts are only understood
Temperature Kelvin- K
Solving Problems in Physics with the use of algebra, statistics, trigonometry and
Time Second -:
In physics,we usethe SI units (International System)Electric Current caleulus
Ampere A(Cs)
for dataandcalculations

CLASSICAL MECHANICS
A. Classical or New tonian Mechanics The position of a .Newton's 1st Law: A body remains at rest or in G. Kinetic Energy & Work
body is given by an equation of motion with position, motion unless in uenced by a force 1. Kinetic energy, K: Kinetic energy is the energy of
velocity and acceleration as variables; mass is the 2. Newton's 2nd Law: Force and acceleration motion; mass, m and velocity, v: K = ½ mv²
measure of the amount of matter; the standard unit determine the motion of a body and predict future The SI energy unit is the Joule (J):
for mass is kg, 1 kg = 1000 g.; inertia is a property of positionandvelocity: F=ma 0R ZF=m a 1J=1kg ms
matter, and as such, it occupies space 3. Newton's 3rd Law: Every action is countered by an
2. Momentum, p: Momentum is a property of motion,
1. Motion along a straight line is called rectilinear; opposing action
de ned as the product of mass and velocity: p =mv
theequation of motiondescribestheposition of theE. Typesof Forces 3. Work (W): Work is a force acting on a body moving
particle and velocity for elapsed time, t
1.A body force acts on the entire body, with the force a distance; for a general force, F, and a body moving
a. Velocity (v): The rate of change of the displacement acting at the center of mass a path, s: W=J Fds
(6)withtime ()y =
A a. A gravitational force, F,, pulls an object toward
the center of the Earth: F = mg
For a constant force, work is the scalar

b.Acceleration (a): The rate of change of the product of the two vectors: force, F, and path, r:
b. Weight = F; gravitational force
dv Av W= Fdcos(0)= F•r
velocitywith time: a= At c. Mass is a measure of the quantity of material,
a & v are vectors, with magnitude and direction
c. Speed is the absolute value of the velocity; scala
independent ofg and other forces
2. Surface forces act on the body's surface
F 0
Maximum work
with the same units as velocity a. Friction, F,, is proportional to the force normal I Nowork
2. Equations of Motion for One Dimension (1-D) to the part of the body in contact with a surface,

Equations of motion describe the future position F:F,-pF. Dynamic Friction

4. Power (P) is energy expended per unit time:
i. Static friction resists the p= 4 Work A Work
(«) and velocity (v) of a body in terms of the initial
movement of a body time At
velocity (v), position (x) and acceleration (a)
ii. Dynamic friction slows Work= P(t)dt
a. For constant acceleration, the position is related
the motion of a body The Sl unit for power is the Watt (W):
to the time and acceleration by the following
For an object on 1W= 1 Joulelsecond = 1 J/s
equationofmotion: x() =x, + yt + ½at Work for a constant output of power:
horizontal plane: Cireular Motion
b.For constant acceleration, the velocity vs. time is W=PAt
given by the following: y,(0) =v,+at
F,- uF=mg
Netforce =F -F. H.Potential Energy & Energy Conseryation
c. If the acceleration is a function of time, the
equation must be solved using a = a(t)
F.CircularMotion 1. The total energy of a body, E, is the sum of kinetic,
1.Motion along a circular path uses K, & potential energy, U: E=K+ XU
B.Motion in Two Dimensions (2-D) polar coordinates: (r, 0 ) 2. Potential energy arises from the interaction with a
1.For bodies moving along ay Polar 2. Key Variables: potential from an extermal force
straight line, derive x- and y-
Potential energy is energy of position: U(r); the form
equationsof motion The distance from the
ofU depends on the force generating the potential:
Meter rotation center(centerof
Gravitation: U(h) = mgh
mass)
y=v,t+ha, t Electrostatic:U(r,J= 92
2. For a rotating body, use polar Tu
Polar: (,0) The angle between r and
Radian If there are no other forces acting on the system, E is
coordinates, an angle variable,xr cos., the (x) axis
constant and the system is called conservative
0, and r, a radial distance from y=r sine,
the rotational center O Radian/second The angular velocity I. Collisions&Linear
Momentum Collisions
1.Types of Collisions
C MotioninThreeDimensions (3-D)
a Radian/second The angularacceleration a. Elastic: conserve energy
1.Cartesian System: Equations of Spherical b. Inelastic: energy is lost as heat or
motion with x, y and z components deformation
2. Spherical Coordinates: Equations The circular motion arc 2. Relative Motion & Frames of
Meter
of motion based on two angles s=r (0 inrad) Reference: A body moves with
(0 and ) and r, the radialdistance velocity v in frame S; in frame S' the velocity is v'; if
from the origin v,' is the velocity of frame S' relative to S, therefore:
3.Tangential acceleration & velocity: y, = ro; a, = ra;
D. Newton's Laws of Motion v and a along the path of the motion arc
v=V'+
x=r sinpcos., 3. Elastic Collision
Newton's Laws are the core y=r sino sin),
principles for describing the motion cosp 4.Centripetalacceleration:a, =: a isdirected ConserveKineticEnergy: ½mv-% mv
toward the rotational center ConserveMomentum: Emy,-Emv, 2
of classical objects in response to ty+z?
forces; the SI unit of force is the a. The centripetal force keeps the body in circular 4. Impulse is a force acting over time
Newton, N: IN=1kg m/s²; the cgs unit is the dyne: motion with a tangential acceleration and velocity Impulse = F At or [F() dt
1 dyne = lg cm/s Impulse is also the momentum change: Píin - Pinit

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 Classical Mechanics(continued) Qutckstuacly
J.RotationofaRigid Body IM.OscillatoryMotion WAVE MOTION
1.Center of Mass: The average" position in the 1. SimpleHarmonicMotion
body, accounting for the object's mass distribution a.Force: F--kAx A. Examples of Types of Waves
2. Moment of Inertia, I: The moment of inertia (Hooke's Law) •Transverse • Longitudinal
is a measure of the distribution of the mass about
the rotational axis: Emr?
b.PotentialEnergy:U, -+kAx'
c.Frequency of the oscillation:
m
Hooke's
Traveling
•Harmonic
• Standing
• Quantum mechanical
r, is the radial distance from m, to the rotational Law 1.General form for a transverse OR traveling wave:
axis Spring y= (k-vt) (to the right) OR y = f(x+ v) (to the left)
Sample I for bodies of mass m: 2. Simple Pendulum 2. General form for a harmonic wave:
rotating cylinder(radiusR): m R a. Period of oscillation: y=A sin (kx – ot) OR Standing Wave
twirlingthinrod(lengthL): m:
rotatingsphere(radiusR): mr T-2x y=A cos (kx – ot)
StandingWave:Multiplesof 2 ts
b.Frequencyofoscillation: the length of the oscillating material
Rotating Bodies Simple 4. Superposition Principle: Overlapping 312 2
Pendulum waves interact => constructive and
N. Forces in Solids & Fluids destructive interference

1.0, the density of a solid, gas or liquid: a. Constructive Interference: The

3. Rotational Kinetic Energy -I p=mass/volume= MV wave amplitudes add up to produce
The rotational energy varies with the rotational 2. Pressure, P, is the force divided by the area of a wave with a larger amplitude
velocity and moment of inertia, than either of the two waves Harmonie Wave
the forces acted upon: P = force/area
4. Angular force is de ned as torque, r. T = Ia = The SI unit of pressure is the Pascal, Pa: b. Destructive Interference: The
wave amplitudes add up to produce
rf(angular
acceleration
force) 1 Pa =1 N/ m²
a. Pascal's Law: For a uid a wave with a smaller amplitude
5. Angular momentum is the momentum associated Pascal's Law
than either of the two waves
withrotationalmotion:L- lo =rp=Jrvdm enclosed in a vessel, the 24
Torque is also the change in L with time: pressure is equal at all
B. Harmonic Wave Properties
points in the vessel
t=rF= dL
dt b.Pressure Variation
gular Wavelength(m) Distance between cycles
K. Static Equilibrium & Elasticity Momentum with Depth
P,; The pressure below
Period T (sec) Time to travel 1 cycle
1.Equilibrium is achieved when:
Ef= 0 Et 0
the surface of a liquid: P, = P, +pgh Frequencyr(Hz) Cyclespersecond: f= 1T
h is the depth, beneath the surface
The body has no linear or angular Angular
acceleration pis the densityof the water o(rad/s) -2r/T= 2xf
Frequency
P, is the pressure at the surface
2. Deformation of a solid body
Wave
a. Elasticity: A material returns Height ofwave
to its original shape after the force acting on it Pressure
Air 4 Amplitude
is removed Variation vvwwwwwpwwwSurthce |Speed v (m/s) Linearvelocityv =f
b. Stress & Strain
i. Strain is the deformation of the body Liquid
C. Sound Waves
i. Stress is the force per unit area on the body 1. Wave Nature of Sound: Sound is a compression wave
c. Hooke's Law: The stress is linearly c. Archimedes' Principle: An object of volume
that displaces the medium carrying the wave; sound cannot
proportional to the strain; stress = elastic V immersed in liquid with density p, feels a
travel through a vacuum
modulus x strain: buoyant force that tends to force the object
2. General Speed of Sound:
i. Linear Stress: out of the water: F, =p Vg
a. B is the bulk modulus, the volume compressibility of
Young's Modulus, symbolized Y Air the solid, liquid or gas
ii. Shape Stress: Archimedes" b.p is the density
w w 0 Surface
Shear Modulus, symbolized S Principle 3. For a Gas: v=
iii. Volume Stress: Liquid y=CJC, (the ratio of heatcapacities)
Bulk Modulus, symbolized B
4.Loudness - Intensity & RelativeIntensity
L. UniversalGravitation Loudness (sound intensity) is the power carried by a
3. Examine Fluid Motion & Fluid Dynamics
sound wave
a. Properties of an Ideal Fluid
a. Relative Loudness - Decibel Scale (dB):
M, .. Universal
Gravitation .. M, i.Nonviscous - minimal interactions
ii. Incompressible – the density is constant (aB) - 10os (.)
ii. Steady ow -no turbulence
1. Gravitational Force & Energy i. The decibel scale is de ned relative to the threshold
iv. At any point in the ow, the product of area of hearing, I,; P4,) = 0 dB
a.Gravitational
energy:U, MM, and velocity isconstant: A, v, = A, Y, ii.A change in 10 dB, represents a 10x increase in sound
b.Gravitational
force:F, - GM,M, b. Variable Fluid Density intensity, I
If the density changes, the following b. Doppler Effect
F, is a vector, along r, connecting M, and M,
equation described properties of the uid: The sound frequency shifts (I) due to relative motion
c. Acceleration due to Gravity, g: For an object
PAY, -P,A,Y, of the source of the sound and the observer or listener:
on the Earth's surface, F, can be viewed as
V, - speed of the observer; v, - speed of the source;
F -mg: g is theaccelerationdue togravityon ES
Varlable Fluld
v- speedofsound
the Earth'ssurface:g =9.8 m/s
Density i. Case 1: If the Doppler Efect
2. Gravitational Potential Energy, U,
+-) ->S
source of sound
a. The Earth's gravitational potential = A is approaching
Flow Through a Hose
>U =mgh the observer, the
b. Weight is the gravitational mD c. Bernoulli's Equation is a more general frequency increases:
force exerted on a body by the description of uid ow ii.Case #2: If the
Earth:Weight= F, =mg i. For any point y in the uid ow: source of sound is
moving away from
Weight is not the same P+%pvtpgy= constant the observer, the
90000000000000 ii.For a uid at rest (special case):
as 1mass frequency decreases:
Gravitational
Potential P,-P, -pgh
Energy

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 THERMODYNANMICS
Thermodynamics is the study Thermodynamlcs e. Carnot's Law: For ideal gas: C, -C, = R c. Reversibile, isothermal expansion of an ldeal Gas
of the work,heat & energy of Carnot's Law is exact for monatomic gases; it against Pi gasexpands from V, to V, using an
aprocess must be modi ed for molecular gases in nite number of steps; the system remains in
IA. KeyVariables system) cquilibrium: W=n RT in
AE C.ldealGasLaw:PV n RT
This type of process gives the maximum work
1.The ldeal Gas Law
Heat: Q +Q added to the system a. Pressure, P: The standard unit is the Pascal (Pa), but
Single Step Expansion
the bar is more commonly used: I bar = 10' Pa
Work: W +W done by the system
b. Volume, V: The standard unit is the m, but the
Energy: E | System internal I liter, L, is more common: 1 L= 1 dm' Before Exxpansion

Enthalpy: H H-E+PV c. Temperature, T: The standard temperature unit is

absolute temperature, the Kelvin scale: T(K)
P
Entropy: S Thermal disorder d. Amount of gas, n: # of moles of gas (mol) P
Temperature: T Measure of thermal E e.R is a proportionality constant, the gas constant,
A er Expansion Work Performed
given the symbol R: R=0.083 L bar mo!K
Pressure: P Force exerted by a gas
2.Applications of Gas Laws
E. TheKineticTheoryofGases
Volume: V Space occupied a. Boyle's Law (constant temperature, T): Pressure is
1. Gas particles of mass, M, are in constant motion,
proportional to l/volume
with velocity, v, exerting pressure on the container
1.Thermodynamic variables are variables of state b. Pressure is proportional to temperature, with
and are independent of the process path; other volume xed 2. Equations for Energy of an Ideal Gas:
variables are path-dependent c. Charles' Law (constant pressure, P): Volume is E= My² and E=RT
2. Types of Processes: Experimental conditions can be proportional to temperature
a. Average Speed of a Gas Molecule:
controlled to allow for different types ofprocesses d. Avogadro's Law (constant P and T): Volume is

Condition Constraints Thermodynamic

proportional to the # of moles,
e. General Ideal Gas Law Application
V M
= /3RT
Result b.GasSpeed& Temperature: V, isproportional
i. Use PV =n RT to examine a gas sample under
Isothermal 4T= 0 AE=0, Q=w speci c conditions of P,V, n and T
to T;a changefrom T, to T,changesthespeed

AE =- w
Adiabatic=0
No heat ow PVT= constant
Boyle's Law Charles Law
c. Gas Speed & Mass: V is proportional to V

d. Kinetie Energy for 1.00 Mole of an Ideal Gas:

Isobaric AP 0 W- PAV
Fixed presure AH =Q
Pressure (Pa)
K-RT
Temperature (K)
AV = 0 AE =0 e. For a Real Gas: Add heat capacity and energy
IsochoricFixe volume W=0 terms for molecular vibrations and rotations
D. Enthalpy & Ist Law of Thermodynamics
F. Entropy& 2ndLaw ofThermodynamics
B. Temperature & Thermal Energy 1.W and Q depend on path of the process; however,
The 2nd Law of Thermodynamics is concerned with
1.Temperature measures thermal energy AEİSindependentofpath
the driving force for a process
a. The SI unit is Kelvin, absolute temperature: 2.1st Law ofThermodynamics:AE =Q-W
T(K) = TCC) + 273.15 a. The change in energy of the system (AE) is 1.Entropy, S
T is always in Kelvin, unless noted in the determined by the difference between the heat Entropy measures the thermal disorder of a
equation gained (Q) by the system and the work performed system:ds =
b. Zeroth Law of Thermodynamics: If two bodies, (w) by the system on the mechanical surrounding
Entropy is a state variable, like E & H:
#1 and #2, are separately in thermal equilibrium 3.Enthalpy, H AS (universe) = AS (system) + AS T.
with a third body, #3, then #1 and #2 are also in Enthalpy is a new state variable derived from the 1st (thermal reservoir)
thermal equilibrium Law of Thermodynamics at constantpressure: 2.2nd Law of Thermodynamics:
2. Thermal Expansion of Solid, Liquid or Gas H=E+ PV AH = AE + PAV For any spontancous process,
a. AH =Q for a process at constant pressure; the AS>0; AS 0 for a system s
a.Solid: aAT
difference between E and H is the work performed at equilibrium or for a reversible
by the process
b.Liquid: BAT process
Heat Flet
. Endothermic: Positive AH; the system absorbs
heat from the surroundings (EX: evaporation of 3.Examples of Entropy Changes
c.Gas:AV= CT) nR (Charles' Law) a. Natural Heat Flow: Heat ows from T,, o
liquid to gas; melting of a solid)
3. Heat Capacity, C i. Exothermic: Negative AH; the system releases b. Entropy & Phase Changes:
C depends on AT and Q, the heat lost or gained: heat to the suroundings (EX: combustion of fuel,
A H(change)
condensation of vapor to liquid) AS(change)
T (change)
C= A ORQ=CAT b.PhaseTransitions:solid - liquid - gasAphase
a. Speci c heat capacity is C per gram change coesponds to a change in enthalpy: solid>liquid positiveAS As,
i. Enthalpy of vaporization: AH, solid-→>liquid positiveAS AS
b. Molar heat capacity is C per mole
c. Two special experimental cases: i.Enthalpy offusion: AH,
c. Entropy & Temperature for an Ideal Gas:
i. Heat capacity for constantpressure, C: c. Enthalpy & VariableTemperature: AH=Jc,dT
AHis the keyvariable For constant C,: AH = C,AT
ST);AS- nC,in ()
Increasing T increases the disorder
ii.Heat capacity for constant volume, C,: 4.Examplesof Work: W =J Pdv
AE is the key variable a. P opposes the AV for an expansion; P causes the d. Entropy & Volume for an Ideal Gas
AV for compression; W depends on the path A gas expands from V, to V,:
d.ldealGas:C, = R ANDC, =R
b. Single step isobaric expansion from V,
i. The ratio of these two heat capacities is called y
to V, against an opposing pressure, P
sV): AS=nR In(
ii. For IdealGas:Y -167 W=(V,-V,)P.=AVPut The disorder of a gas increases if it expands

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 Thermodynamlcs (continued) CurtekStudy
G. Heat Engines 2. The ef ciency of an engine, 1. is de ned as the
1.Thermal Engine: A heat
engine transfers heat, Q.
ratioofWdividedby Q:n0 P Carnot Cycle
2he
from a hot to a cold A
3. Idealized Heat Engine: The Carnot Cycle Chet
reservoir, to produce
work, W a. The Carnot Cycle consists of two isothermal B AT=0
a. The lst Law of steps and two adiabatic steps Thot
Thermodynamics states
i. For overall cycle:
that the work, W, must o.
equal the difference
AT = 0, AH = 0 and AS 0
D AT0
between the heat terms:
W=Q,Q
Thermal Engine
b. CarnotThermalEMciency= 1=l-
Qeotd
C
ELECTRICITY & MAGNETISM
c. For a material with dielectric constant x : 2.Ohm's Law: Current density, J, is in proportion

V) -v(vacuum) to the eld; o is called the conductivity: J = oE

3. Resistance
Electric Ficlds & Electric Charge F«)-F(vacuum) a. The resistance, R, accounts for the fact
that energy is lost by electron conduction;
A. Electric Ficlds & Electric Charge D. Capacitance&Dielectrics resistance is de ned as the voltage divided by
Examine the nature of the eld generated by an 1.A capacitor consists of two separatedelectrical the current: R =
electric charge and the forces between charges conducting plates carrying equal and opposite b. The SI resistance unit is the Ohm, 2
1.Coulomb, given the symbol C, is a measure of charge. A capacitor stores charge/electrical
c. I ohm () = Ivolt(V)
the amount of charge: potential energy l amp (A)
1 Coulomb = 1 amp• 1 sec 2. Capacitance, C, is de ned as the ratio of 4. Resistivity: The inverse of conductivity is
e is the charge of a single electron: charge, Q, divided by the voltage, V, for
resistivity, given thesymbol p : p =
e= 1.6022 x 10-1" C capacitor: C=;v is themeasuredvoltage;
Qis thecharge V 5.Voltage for current I owing through a
2. Coulomb's Law for electrostatic force, F
conductor withresistanceR: V= IR
F 4TE, 4 a. Energy stored in a charged capacitor:
6. Power Dissipation: Power is lost as I passes
3. Electrie Field, E, is the potential generated U=i Qv = cv through the conductor with R:
Power=VR= PR
by achargethatproduces F oncharge4,: b. Parallel plate capacitor, with a vacuum,
7. Resistors in Circuits: Certain groups of
E-Fa with area A, and spacing d:
resistors in a circuit are found to behave as a
4. Superposition Principle: The total F and E have
Capacitance:
i. C= . A single resistor
contributions from each charge in the system:
ii.Energy Stored: a.Forresistorsinseries: R R
F=EF. E-ZE
B. Sources of Electric Fields:Gauss's Law
U=AdE b.Forresistorsin parallel:R
ii. Electric Field:
1.Electric ux, , givesrisetoelectric eldsand
Coulombic forces
E-- Parallel Plate Capacitor
Two Resistors in Series Two Resistors in Parallel

RJR,
2.Gauss'sLaw: D= JE• dA -
Theelectric ux, ., dependsonthe totalcharge
c. Parallel plate capactor,
dielectrie material with R
in the closed region of interest

C. Electric Potential & Coulombic Energy

dielectric constant k,
with area A, spacing d R
C- KEa -KC,
1.Coulombic potential energy is derived from
R R+R
Coulombic force using the following equation:
C= vacuumcapacitor Resistors in Circuits r R,R
U=F dr i. Capacitors in Circuits: A group of
capacitors in a circuit is found to behave F. Direct Current Circuit (Da
a. Coulombic Potential Energy:
like a single capacitor

U 99
1. Goal: Examine a circuit containing hatf
4TEO i.CapacitorsinSeries: C resistors and capacitors; deternıine voli
current properties
b. Coulombic Potentia/Voltage ii.Capacitors in Parallel: Cu -Sc. 2. Key Equations & Concepts
i. The Coulomb potential, V(), generated by
q is obtained by dividing the U, by the EME:Thevoltageof acircuit )
Two Capacitors in Series Two Capacitors in Parallel electromotive force, denoted emf
testcharge,q: v(g) = 4T86T
U= V()|
c. Foranarrayofcharges,q, V,2V,
GlGl a. This voltage accounts for
V,, and the circuit voltage
emf= V,+ IR
2. Potential for a Continuous Charge Distribution: b. The battery has an intemal
Cio G+C,
V- g 4nE,
or
V,=Ir
3.Circuit Terminology
Capacitors in Circuits
3.The Dielectric Effect a.Junction:Connectionof es ore
a. Electrostatic forces and energies are diminished
-GG
Cat"C+C, conductors

by placing material with dielectric constant b. Loop: A closed conductor path

between the charges E. Current & Resistance: Ohm's Law c. Replace resistors in series or parallel with

b. Voltage and electrostatic force (V & F) depend 1.Current & Charge: The current, I, measures R
on the dielectric constant, k the charge passing through a conductor over a 1. Replace capacitors in series or parallel with

time; totalcharge,Q: Q =1t C

4

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 Electricity & Magnetism(continued) QulckStuudy
4. Kirchoffs Circuit Rules 3.Magnetie Moment a. Gauss's Law is based on the fact that isolated
a. Constraints on the Voltage A magnetic moment, denoted M, is produced magnetic poles (monopoles) đo not exist
i. For any loop in the circuit the voltage must
bethesame: 2V =ZIR
by a current loop
a. A current loop, with current I and area A, I Faraday'sLaw -Electromagnetic Induction

ii. The energy must be generatesa magnetic moment of strength M:Faraday's Law: Passing a magnet through a current
conserved in a circuit loop M=1A loop induces a current in the loop

b. Constraints on the Current b. Torque on a loop: A loop placed in a magnetic

i. The current must balance at ,=l,+h cld will experience a torque, rotating the
every node or junction Constralnts on loop:= MB Faraday's Law
Current
ii. For anyjunction: 21-0
iii.The total charge must be conserved in the
circuit; the amount of charge entering and
leaving any point in the circuit must be
equal
7
G.MagneticFicld,B
1. Magnetic Field: A moving electric charge or 1.Faraday's Law of Induction
current generates a magnetic eld, denoted The EMF induced in a circuit is directly
by the symbol B; the vector B is also called proportional to the time rate of change of the
the magnetic induction or the magnetic ux magneticux, ,passing
throughthecircuit:
Torque on a Loop
density EMF- Eds AND EMF =
a. The SI unit for a magnetic eld is the Tesla, T dt
b. The SI unit for magnetic ux is the Weber, Wb
a. Special Case: Uniform eld B over loop of
4.U (magnetic): Magnetic potential energy area A; 0 is the angle formed by dA and B:
IT-Wm' N -*m arises from the interaction of B and M:
U (magnetic) = - M• B
EMF = (BA cos 0)
c. The CGS unit is the Gauss, G: 1 T= 10 G
5.Lorentz Force: A charge interacts with both b. Motional EMF: Moving a conductor of
d. For a bar magnet, the eld is generated from
E and B, the force is given by the following length 1 through a magnetic eld B with a
the ferromagnetic properties of the metal
expression:F = q E+qv•B speed v induces an EMF (B is perpendicular
forming the magnet
i. The poles of the magnet are denoted North/ a. B and E contribute to the force to the bar and to v): EMF = - Blv
South; the eld lines are shown in the gure b. The particle must be moving to interact with c. Lenz's Law: The direction of the induced
below the magnetic eld current and EMF tends to maintain the
original ux through the circuit; Lenz's Law
H. Sources of Magnetic Fields is a consequence of energy conservation
MagneticLines
of Force 1. Biot-Savart Law: Current generates a magnetic
eld J. Electromagnetic Waves
a. Given the current I and the conductor
Electromagnetic Wave
segment of length dl, the induced magnetic
eld contribution, dB, is described by the
following: dB
b. The total magnetic eld for the conductor is

e. For a current loop, the

by the motion of the charged particles in the
eld is generated
givenby: B= d'r
2. The magnetic eld strength varies as the inverse
current. square of the distance from the conducting 1. Electromagnetic waves are formed by tran s
element B and E elds
Lines of Force
3. Special Case - In nitely long straight wire: a. The relative eld strengths are de ned by
B(a) = ais the distance from the wire;
following
equation:c
I is the current; B, is inversely proportional to a b. The speed of light, c, correlates the mag
constaņt, H and electrie constant.
c=
c. In a vacuum, an electromagnetic wave,
wavelength, \, and frequency, f, travels
speed of light, c: c = f
2. Magnetic Force: F on charge, 4, d. X-rays have short wavelength, comparec
moving at velocity, v, in magnetic cld B: radio waves
F, qvB= qvBsin0 Biot-Savart Law e. Visible light is a very small part
spectrum
a. 0 is the angle between
vectors v and B K.Maxwell's Equations
i. For v parallel to B; F= 0 A•B
4. Ampere's Law: For a circular path around wire, Summarizethegeneralbehaviorof electricals
(0= 0, minimum force)
B magnetic elds in free space
ii. For v perpendicular to the total of the magnetic ux, B• dS, must be
B; F= qv B (0 = 2, consistent with the curent, I: f B • dS - 1. Gauss's Law for Electrostatics:
maximum force) A
Right-Hand 5.
Magnetic
Flux, . fEdA-
2 ii. The "right hand rule"
de nes the force Rule a.The magnetic ux, ,, associatedwith an 2. Gauss's Law for Magnetism:
direction area, dA, of an arbitrary surface is given by
$B• dA=0
b. Force on a conducting segment: For a current the following equation: o,-fB• dA; dA is
I passing through a conductor of length I in vector perpendicular to the area dA 3. Ampere-Maxwell Law:
a magnetic eld B, the force is given by: do
F=II|·B b. Special Case - Planar area A and uniform B fB•ds=H,I+H
i. For a general current path s: atangleI withdA: -BA cos 0
4.Faraday's
Law:fE: •dS -9
dt
F=1[ ds•B 6. Gauss's Law: The net magnetic ux through any
closed surface is always zero: B dA = (
ii.For aclosedcurrentloop: F=0

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 BEHAVIOR OF LIGHT
A Basic Properties of Light B. Lenses & Optical Instruments 2. Key Varlables & Concepts
.Light exhibits a duality, having both wave 1.Lenses and mirors gencrate images of objects a. Constructive interference occurs when
wave amplitudes add up to produce a new
and particle properties Mirrer
wave with a larger amplitude than either of
2. Key Variables
the component waves
a. Speed of light in a vacuum, e
b. Index of refraction, n: y=y,ty,
The index of refraction, symbolizedn Ob)

is the ratio of the speed of light in a

vacuum divided by the speed of light in the ***
material: c(vacuum)
n 2. Lenses and mirrors are characterized by a
c(material)
number of optical parameters:
c. View light as a wave -focus on wave
a. The radius of curvature, R, de nes the
properties: wavelength and frequency
shape of the lens or miror; R is two times Constructlve Interference
i. For light as an electromagnetic wave:
thefocallength,f: R 2f b. Destructive Interference occurs when
iLight is characterized by its wavelength wave amplitudes add up to produce a new

("color"), or by its frequency, f |Lens & Mirror Properties wave with smaller amplitude than cither of
d. View light as a particle in order to the component waves; the wave amplitudes
understand the energetic properties of light Parameters + sign -sign cancel out
i. Energy is quantized in packets called
photons converging dìverging J' y=y,ty,
ii. The energy of photon depends on the lens lens
focallength
frequency, f with the proportionality concave convex
constant h, Planck's Constant: miror mirror
E(photon) =hf
virtual
3. Re ection & Refraction of Light objectdistancereal object
object
Destructive Interference
Re ection of Light
Incident virtual c. Huygens' Principle: Each portion of wave
s' image distance real image
Ray image front acts as a source of new waves
3. Di raction of light from a grating with
spacing d produces an interference patterm
object size erect inverted
0. governed by the following equation:
Re ected
d sin = mì, (m =0, 1,2, 3,.)
Ray n image size erect inverted 4. Single Slit Experiment:
For a wave passing through a slit of width
a. Law of Re ection: For light re ecting a, destructive interference is observed for:
b. The optic axis: Line from base of object
from a mirrored surface, the incident and sin 9 = m/a, (m =0, +l, +2, 13,..)
through center of lens or miror
re ected beams must have the same angle 5.X-ray diffraction from a crystal with atomic
with the surface normal: 0, = 0 c. Magni cation: The magnifying power of a spacing d gives constructive interference for:
lens is given by M, the ratio of image size 2 d sin 9 = mà, (m= 0, 1, 2, 3,...)
b.Refraction:
Light changes Refraction of Light toobject
size: M=
speed as it d. Laws of Geometric Optics
passes through i. The mirror equation: The focal length, Fundamental Physical Constants
materials with 6,: image distance and object distance are
Mass of
different indices described by the following relationship: m,9.11x10 kg

+-
Air Electron
of refraction;class S9
this change in Massof Protonm1.67x10" kg
speed bends the ii.The object and image distances can also be
light ray as it used to determine the magni cation: Avogadro
Constant
N, 6.022x10mo!
passes from n,
to n. Elementary
e. A combination of two thin lenses gives a 1.602x10-9 C
i. The angles of the incident and refracted Charge
lens with properties of the two lenses
rays are govened by Snell's Law:
Faraday
n, sin 8,=n, sin 0,; n, n,; indices of i. The focal length is given by the following 96,485 C mol!
Constant
refraction of two materials equation:=+
c.InternalRe ectance: sinl.; light 3. General Guidelines for Ray Tracing Speedof Lightc 3 x10 m s!
passing from material of higher n to a lower a. Rays that parallel optic axis pass through "r"
n may be trapped in the material if the angle b. Rays pass through center of the lens Molar Gas
K 8.314 JmotK
of incidence is too large unchanged Constant
c. Image: Formed by convergence of ray
4. Polarized Light: The eld of the
trac Boltzmann
electromagnetic wave is not spherically
d. Illustration of
k 1.38x10 JK-
Constant
symmetric (EX: plane (linear) polarized light, Ray Tracing
ray tracing for
circularly polarized light) a Converging Gravitation
a. One way to generate a polarized wave is by Lens
G 6.67x10!"m kg's
Constant
re ecting a beam on a surface at a precise
angle,called 0 C. Interference of Permeabilityof
Light Waves |Space
4nx 10'N A
b. The angle depends on the relative indices
1. Goal: Examine
of refraction and is de ned by Brewster's
constructive and Permittivity of
Law: tan 6,= 8.85 x 102 Fm
destructive interference of light waves | Space

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