Physics Quick-Study Guide

~,= m WHAT IS PHYSICS ALL ABOUT? l . I . • _.-. ..~--- - ---~~~~i~~ - Physics seeks to understand the natural phenomena thai . IOase Quantity Symbol Uuit . ~ ph~'Siol1 quantities are derived from these basic units: -I occur in our universe; a descript ion Of a natural Lellglh I , "~ . "'"" Meter - m PreIiRs Uenole fructions or multiples of units; many variable II""" III.. phenomenon uses many specific terms, defini ti ons and Mass m, M Kilogram _ kg symbols are Greek letters mathematical equations Temperature T Kelvin _ K ~I a t h SI..1/ls: Many physical concepts are only understood Solving Problems in Physics Time t Second _ , \\i th the use of algebra, statistics, trigonometry and Tn physics, we use the SI units (International System) Electric Current I iAmpere _ A Ie SI calculus for data and calculations - - - - - - - - - ________ c_._.'--_ _ _ __ _ position of a I. Newton's 1st Law: A body remains at rest or in G. KiuNic Energy & Work motion with position, motion unless intluenced by a force I. 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 = ±mv' measure of the amount of matter; the standard unit for determine the motion of a body and predict future The Sl energy unit is the Joule (J): mass is kg, I kg = 1000 g. ; inertia is a property of position and velocity: F = m a OR ~F = m a IJ = I kg m 2/s 2 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, I. Motion along a straight line is called rectilinear; opposing acti on defined as the product of mass and velocity: p = m v the equation of motion describes the position of the E. T~ pes of Forc~s 3. Work (W): Work is a force acting on a body moving particle and velocity tor elapsed time, t . A body force acts on tbe 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 () dt s Wit. h·time ( t) : v = cis = Lit Ll s acting at the center of mass a. A gravitational force, Fg, pulls an object toward a path, s: W = J F ds For a constant force, work is the scalar product of b. Acceleration (a): The rate of change of the the center of the Earth: F~ = mg the two vectors: force, F, and path, r: b. Weight = Fg; gravitational force dv Ll v W = F d cos (0) = F • r velOCity with time: a = dt = Lit c. Mass is a measure of the quantity of material, independent of g and other forces F__ D --' r F_ _ D a & v are vectors, with magnitude and direction c. Speed is the absolute value of the velocity; scalar 2. Surface forces act on the body's surface a. Friction, F f, is proportional to the force normal to Maximum work r , No work with the same units as velocity the part of the body in contact with a surface, 4. Power (P) is energy expended per unit time: 2. Equations of Motion for One Dimension (I-D) F".: Fr = ~ FII Equations of motion describe the fi.lture position (x) i. Static friction resists the Dynamic Friction P = Ll,",:,ork = LlWork and velocity (v) of a body in terms of the initial Ll time Ll t F" velocity (Vi), position (xo) and acceleration (a) a. For constant acceleration , the position is related to move-ment of a body ii. Dynamic friction slows ~ Work = JP(t)dt the time and acceleration by the following the motion of a body For an object on a "1- 0 The SI unit for power is the Watt (W): 1 W = I Joule/second = I J/s equation of motion: x(t) = X u + Vit + t2 ta horizontal plane: Circular Motion Work for a constant output of power: b. For constant acceleration , the velocity vs. time is Fr=/lFn=/lmg W = PLlt -,<.. given by the following: v , (t) = V i + at Net force = F, - Fr II. Pntential Energy & Energ~ Cnnsenalinn c. If the acceleration is a fi.lI1ction of time, the F. Circular i'liotion I. The total energy of a body, E, is the sum of kinetic, equation must be sol ved using a = aCt) I. Motion along a circular path uses B. i\lotioli in Tllo DiIl1~II,itHl~ (2-0) K, & potential energy, V: E = K + ~U polar coordinates: (r, (J) r I. For bodies moving along a y Polar 2. Potential energy arises from the interaction with a straight line, derive x- and y­ 2. Key Variables: potential from an external force equations X = vix t +ta x t2 Y = Vi,· t of + fa, t' motion 1( ~x I' Meter The distance from the rotation center (center of mass) Potential energy is energy of position: VCr); the form of V depends on the force generating the potential: Gravitation: U(h) = mgh . U() q,q, Tile angle between rand ElectrostatIc: r" =--r;-;­ 2. For a rotating body, use polar Polar: (I', e) B Radian If there are no other forces acting on the system, E is coordinates, an angle variable, x = r cose. the (x) axis constant and the system is called conservative o, and r, a radial di stance from y = I' sine, 1'2 = x2 + y2 w Radian/second The angular velocity I. Collisions & Lilll'ar i\loml'nllllll the rotational center Collisions I. Types of Collisions ." C. i\lolion ill Three Dimen,ions (3-1» mJ a Radian/second 2 The angular acceleration a. Elastic: conserve energy 1. Cartesian System: Equations of " ?At.. . ~ Spherical b. Inelastic: energy is lost as heat or motion with x, y and z components z defonnation "m .. . ; I. The circular motion arc M -~!r ,= 2 2. Spherical Coordinates: Equations s Meter 2. Relative MotiOn & Frames of of motion based on two angles s = rO (0 in rad) I J' Reference: A body moves with velocity v in frame (0 and cp) and r, the radial distance I S; in frame S' the' velocity is v'; if V; is the velocity from the origin. t, i 3. Tangential acceleration & velocity: of frame S' relative to S, therefore: v = V s ' + v' .'C v, = rw; a, = ret; v and a along the path of the 3. Elastic Collision Newton 's Laws are t Ie core X = r simp cosS. principles for describing the motion y = ,. sin<p sinS, motion arc v? Conserve Kinetic Energy: L: t m v,' = L:tm v ,' m z = I' cos<p, of classical objects in response to ,.2 =x2 + .1"2 . . . 2 forces. The SI unit of force is the z 4. Centripetal acceleration: a, = toward the rotational center r; a is directed Conserve Momentum: L: m v, = L: m v, 1 4. Impulse is a force acting over time Newton, N: IN=lkg m/s2; the cgs unit is the dyne: 1 dyne = Ig cm/s 2 3. The centripetal force keeps the body in circular r.Jotion with a tangential acceleration and velocity Impulse = F Ll t or J F (t) dt Impulse is also the momentum change: PCm - Pinit 1 Pressure... i. . 1 _-I: speed of sound =(:.4 1 " T=r.. --. Ug . Volume Stress: 3..Simple a. Frequency of oscillation: "'Simple the length of the oscillating material 2~1f 4. 1Il1inrs:l1 Gnnitatioll 3. Stress is the force per unit area on the body 'Vave Nature of Sound: Sound is a compression wave that c. 1'1 L: c. Period of osci lla . gas or liquid: a./fi a.. Linear Strcss: buoyant force that tends to force the object out of the water: Fh = . sOlmd cannot havel V immersed in liquid with density (J. L = Iw = ~ • p = f r • v dm tbe pressure is equaJ at all waves B.. Relative Loudness . Shape Stress: Archimedes' Principle b. 01 · ' Haoke's • Harmonic • Quantum mechanical ri. The decibel scale is defined relative to the threshold . g is the acceleration due to gravity on the 8.. Angular momentum is the momentum produce a wave with a smaller a. I described properties of the fluid : c. . Potem: 3! £ ~. the following equation ii. the volume compressibility of Young's Modulus. is the force divided by the area of velocity and moment of inertia.3. (hcilblo~ 'totiooII WAVE MOTION 1. . Steady flow ... represents a lOx increase in sound Fg is a vector. In: POo) = 0 dB b. /' .~:~) 0=> <=S f- a. General form for a transverse OR traveling wave: Sample I for bodies of mass m: f=2il'\rn Spring y = f(x· vt) (to the right) OR y = f(x + vt) (to the left) rotating cylinder (radius R): t m R' 2. symbolized Y the solid. Nonviscous . Gravitational Potential Energy. Acceleration due to Gravity. M2 i.0 = mass/ volume = M / V 11. Constructivc Interference: The 3. Incompressible . Simple Pendulum 2. __.-­ a.. The rotational energy varies with the rotational wave with a larger amplitude than 2.·1.the density is constant a. Variable Fluid Density of hearing.-mU a. y = A sin (kx .iVI 2 b. General Speed of Sound: v = . Destructive Interference: The The SI unit of pressure is the Pascal. g: For an object on b. feels a through a vacuum proportional to the strain.­ Earth's sOOace: g = 9. Elasticity: A material returns to its original Amplitude Pressure­ shape after the force acting on it is removed Variation Speed v (m/s) Linear velocity v = Af b. Hooke's Law: The stress is linearly displaces the medium carrying tlle wave. Examine Fluid Motion & Flnid Dynamics r= Cp i C" (the ratio of heat capacities) 4.0 g Y = constant ii. Archimedes' Principle: An object of volume c. Moment of Inertia. Fn::quenc:. Pressure Variation with Wavelength A (Ill) Distance between cycles dt P Momentum Depth K. Bernoulli's Equation is a more general approaching the b..' luids destructive interference I. the Potential P.. : b body.v ­ 2. Fg can be viewed as Fg = m The sound frequency shifts (f'/t) due to relative motion of the source of the sound and the observer or listener: Vo ­ g. T: b. Souud Wu\'es ii. I either of the two waves Harmonic Wave the forces acted upon: P = force/area 4.minimal interactions sound wave ii.. : . the Earth's sOOaee.constructive and :-i.F=dL AJlgular b. For a Gas: v = jrRT M Bulk Modulus. F ~~.Achange in 10 dB . F GM.Decibel Scale (dB): Gravitational Force & Energy iii. For a t1uid at rest (special case): frequency increases: ii. v. The Earth 's gravitational Flow Througb a Hose i. Pascal's Law: For a Pascal's Law amplitude than either of the two associated with rotational motion: M ' ~'.= -GM. Doppler Effect PI A. Static Equilibrium & Elasticit) Period T (sec) : Time to travel I cycle 't P 2: The pressure below the surface of a liquid: 1._. Properties of an Ideal Fluid Loudness (sound intensity) is the power carried by a il1\. Gravitational force: • = --1'-2­ If the density changes. Angular force is defined as torque. the density of a solid . = p.. B is the bulk modulus. connecting MI and M2 intensity." . At any point in the flow. beneath the surface Angular Iw ~ The body has no linear or angular . symbolized B L.0 V g 2. pgh Frequency f(Hz) Cycles per second: f = I/T L:f=O L:T=O b is the de pth. Strain is the deformation of the body C. = p.A. Weight is the gravitational I!II description of f1uid tlow observer. Case 1: If the sQurce potential => U g = mgh (( III ~I of sound is c. the product of area P(dB) = 10 log (t) a. -= · Transverse 'Traveling • Longitudinal • Standing a measure of the distribution of the mass about Itl the rotational axis: m.. Pa: T = Ia = r • f (angular acceleration force) wave amplitudes add up to I Pa = 1 N / m2 5.--.... speed of the source. ' ' I energy: U.. Rotational Kinetic Energy = t LQ2 wave amplitudes add up to produce a .no turbulence iv.umplcs of T) Ill'S of W:wcs 2.8 rnIs 2 Dopplcr Effcct Density O· v. _ . p. along r. Stress & Strain ~. -P. Superposition Principle: Overlapping 3/21.=pgh <=0 S=> frequency decreases: Energy 2 .. is the radial distance from mi to the rotational axis I T La" I. (he force exerted on a body by the Earth: Weight = F g = mg Weight is llllt the same as mass Ti Gravitational I i. Case #2: If the source of sound is moving away from the observer. liquid or gas ii. symbolized S iii. Deformation of a solid body Wave A Height of wave a.0 is the density of the water w (rad/s) = 271/ T = 2m Frequency acceleration PI is the pressure at the surface 2.w t) OR Standing Wave rotating sphere (radius R): *m 1" T = 2rrl g T y = A cos (kx . v. For any point y in the fluid flow: p + +. lIarmonic Win e Properties Torque is also the change in L with time: points in the vessel '. f = Pendulum waves interact => ._ . I: The moment of inertia is Lm\'! b. F. General form for a harmonic wave: twirling thin rod (length L): +.0 is the density Shear Modulus.: ~· qO fluid enclosed in a vessel. Rntation of a I~il:id Rod~ > \I. P. Forces in Sulids & .M GravltatlOna -1'-­ 2 and velocity is constant: AI VI = A2 v2 i. Equilibrium is achieved when: + ' ~I P. stress = elastic modulus x strain: i. v. Center of Mass: The "average" position in the I .Intensity & Relative Intensity .0 v' + . [lh '\0 ~ CO Variable Fluid spced of the observer. . Universal Gravitation . Loudness ..\.w t) 3 Standing Wave: Multiples of A/2 fits Rotating Bodies b. accounting for the object's mass distribution ~ k . RT 1. EX: eo.. P !1 V Entropy is a state variable. n: # of moles of gas (mol) Entropy: S Thermal disorder e. Boyle's Law (constant temperature. Amount of gas.:m ofTh~rn". S 3. Heat capacity for constant volume. j. . 2nd Law of Thermodynamics: a.dQ b. Applications of Gas Laws Pressure: P Force exerted by a gas a.. . The SI unit is Kelvin .:r Condition Constraints b. F . -. Entropy & Volume fOl' an Ideal Gas L1 Y for compression. liquid positive L1 S i1 Sf. are in constant motion. are separately in thennal H = E \.c:j.. '. H Entropy measures the thermal disorder of a system: T is always in Kelvin. Molar heat capacity is C per mole c. ldeal Gas: C" = "2 RAND C. Solid: 'tL = T aLl i. Phase Transitions: solid . Volume: V b. . #1 and #2.l\t. M... c.'tate variable derived from the 1st dS . R is a proportionality constant. . givel] the symbol R: R=O. absolute temperature: gained (Q) by the system and dIe work performed the d"iving force for a process (W) by the system on the mechanical surrounding T(K) = T (OC) + 273. isothermal expansion of an Ideal Gas g rlhe work.. Temperature measures thermal energy dete. Entropy & Phase Changes: C = L1<. = 0 for a system at heat from the ~n).1IpCI[lIIion of b.'Old C depends on L1 T and Q. Q=O L1E= . W depends on the path A gas expands 11"om V I to V 2: i. with with velocity.gas from ThoI to T. ~ . i1 H =Q or II process at constant pressure: the C. Enthalpy of \'8porization: tl. exerting pressure on the container L volume fi xed 2.'" is propOltional to Ili Isobaric L1P = O W = PL1Y d. . . gas expands from V I to V 2 using an process infinite number of steps. then #1 and #2 a. The Ideal Gas Law process gives the maximum work a. . F or Id ea I G as: II. Thermodynamic variables are variables of state = ! RT c.. P): Volume is and are iudependent of the process path.PV ~ H = !:1 E . . Equations for Energy of an Ideal Gas: I. solid pos itive L1 S C. P\" = n RT equilibril.•. C b. T): Pressure Eo Thf Kinetic TheUl'~ of Gast's is proportional to I/volume Gas particles of mass. a change from T] to T2 Isothermal L1 T = 0 L1E = O.'. The change in energy of the system (i1 E) is F. W e. .m" is Result spec ific conditions of P.d~munic. the Kelvin scale: T(K) d. --: . L1 T c. C p : L1 H is the key variable For constant C p : i1 H = C. n controlled to allow for different types of processes e..66­ I The disorder of a gas increases if it expands 3 . = R c . Use PV = n RT to examine a gas sample und.2 Isochoric c. Two special experimental cases: i1H = f C"dT liqu id .. S (universe) = i1 S (system) + C. Single step isobaric expansion from V I to V 2 Y agai nst an S(Y): i1S = n R In(V: ) opposing pressure.T bodies. [l]trOI}~ & 2nd l.'Y of a Q W Carnot's Law is exact for monatomic gases. Endothermic: P05ith ~ H : :he s:~ IIbsoItb For any spontan eous process. Exothermic: ). Gas: Ll V = (T. I] and T proportional to /T .' OR Q = C LlT i. Types of Processes: Experimental conditions can be proportional to the # of moles.W Adiabatic No heat flow PY. C\": 4.00 Mole of an Ideal Gas: 1>.. Pressure is proportional to temperature. = "35 = 1.WJlt ~~-~. Enlh:llp~ & 1st I. Avogadro's Law (constant P and T): Volume is a.. Liquid or Gas performed b) the proc~. :"atural Heat Flow: Heat nows 3. . Heat Capacity. but Single tep Expansion Heat: Q +Q added 10 Ihe system the bar is more commonly used: I bar = lOS Pa Work: W +W done by the system b....m: W = n RT In (~: ) . . the gas constant. Thermal Expansion of Solid. . . V: The standard unit is the m 3. . W and Q depend on path of the process.083 L bar mol'! K'! Tem pera ture: T Measure of thermal E Aft6r E. I d~lIl (. . Kiuetic Energy for 1. #3. 1st Law of Thermodynamics: i1 E =Q. however.. Enthalpy of fusion: i1 Hb b. the heat lost or gained: A phase ehange corresponch t a change In eruhal.. This type of J.Liqo·id ..)nR (C harles' Law) heat to the surroundings I EX. . . For a Real Gas: Add heat capacity and energy terms for molecular vibrations and rotations a. Entropy. = constant 'Temperawrc (1:. . P opposes the L1 V for an expansion..lIS Lm . = "23 R d. ~ .mined by the difference between the heat The 2nd Law of Thermodynamics is concerned with a. S (thermal are also in thermal equilibrium d ifference between E and R i.Ll H (change) Heat Flow a. . Y = ° Fixed volume L1E = Q vV = () i1 E is independent of path 2. ~---~. Examples of Work: W = f PdV S (T): Ll S = n e In " (i:) L1 E is the key variable Increasing T increases the disorder 5 a. ..1 ( h ) . P: The standard unit is the Pascal (pa). b. L. The ratio of these two heat capacities is called r b. . .\". ­ _I Thermodynamics is the study ThennodYDomic~ e. .15 I. S. P causes the d."" i. Pressure.T(change) ii. Average Speed of a Gas Molecule: 2. Volume.:)Jl! ."f'gau\ J H : the s:= reI process c. . unless noted in the equation Enthalpy is a new .'cpansion Work Performed 2. Entropy. it against P eXl. combustion 0: f L 3. Fixed pressure L1 H = Q K -1l. Enthalpy & Variable Temperature: solid . . 3.. 2. is more common: I L = I dm 3 Energy: E System internal E c. Enthalpy. T: The standard temperature unit is BefQJ'e Expansion Enthalpy: H H = E + PV absolute temperature . Gas Speed & Temperature: V.. Reversible. other proportional to temperature E = t M v' and E variables are path-dependent d. Temperature.p) .) c. General Ideal Gas Law Application v = j3~1 Thermodynamic i. Zeroth Law of Thermodynamics: If two Law of Thermodynamics at cOllstant pressure: . Specific heat capacity is C per gram c ange . E a mples of Entropy Changes condensatioll of vapor liquid. r = CC ".. ::-:: ~ . P ext.aw of Thcrmtld~ namics I. --. like E & H: equilibrium with a third body.C.. heat & eneq. . Liquid: LlyY =/3LlT liquid to gas: mdung of a: lid equilibriwn or for a reversible ii. .PT. v. Charles' Law (constant pressure. H. -~ . the system remains in must be modified for molecular gases (". Heat capacity for constant pressure. but the liter.the work resen'oir) 2. & Temperature for an Ideal Gas: ii .Q = w changes the speed by Vffz T. Gas Speed & Mass: v..' THERMODYNAMICS . Carnot's Law: For ideal gas: C p . . determine voltage and ii. For a material with dielectric constant K: 2.\T ~ O equal the difference Tbermal Engine N Qctlld C T.-. Two Capacitor~ in Series Two Capacitors in Parallel electromotive force. The Caroot Cycle consists of two isothermal work. Carnot Thermal Efficiency = TJ = 1 . measures the R. d. Dicl~ctrks energy is lost by electron conduction.. Electric I-iclds <'( F.6022 x 10. TJ. Potential for a Continuous Charge Distribution: 2: V.. Replace resistors in series or parallel with constant K between the charges I. d EoA c±JJ f E • dA = % > 2. Parallel plate capacitor. Capacitors in Series: C " L. Coulomb's Law for electrostatic force . The Dielectric Effect e. Voltage for current I flowing through a charge that produces FcOlli on charge qo: U = -'C = -j-QV = t cv' conductor with resistance R: V = IR 6.J C. Electric Field. b. 4 ..19 C single electron: .. ([I. denoted emf U = V(q)q' ~ a. W a. is in proportion to the field. R. b. is defined as the ratio of charge. to produce a. V. and spacing d: Power =VR = 12 R 4. Voltage and electrostatic force (V & F) depend charge passing through a conductor over a time..c. accounts for the' fact that A.g 2. '" m Examine the nature of the field generated by an I. The battery has an internal resistance. Circuit Terminology or Capacitors in Circuits a..-. R t Rz U.. Clot . resistors and capacitors. Power Dissipation: Power is lost as I passes b.Il1C~ . Capacitance.. uhl between the heat tenns: b. S = 0 . spacing d: C. depends on the total charge in the closed region of interest dielectric constant K. /::.. Sources of Electric Fields: Guuss's La" U = -k oAdE' a. Resistors in Cit'cuits: Certain groups of contributions from each charge in the system: resistors in a circuit are found to behave as a ii. dr C. Two Resistors in Series Two ResIstors in Parallel dielectlic material with The electric flux. Key Equations & Concepts EMF: The voltage of a circuit is called the test charge.L • . Electric flux.L R. . Direct Current Circuit (DC) a single capacitor U ". given the symbol C. gives rise to electric fields and iii.~ Cou lomhic Encrg~ Coulombic potential energy is derived from C -. Junction:.'clrie POIl' fllial .ul = 47Z'E or 1. must Q. ratio ofW divided by Qho.Q..m = 2: R. . 2. Resistance a. For resistors in parallel: 11".. llrul En:.C . Q is the . Current & Charge: The current.-"". Capacitors in Parallel: Coo.. C ' C = cod A I. 0' is called the conductivity: J = O'E Electric Fields & Electric Cbarge 3. Vb' and the circuit voltage. ( II ncn! & Rcsistul1cc: Ohm 's L. H = 0 and /::. F = _1_ q. A capacitor stores charge/electrical by the current: R = TV '"'" the amount of charge: potential energy '" ~ 0 1 Coulomb = 1 amp· 1 sec 2. Goal: Examine a circuit contallllng battery. q': V(q) = 14- q = 1 -7Z'Eo 4 f. RO .I:. ~ emf= Vb + IR b. dielectric F:.-----. TNld T . is the potential generated by a 'Q' 5.. 0 i< C = ~.hl T\'11ld /::.---" .-----···--r c. . Connection of three or more 3.. The I sl Law of steps and two adiabatic steps T Iw .lectric Charge II. given the symbol p: p = ~ ! coul t ~ 3. The efficiency of an engine. V is the measured voltage.apacltance: 7. = c. W.. ([I. Capacitors in Circuits: A group of Resiston in Circuits or R IOI - RIRI R.:im" JdI:T .. Loop: A closed conductor path diminished by placing material with."" = f F. Resistivity: The inverse of conductivity is F. A capacitor consi sts of' two separated electrical resistance is defined as the voltage divided !1l z electric charge and the forces between charges conducting plates carrying equal and opposite « u I. This voltage accounts for the battery. ~ charge .G. C . E. = vacuum capacitor i. V(q). Coulombic PotentialNoltage _1 = . Q. b. Coulomb. Idealized Heat Engine: The Carnot Cycle {thn' reservoir. Coulombic Potential Energy: capacitors in a circuit is found to behave like 1 qq' 1'. Gauss's Law: (/).q'f 41r'€1' r2 a. I. for a capacitor: 1volt(V) c. qj' V ~"d = 2.C1+C z conductors a.. E = Fcou' through the conductor with R: qo with area A. KEoA - d . FeDlI1 : 4. T = 0. .. = 2: J.v ELECTRICITY 8& MAGNETISM r. Replace capacitors in series or parallel with on the dielectric constant.+R z a.--. '---. Electrostatic forces and energies are b. with area A. The SI resistance unit is the Ohm.: TJ = ~ p Carnol Ctclc from a hot to a cold A 3... r: Vb = I r V = _l _ fdrq 47Z'Eo 3.'. Thermodynamic states · .L_ .1. = 2: c 2.m c. The resistance. The Coulomb potential. is defined as the Thermal Engine: A heat engine transfers heat. Ohm's Law: Current density. 1 ohm (Q) = 1 amp (A) . For an array of charges. Superposition Principle: The total F and E have . denoted IR: c.-. generated by current properties q is obtained by dividing the UCOlo I by the iii. For resistors in series: R. Parallel plate capacitor.. Q ::J W e is the charge of a e = 1. Ca(lacil. Q: Q = I • t C.. divided by the voltage.o. EI. with a vacuum. is a measure of charge.. For overall cycle: that the work. r ·-----.o. I. Energy Stored: single resistor B.. Energy stored in a charged capacitor: resistivity.. J. Ii 0 Coulombic force using the following equation: .' .. i. u i. Electric Field: Coulombic forces E=Y =~ Parallel Plale Capacitor b. K total charge. The energy must be a. the force is given by: dw. The'SI unit for a magnetic fi eld is the Tesla. an electromagnetic wave. X-rays ha ve short wavelength . associated with an defines the force direction area. The poles of the magnet are denoted a. F = q v B (0 = n/ 2.. the total of the magnetic flux . . denoted M. denoted by The EMF induced in a circuit is directly the symbol B. is described by th e . The speed of light.The total charge must be conserved in the circuit.. corre lates the magnetic I is the cllrrent. Lenz's Law: The direction of the induced Magnetic Lines of Force I'~~~~*~~~g~e~nerates a magnetic current and EMF tends to maintain the original flux through the circuit. B. t1 . The total magnetic field for the conductor is E lit e. travels at the velocity.\I"X\\eIrs [lluatiollS Summarize the genera l behavior of electrical and magnetic fields in free space ii. i\l a~lIl't it Field. 4. passing through the circuit: = f E ds a. b. E . For any junction: Constraints on rotating the loop: T =M •B Current ~I = 0 iii. Given the current I and the conductor segment . Wm f E. Special Case . CPO' . A current loop. \a consistent with the current. I. (/). LI\\ . H I.:. Magnetic Force: F mag on charge. Band E contribute to the force speed v induces an EMF (B is perpendicular NOIth/South. C == Iti:i"o B c. In a vacuum . Gauss's Law is based on the fact that isolated be the same : ~V =~IR . For a current loop. Gauss's Law: The net magnetic flux through any a. Visible light is a very small part of the spectl1ll11 t. M•B 5. Eleclromagnetic Wan's of length dl. Wb EMF AND EMF = . Lenz's Law is a consequence of energy conservation a. v. c. Ampere's Law: For a circular path around wirc. Gauss ' s Law for Electrostatics: B.B I v figure below field c. The magnetic field strength varies as the I. Ampere-Maxwell Law: magnetic field B.­ by a current loop magnetic poles (monopoles) do not exist ii. the amount of charge entering and leaving any point in the circuit must be equal (. d /1" I dl • r ~ followlllg: B = 411'--1-­'- b. s = A •m from the interaction of Band M: area A. dA = 0 b. the vector B is also called the proportional to the time rate of change of the magnetic induction or the magnetic flux density magnetic flux . minimum forc e) fA ' t' . Faraday' Law every node or junction ii. Magnetic Moment closed surtace is always zero: f B • dA == 0 A magnetic moment. Faraday 's Law of Induction current generates a magnetic field.. 2. (j is the angle between radio waves vectors v and B i. with 2. compared with a.Planar area A and uniform B at e 4. Gauss' s Law for Magnetism: a. G: 1 T = 10" G U (magnetic) =.--< . 4. Lorentz Force: A charge interacts with both E -d d. U (magnetic): Magnetic potential energy arises Wb N m N a. For v perpendicular to ~ I .ElectrolllaJ. For v parallel to B. Motional EMF: Moving a conductor of forming the magnet length I through a magnetic field B with a i. The magnetic nux. For a bar magnet. Kirchoff's Circuit Rules ii. Magnetic Flux.Infinitely long straight wire: . is inversely p roportional to a constant. moving at wavelength.I. ds = /1" I + /10 10" 1ft i. For a closed current loop: F = 0 6. maxmlUl11 . the induced magnetic field Electromagnetic Wave contribution. For any loop in the circuit the voltage must 3. of an arbitrary surface is given by fB. Faraday's Law: f E • dS == . 3. The SI unit for magnetic flux is the Weber.~tW'" 4.orce C ) Right-Hand . Torque on a loop: A loop placed in a i. b. Electromagnetic waves are formed by inve rse square of the distance from the transverse Band E fie lds conducting element a. F=O ( 8 = 0. and the electric constant.and frequency. with current I and area A. /1" . Special Case: Unifonn tield B over loop of IT = ITi' = C . dA. Th e " right hand rule" Rule 2. the field is generated from EMF == Ift(BA cos e) the ferromagnetic properties of the metal and B. the field is generated by /10 given by: B == 411' I J-r-"­ dl • r B / \ r the motion of the charged particles in the current. mu st be e. I: f B • dS == /1" I . F"nItJa~'. For a genera l current path s: b. Constraints on the Voltage i. the force is given by the following expression: F = q E + q \' • B b. Force on a conducting segment: For a CUlTent I passing through a conductor of length I in a the following <:: quation: (/Jm = JB • dA . f. is produced a.~t(/Jm F == I Jds • B angl e I with dA: (/Jm == B A cos . q. The CGS unit is the Gauss. ~ A 5. Constraints on the Current M=IA current loop induces a current in the loop I.ollowlng equatIon: B =c B (a) == :. The field lines are show in the b. The current must balance at magnetic field will experience a torque. The paJticle must be moving to interact with to the bar and to v): EMF = . c: c == fA Fm" = q V' B == qvB sin e d. (j is the angle formed by dA and B: c. dB . F= I I· B dA is vector perpendicular to the area dA fB .. Special Case . T b.. dA = Qeo iii. B • ciS.:lH'til" Induction conserved in a circuit loop generates a magnetic moment of strength M: Faraday's Law: Passing a magnet through a b. . in magnetic tield B: speed of light. i . 2.a is the distance from the wire. Magnetic Field: A moving electric charge or I. The relative field strengths are defined by the 3.1 1 Biot-Savart Law E(I. For light as an electromagnetic wave: shape of the lens or mirror.' . Destr uc the interference occurs when ii.. The object and image distances can also be . l Lens & Mirror Prope rties I \V.. 0 :::1 m mirror mm'or fi'equency.' through center 01 the le ns onstant rn 0 iiiiiiii f'i") of incidence is too large un 'bango"d r-=lr-=I=N I 22=. (m = 0. Polarized Light: The E field o f the c.I s.) R:I) In erte<! 4.I mm ====00 k electromagnetic wave is not spheric atl) trac ings Constant ~~-r-- symmetric (EX: plane (linear) polarized Iigh l. Key Variables the component waves a.\ Images & O bjects c(vacuum) --r---+-l.2 ConYerging Constunt a.3 8x 10'23 JK .' Inverted spacing d produces an interference pattern governed by the following equation: Rcncctcd d sin e = rnA. 2. Speed of light in a vacuum.Refraction: lens is given by M. defines the . f. !virtual cu w E (photon) = h f 3.-' 2.:. (m = 0.27 kg speed bends the ii. Key Variables & Concepts having both wave I. Planck's Constant: i ::i I obj.. destructive interfe re nce of light waves Space -- 6 .s =-4h = M I Elementary i. a. n: J y The index of refraction. sin 0. Light is characterized by its wavelength ("color").. II ' . l---- light ray as it used to determine the magnitication: Avogadro A 6.485 C mol' I Co nsta nt ~~ Ln T. or mi rror sin 0 = m).l\ e JllII)-ilud es add up to produce a new v.67xIO. Image: Fanned b~ con\ergencc of ray Boltzmann 1. T he op tic axis: Line from base of object destructive interference is observed for: from a mirrored surface. image di stan. Constructive interference occurs when and pal'ticle properties I _. Ell 18.sign ca nc~ 1 out understand the energetic properties of light ~E i.. + sIgn 1. -. /. . n2: indice:. R is two ti mes ollStructiw Inte rference the focal length. o f i.. 2.l 3"0_0 r=lru=o I rn _ _ _ ~ c:(]ru=f'i") passing from material of higher n to a lower a. Index of refraction. Ra\' p3. Lenses and mirrors generate images of objects a.. R.. c b. f.-. / N divided by the speed of light in the material: . ReOeetlon of Ugh I Incidenl virtual c.. One way to generate a polarized wave is by Lens reflecting a beam on a surface at a precise Permeability of angle. 1. General Guidelines for Ray Tracing Speed of Light c 3 xlOR m s.. Laws of Geometric Optics ._ I .. = n.. called 0. The mirror equation: The focal length. ~ .85 x 10.. the inci d~nt and renected beams must have the same angle tbmllgh center of len. to obj ect Size: :VI = h' 11 ~ 2 d sin e = rnA. properties: wavelength and frequency i. The radius of curvature. (m = 0. View light as a particle in order to . 3. 1 1 rn"" --­ 10 oWin g eq uutlon : f = rurn _ __ c.) 5.67x10. ./a. . .-... The angles of the incident and refracted e.:e rea l image Ray image front acts as a source of new waves _'..10 47< x 10'7 N A...'J.022 x 10l J mol' I passes li'om n I Constallt to n2 -".:n e \ ith mail er amplitude than either of ~' arameters 1 the ClImpOllen t waves: the wave amplitudes d.---+---~--x o n= 2.3 1 kg h EI~C(ron of refraction. Huygens' Principle: Each portion of wave .1.314 J mol. Rays lh3t parallel oplic axi~ pa s through Molar Gas ~~_o ''f' R 8. the ratio of image size Light changes Refraction of Light ..: p . View light as a wave-focus on wave a. 1 1 1 this change in Glass s+'S'=f Mass of Proton m~ 1 1...11 m3 kg. .:r 4.2 Space b. :Vlagnification: The magnifying power ofa spacing d gi ves constructive interference for: b. Af = c b. Energy is quantized in packets called ! converging diverging CII e :ll photons lens liens :ilu ::l If focal length o?iE> z " 8 concave u ii. d..---.­ n 1 sin 01 = n. f: R = 2 f -. + '[1 reli'action of two materials . Diffraction of light from a grating with ere. ~: : Light . Law of Renection: For light re fl ec tin g b. The focal length is given by the 5 96..l K.1 2 F m. A combination of two thin lenses gives a e 1. Internal Renectance: sine. ~ passes through Fundamental Physical Constants i. or by its frequency. lll u~ lra t ion 0 1 R:o) raCing I (» I circularly polarized light) ray rracing for a Grnvi tation G 6. Lenses and mirrors are characterized b~ :I c (material) number of optical parameters: c.602x I 0-19 C D If'I­ Charge I (» rays are governed by Snell's Law: lens with properties of the two lenses ~ If'I faI1lday rnD 0 . The angle depends on the relative indices of refraction and is defined by Brewster's constructi ve and Pennittivity of n·.-N n may be trapped in the material if the an g l ' b.j . II XI O. with the proportionality ~~ ~ "! '" 'O~ constant h.­ I ====... Single Slit Experiment: For a wave passing through a slit of width a. d.:.) speed as it .. materials with image distance and object distance are different indices described by the following relationship: Mass or In ~ 19. is the ratio of the speed of light in a vacuum «' . Renection & Refraction of Light distance real object I I obJect • I i 0> ::1­ ~ :::I ~ u a: 0. c.: nl.. ± 2. ± 1. l Law: tan e.'V:'. The energy of photon depends on tbe *"" ~ ~ "._ i~. wave amplitudes add up to produce a new wave with a larger amplitude than either of .2. :1. X-ray diffraction from a crystal with atomic with the surface normal: 01 = 0. symbolized n. 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