* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Review for final
Survey
Document related concepts
Work (physics) wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Magnetic field wikipedia , lookup
Time in physics wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Magnetic monopole wikipedia , lookup
Speed of gravity wikipedia , lookup
Electromagnetism wikipedia , lookup
Maxwell's equations wikipedia , lookup
Electric charge wikipedia , lookup
Field (physics) wikipedia , lookup
Superconductivity wikipedia , lookup
Electromagnet wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Transcript
Review for final Schedule • Dec. 3-5 (Wed-Fri) – Review for final ! Dec. 3 (Wed) – HW set #12 due at 11pm ! Dec. 8 (Mon) – Corrections #3 due at 7am ! Dec. 8 (Mon) – Final Exam 5:45-7:45pm • Section 1 – N130 BCC (Business College) • Section 2 – 158 NR (Natural Resources) Final Exam • If >2 finals on Mon. may take make-up final exam on Tues. from 8-10am ! Email Prof. Tollefson with list of other finals • Allowed 3 sheets of notes (both sides) and calculator • Covers Chapters 22-37, HW sets 1-12 • Exam will have 20 questions • Need photo ID Electric Fields • Point change q F =k ! ! q q0 2 q E=k 2 r q V =k r r E points away from positive charges and towards negative charges Superposition principle (many charges) r r r r F = F1 + F2 + ... + Fn r r r r E = E1 + E2 + ... + En n V = ∑Vi i =1 Electric Potential ! Electric potential from field r r ∆V = − ∫ E • ds f i ! Constant field over distance d ∆ V = − Ed ! Work done moving charge q0 W = q0 ∆V Electric Potential ! Blue lines are the electric field ! Dashed lines are equipotential surfaces where all points are at the same potential ! V decreases by constant intervals from the positive charge to the negative charge Guass’ Law ! Electric flux r r Φ = ∫ E • dA r r E • dA = E dA cos θ ! Gauss’ Law ! Net charge qenc is sum of all enclosed charges and may be +, -, or zero r r ε 0 Φ = ε 0 ∫ E • dA = qenc Conductors (example) ! ! ! ! ! ! Charge q1 inside E=0 inside conductor Thus Φ=0 for Gaussian surface (red line) So net charge enclosed must be 0 Induced charge of q2 = -q1 lies on inner wall of conductor Shell is neutral so charge of q3 = -q2 on outer wall Electric Potential Energy ! Work required to assemble the charges 11 12 U =U12 +U13 +U14 +U23 +U24 +U34 ! where etc q1q2 U12 = k d 13 14 Motion in a B Field ! Force on a charged particle due to a magnetic field is ! FB does not change the speed (magnitude of v ) or kinetic energy r r r FB = qv × B of particle ! Charged particles moving with v ⊥ to a B field move in a circular path with radius, r ! Force on a current carrying wire due to a magnetic field is mv r= qB r r r FB = iL × B Motion in a B Field r r r FB = qv × B • Right-hand rule – For positive charges - when the fingers sweep v into B through the smaller angle φ the thumb will be pointing in the direction of FB ! For negative charges FB points in opposite direction Motion in a B Field mv r= qB ! Circular motion ! Period (time for one revolution) 2π r 2π m = T= v qB ! Frequency (the number of revolutions per unit time) ! Angular frequency: 1 f = T ω = 2π f B Fields from Currents ! B field a distance R from a long straight wire carrying current i µ 0i B= 2π R ! B field is tangent to magnetic field lines B Fields from Currents ! right-hand rule ! Point thumb in direction of current flow ! Fingers will curl in the direction of the magnetic field lines due to current B Fields from Currents ! Force on a wire carrying current, i1, due to B of another parallel wire with current i2 µ 0 Li1i2 F= 2πd ! ! Force is attractive if current in both wires are in the same directions Force is repulsive if current in both wires are in the opposite directions B Fields from Currents ! For ideal solenoid: B = µ0in n is the number of turns/length Faraday’s Law ! Magnetic flux r r Φ B = ∫ B • dA = BA cosθ ! Faraday’s law (N loops) ! Lenz’s law – induced emf gives rise to a current whose B field opposes the change in flux that produced it dΦ B E = −N dt Faraday’s law • We can change the magnetic flux through a loop (or coil) by: ! Changing magnitude of B field within coil ! Changing area of coil, or portion of area within B field ! Changing angle between B field and area of coil (e.g. rotating coil) dB E = − NAcosθ dt dA E = − NB cosθ dt d( cosθ ) E = − NBA dt Generators ! ! Generator with N turns of area A and rotating with constant angular velocity, ω Magnetic flux is Φ B = BA cos ω t ! Emf is E = NBAω sinωt t Circuits ! Current ! Resistors ! ! dq i= dt Ohm’s law Power lost V = iR 2 V P = iV = i R = R 2 Circuits ! Definition of capacitance: C = q V ! Parallel plates of area A and separation d C= ε0 A d Circuits ! Junction rule: iin = iout ! Loop rule: sum of potential changes around each loop is zero Circuits ! Parallel C eq = Capacitors Series n ∑C i i V same on each ! Total q is sum ! ! Resistors 1 = R eq ! n ∑ i 1 Ri V same on each 1 = C eq n ∑ i 1 Ci q same on each ! Total V is sum ! n Req = ∑ Ri i ! i same in each ! Total V is sum Elements of RLC circuits Resistor ! ! Energy stored Voltage change U = 0 V = (− )iR Inductor U B 1 = Li 2 di V = −L dt Capacitor 2 U E 1 q2 = 2 C q V = (− ) C (-) means sign relative to the direction of current flow ! Power lost P=i R 2 P=0 P=0 LC Circuits ! Charge q = Q cos(ωt ) dq i= = −Qω sin( ωt ) dt ! Current ! Angular frequency ! No power loss ω= 1 LC RLC Circuits ! Charge on capacitor q = Qe ! − Rt / 2 L cos(ω ′t ) Angular frequency ω ′ = ω 2 − ( R / 2 L)2 ! Natural frequency ω= 1 LC AC Circuits Resistive load E = E msinω d t , ω d = driving frequency VR IR = R Capacitive load VC IC = XC 1 XC = ωd C Inductive load VL IL = XL X L = ωd L X is the reactance AC Circuits E = E msinω d t , ω d = driving frequency ! Input ! Current (same everywhere) Em I= Z i = I sin(ωd t − φ ) X L − XC tan φ = R ! Solution ! Z is the impedance ! I is maximum on resonance where X L = XC X L ( ωd ) = XC ω2 Z = R 2 + ( X L − X C )2 Z=R ωd = ω 2 EM Waves E = E m sin( kx − ω t ) B = Bm sin( kx − ω t ) v = c = fλ = 1 µ 0ε 0 = 3 × 108 m/s Direction and power per unit area Intensity I= 1 2µ 0c E m2 r 1 r r S= E×B Pressure µ0 I pr = c 2I pr = c absorption reflection Polarization ! Polarization is the direction of the E field ! Intensity of unpolarized light with intensity I0 after hitting a polarizing sheet I = ! Intensity of polarized light with intensity I0 after hitting a polarizing sheet I = I 0 cos θ 1 2 I0 2 Reflection & Refraction ! Reflection: θ 1′ = θ 1 ! Refraction (Snell’s law) n2 sin θ 2 = n1 sin θ1 • Index of refraction speed in vacuum c n= = speed in medium v ω1 = ω 2 • Critical angle (no refracted wave) v1 λ1 n2 = = v2 λ2 n1 n2 θ C = sin n1 −1 Mirrors ! ! ! Plane – flat mirror Concave – caved in towards object Convex – flexed out away from object 1 1 1 + = p i f ! ! ! ! ! ! ! f = 12 r r = radius of curvature f = focal length, f>0 concave, f<0 convex p = position of object i = position of image real images on side where object is virtual images on opposite side lateral magnification: h′ m = h i m=− p Thin Lenses ! ! ! ! ! Real images: opposite side - virtual images: same side Diverging lens (f<0): smaller, same orientation, virtual images Converging lens (f>0): both real and virtual images Image position and magnification: 1 1 1 Lens maker’s equation: 1 1 1 = (n − 1) − f r1 r2 p + i = f i m=− p Interference and Diffraction • Diffraction minima given by (a=slit width) y' = a sinθ ' = m' λ m' λ D , m' = 1,2... a Two-slit maxima given by (d=slit separation) d sin θ = ! mλ mλ D y= , m = 0,1,2... d ! Small angles sinθ = θ (θ in radians) Thin Films ! Phase change at interface ! Refraction at interface (the transmitted wave) never changes phase ! Reflection gives a phase change 1 2 ! λ if n1 < n2 Phase change due to path a-b-c in material n2 over a total length 2L ! 1 and 2 are in phase if 2 L = mλn 2 , m = 0,1,2... ! 1 and 2 are out of phase if 2 L = ( m + ) λn 2 , m = 0,1,2... 1 2 λn 2 = λ n2