Presentation on theme: "BELLRINGER Compare and explain in complete sentences and formulas"— Presentation transcript:
1BELLRINGER Compare and explain in complete sentences and formulas what is the unit for nuclear force.
2CONSERVATION OF ENERGY? Homework due tomorrowWHAT IS THE LAW OFCONSERVATION OF ENERGY?GIVE EXAMPLES.
3There are Four Fundamental Forces: These are responsible for all we see accelerate1) The Electromagnetic Force(We’ll study it this term)2) The Gravitational ForceThese act over a very small range3) The Strong Nuclear Force4) The Weak Nuclear Force
4The Unification of Forces Physicists would love to be able to show someday that the four fundamental forces are actually the result of one single force that was present when our universe began.Superstring Theory is an interesting and promising possibility in this quest:Web Links: Superstring Theory The Elegant Universe The Fabric of the CosmosRecent Physics Discovery!
5Now let’s review the gravitational force… Any two masses are attracted by equal and opposite gravitational forces:F-Fm1m2rNewton’s Universal Law of Gravitationwhere……G=Universal Gravitation Constant = 6.67x10-11 Nm2/kg2This is an Inverse-Square forceGravity is a very weak force
6atom If an atom has the same amount of + and - charge Neutral (no net charge)If it’s missing electronsnet + chargeIf it has extra electronsnet - chargeatom
10Use rubber gloves in the lab Conductors (such as metals, tap or salt water, and the human body) are good at conducting away any extra charge.Insulators (like plastic, rubber, pure water, and glass) will not conduct away extra charge.Metal:“free electrons”Use rubber gloves in the labTouching it with your hand will discharge it
11- - - - - - Grounding Object is discharged or “grounded” + The earth is a huge reservoir of positive and negative charge+-
12Induced Charge (Charging by Induction) What happens when you bring a neutral metal object near a positively charged object?What happens when you bring a neutral metal object near a negatively charged object?Web Links: Charging by Induction 1 Charging by Induction 2
13Current = Charge per Time Electric Currentwire-electronsCurrentask Ben FranklinElectric current is in the direction that positive charge carriers “would” movewhy?Current = Charge per TimeIqtAmperes (A)seconds (s)Coulombs (C)SI units
14Remember, opposite charges attract: q1 and q2 may represent lots of extra or missing electronsand like charges repel:How much force do q1 and q2 exert on each other?Coulomb’s Lawk = electrostatic constant = 8.99 x 109 Nm2/C2Web Link: Orbiting electron
150= permittivity of free space = 8.85 x 10-12 C2/Nm2 Notes on Coulomb’s Law1) It has the same form as the Law of Gravitation: Inverse-Square Force2) But… (can you spot the most basic difference between these two laws?)3) The electrostatic constant (k) in this law is derived from a more fundamental constant:0= permittivity of free space = 8.85 x C2/Nm24) Coulomb’s Law obeys the principle of superpositionWeb Links: Coulomb force, Releasing a test charge
16What is the direction of the net force on the charge in the middle ? Ex:+q-q+qrrWhat is the direction of the net force on the charge in the middle ?What about the charge on the left?What about the charge on the right?
17Find the net force on charge q1 Ex:q2q1= +4.0 Cq2= -6.0 Cq3= -5.0 C.15 m73°q1q3.10 mFind the net force on charge q1
18Smallest possible amount of charge: 1 extra electron: q = x C1 missing electron: q = x C= e = elementary charge…For any charge q:q = ne , where n = 1, 2, 3, etc…Charge is quantizedAlso:Charge is conserved
19- Ex: 1.0 cm + electron proton Calculate both the gravitational force and the electrostatic force, and compare their magnitudes.
20Both of these examples are scalar fields Electric FieldsField – A set of values that defines a given property at every point in spaceTemperature Field:Elevation Field:Both of these examples are scalar fieldsWe need to look at a vector field
21Wind Notice that the wind vectors each have magnitude and direction This is an example of a vector fieldHere is an animated example: Wind Map
22Electric Field (E) – A vector field surrounding a fixed, charged object that indicates the force on a positive test charge (q0) placed nearbyfixed, charged object+test chargeDraw the Electric Field vector at the position of the test charge.Draw the Electric Field vectors at several other positions surrounding the fixed, charged object.Web Link: Force FieldsThe Electric Field is defined as the Force per unit Charge at that point
23Notes on E-field1) The E-field points in the direction of force on a positive test charge2) If a negative charge were placed in the E-field, what do you suppose would happen?3) The E-field is a property of the fixed charges only (it is independent of the test charge)4) E-fields add as vectors5) Given the E-field value at a certain point, we can calculate the force F on any charge q0 placed there:F = q0E
24Ex:.10 m+q0 = 1.0 C(test charge)+q = 2.0 C(fixed charge)a) Find the force on the test charge using Coulomb’s Lawb) Find the electric field at the position of the test chargec) Could you have answered part b without knowing the value of the test charge?
25Electric Field at a distance r from a point charge q
26Electric Field Lines -represent symmetric paths of a positive test charge +The number of lines is arbitrary, as long as they are symmetricThe density of lines represents the strength of the Electric fieldWhat would the Electric field lines look like if there was a negative charge at the center?
27What do you think the Electric Field lines would look like for… A large (), charged, non-conducting sheet?+A charged, non-conducting sheet that is not infinite?++-Two oppositely charged plates? (called a parallel plate capacitor)
33Consider two charged spheres, one having three times the charge of the other. Which force diagram correctly shows the magnitude and direction of the electrostatic forces?d)a)++e)b)++c)f)++
34- Recall… Gravitational Potential Energy or Elastic Potential Energy Now…-+Electric Potential Energy (EPE)Only Conservative Forces have an associated PE
35EPE = -W = -(Fcos)s Recall: PEgrav = mg(h) = -(Work done by gravity)+-Similarly:EPE = -(Work done by electrostatic force)= - (Fcos)sangle between F and sForcedisplacementEPE = -W = -(Fcos)s
36Uniform Electric Field Ex:+2.0 mproton+Uniform Electric FieldE = 4.0 N/Ca) Find the force on the proton.b) Find the work done by that force as the proton moves 2.0 m.c) Find the change in EPE as it moves 2.0 m.d) Find the change in EPE if an electron were to move through the same displacement.
37Work is Path Independent for conservative forces: Ex: GravityEx: Electric Fieldpath 1path 2path 1path 2Work done by electrostatic force on path =Work done by electrostatic force on path 2Work done by gravity on path = Work done by gravity on path 2
38= Total Mechanical Energy (E) += Total Mechanical Energy (E)EPE is a type of mechanical energy, like…+++Kinetic Energy (KE) = ½ mv2Rotational Kinetic Energy (KER) = ½ I2Gravitational Potential Energy (PEgrav) = mghElastic Potential Energy(PEelast) = ½ kx2is conserved if there are no non-conservative forces present (ie friction).
39Uniform Electric Field E = 150 N/C Ex:+1.0 mproton+Uniform Electric FieldE = 150 N/CA proton released from rest into this electric field will be going how fast after traveling a distance of 1.0 m ?Can you think of two different methods to use in solving this problem?Do they yield the same answers?
40EPE q E In both previous examples, we saw that… q 2q Twice the charge has twice the EPEWe would like to have a new quantity that describes the “Potential” at various points in the electric field independent of the charges in it:= EPE per chargeAlso called Potential or VoltageSI Unit = J/C = 1 Volt
41From the definition of Electric Potential, we can show that when a charge is moved from one point to another in an electric field:12EWork done by the Electric Field= -Charge that was movedDifference in Potential between its old and new positionsW = -q0(V)
42V (in Volts) = Potential EPE (in Joules) = Electric Potential Energy Let’s make sure that we understand the difference between Potential and Electric Potential Energy:V (in Volts) = Potentiala property of a certain position in an Electric Field with or without charges placed thereE-EPE (in Joules) = Electric Potential Energya property of charges placed at a certain position in an external Electric Field+EWeb Link: EPE vs Potential
43We now have a new SI unit for Electric Field: Volts / meter E = 3 N/C = 3 V/mExWe now have a new SI unit for Electric Field:Volts / meterThere is a force of 3 Newtons on each 1 Coulomb of charge in the fieldThe Potential changes by 3 Volts for every 1 meter of distanceWe also have a new energy unit (not SI):The electron-Volt (eV) amount of energy gained (or lost) when 1 electron moves through a potential difference of 1 volt--1 V
44Equipotential Surfaces adjacent points at the same electric potential E-fieldEquipotential Surface
47Notes on Equipotential Surfaces 1) Equipotential surfaces are always perpendicular to Electric Field linesWeb Link: Electric Field Lines2) If a charge moves on an equipotential surface, the work done by the Electric Field is zero:FEquipotential SurfaceE-Field+sWeb Link: Equipotential surfaces
48Potential gets higher in this direction In the case of a Uniform Electric Field, it is especially easy to calculate the potential difference between equipotential surfaces:++++----EPotential gets higher in this directionPotential gets lower in this directionE is in Volts/meterE = V/sV = E(s)
49Find the potential difference between the plates. Ex:E = 5.0 V/m.30 mFind the potential difference between the plates.
50In the lab, we could use a Voltmeter to simply measure the potential difference:
51This means there is a potential difference (V) of 12 Volts between the terminals of the battery
52Calculating the Potential due to a Point Charge What is the Potential at this point?k = electrostatic constant = 8.99 x 109 Nm2/C2qNotes:1) Include the sign of q in your calculation! (+ or -)2) Potential Difference can also be calculated:V = V2 – V13) The equation can also be used for a charged sphere:+rTotal chargeDistance from center
54Ex:-electrona) Starting at 1.0 nm from the electron and moving out to 5.0 nm from the electron, what is the change in potential ?b) What is the electric potential energy (in eV) of a proton that is placed at a distance of 5.0 nm from this electron?c) What is the electric potential energy (in eV) of another electron at a distance of 5.0 nm from this one?
55Calculating the Potential due to Multiple Point Charges +What is the value of the Electric field directly between equal charges?What about the value of the Electric Potential there?Electric Potential is a scalar not a vectorV = V1 + V2 + V3 + … (an algebraic sum, not a vector sum)
56Ex:+qdddP-q-qd+qFind the potential V at point P due to the four charges.Web Link: Complex Electric Field
57Capacitor a device that stores energy by maintaining a separation between positive and negative charge(Symbol: )
59+q - -q q = C V Parallel Plate Capacitor This is called “charging a capacitor”+q-V-qV = potential difference of the capacitorq = charge of the capacitorq and V are proportional:q = C VC = Capacitance (a fixed property of each capacitor)SI unit = 1 Farad (F) = 1 Coulomb / Volt
60Dielectrics electrically insulating materials What happens to the Electric Field?Capacitor without a dielectricCapacitor with a dielectricThe Electric Field magnitude is less in a dielectricHow much less depends on the dielectric constant () of the material
61Calculating the Capacitance (C) of a parallel plate capacitor A = plate areadd = plate separation = dielectric constantNotice:Capacitance is independent of both charge and voltage(0= 8.85 x C2/Nm2)Adding a dielectric increases the CapacitanceWeb Links: Capacitance Factors, Lightning
62Energy = ½CV2 How much Energy is stored by a capacitor? Capacitance VoltageWhat’s the energy density in an Electric Field?* For any electric field
63+q-q-q+qdDConsider a parallel plate capacitor with charge q and plate separation d. Suppose the plates are pulled apart until they are separated by a greater distance D. The energy stored by the capacitor is now1. greater than before2. the same as before3. less than before
64Pulse Discharge Machine Here’s a Web Link about a huge capacitor and what can be done with all that stored energy:Pulse Discharge Machine
65Battery or other emf source Web Link: DC ElectricityV+-Imagine a wire:-E-Now imagine bending the same wire into a loop:+-VBattery or other emf sourceEx:emf = 9 Vemf – electromotive “force” – the potential difference between the terminals of an electric power source
67The current arrow points with the “positive charge carriers” I +Web Link: Conventional Current+-+SI unit = Ampere(A) = 1 C/sNotes on Current:1) Remember: charge is conserved2) Current is a scalar, not a vector3) There are two types of current:DC (direct current) charge moves the same direction at all timesAC (alternating current) charge motion alternates back and forthWeb Link: AC vs. DC
68A DC current of 5.0 A flows through this wire: Ex:A DC current of 5.0 A flows through this wire:IHow much charge flows past this point in 4.0 minutes?
69Will the bird on the high voltage wire be shocked?
70applied voltageresulting currentSI unit: Ohm () = 1 V/AWeb Link: ResistanceResistor – a circuit component designed to provide a specific amount of resistance to current flow.(Resistor symbol: )
71Draw the circuit diagram, and calculate the current in this circuit. Ex:1000 9 VDraw the circuit diagram, and calculate the current in this circuit.
73Resistivity = = a property of a material used in making resistors Resistance = R = a property of a given resistor (Ex: 20 , 400 , etc.)Resistivity = = a property of a material used in making resistorsBuilding ResistorsLA(: SI unit = ·m)
74Ex: Aluminum Power Lines Consider an aluminum power line with a cross sectional area of 4.9 x 10-4 m2 . Find the resistance of 10.0 km of this wire.
75Ex: Incandescent Light Bulb 120 VTungsten wire radius .045 mmI = 12.4 AWhat is the length of the tungsten wire inside the light bulb?Web Link: Light bulb
76V = I R “Ohm’s Law” Is it really a law ? ( I V ) It works for resistors:IV( I V )What about other devices?Light BulbIV( I V )DiodeIV“Ohm’s Law” is not really a Law!
77If the device is a resistor: Power = P = IVRate of energy transferSI Unit = 1 Watt (W) = 1 J/sIf the device is a resistor:V=IREnergy dissipated by the resistor as thermal energyP = I V= I2RP = I V= V2/RI=V/R
78Ex: Space Heater120 V1500 W HeaterFind:a) The resistance of the heaterb) The current through the heaterc) The amount of heat produced in 1 hour
79…back to the difference between AC and DC: Web Link: AC vs. DCDC ( ) :VoltagetimeEx:AC ( ) :VoltagetimeEx:V = V0 sin ( 2 f t )radiansVoltage amplitudefrequencytime
80I = I0 sin ( 2 f t ) So what does AC current look like? Light bulb: Resistance RTypical household outlet:V0 = 170 V f = 60 HzI = I0 sin ( 2 f t )= I0 = current amplitudeIt
81How many times a day does the current change direction? Ex: Alarm ClockV0 = 170 V f = 60 HzHow many times a day does the current change direction?
82These are the values that matter AC PowerP = I V = ?peak valuesEx:V0 = 170 VWhat is the rms voltage?These are the values that matterlook familiar??P = Irms VrmsP = (Irms)2 RP = (Vrms)2 / R
83Ex: SpeakerIf the power rating of the speaker is 55 Watts, and its resistance is 4.0 , what is the peak voltage?
86Resistors in Series RS = R1 + R2 Resistors in Parallel R1 R2 (RP < R1 , R2)
87RRConsider two identical resistors wired in series. If there is an electric current through the combination, the current in the second resistor is1. equal to the current through the first resistor.2. half of the current through the first resistor.3. smaller than, but not necessarily half of the current through the first resistor.
88ABAs more resistors are added to the parallel circuit shown here, the total resistance between points A and B1. increases2. remains the same3. decreases
89Ex:For some holiday lights, if one bulb is bad, the whole string goes out. For others, one bulb can go out and the rest stay lighted. What is the difference ?
90current is like a parade I = V/RBasic Circuit:VRR1Series Circuit:VR2Current (I) has the same value everywhere in the circuitRS = R1 + R2Icurrent is like a paradeVR1 + VR2 = VBatteryvoltage is like moneyRSVII = V/RS
92What is the series resistance? Ex:416 V4What is the series resistance?Calculate the current in this circuit.
93What is the parallel resistance? 16 V44What is the parallel resistance?Calculate the current in all branches of this circuit.
94Ex:47 V28 The current through the 47 resistor is .12 A Calculate the voltage V of the battery.
95Ex:V47 28 The current through the 47 resistor is .12 A Calculate the current through the 28 resistor.
96In a series circuit, the current is the same through each resistor VR2In a series circuit, the current is the same through each resistorR1VR2In a parallel circuit, the voltage is the same across each resistorNotice that the terminology will help us remember how to measure current and voltage
102Find the equivalent resistance of this circuit: Ex:Find the equivalent resistance of this circuit:
103Web Link: Kirchoff’s 1st Law Kirchoff’s RulesI) The Junction RuleThe sum of the currents entering any junction is equal to the sum of the currents leaving that junction.Ex:I1+ I2+ I3= I4I2I3I1I4Web Link: Kirchoff’s 1st Law
104The potential differences around any closed loop sum to zero. II) The Loop RuleThe potential differences around any closed loop sum to zero.Web Link: Kirchoff’s 2nd LawEx:R1VR2R3V = I R+-I2I3I1+-+-VR1 = I2R1+-VR2 = I2R2VR3 = ?This loop (clockwise):Write out the equations for this loop and the outer loop+V - I2R1 - I2R2 = 0
105Here are the steps for applying Kirchoff’s Rules to solve for unknown currents and voltages in a circuit:Step 1) Label all the different currents in the circuit I1, I2, I3, etc. (current direction is arbitrary)Step 2) Apply the junction rule at each junction (one junction will yield redundant information)Step 3) Indicate which end of each device is + and -I+-+-Step 4) Apply the loop rule to each independent loopStep 5) Solve the equations for the unknown quantities
106Use Kirchoff’s rules to find Ex:3.0 8.0 V4.0 V1.7 A5.0 Use Kirchoff’s rules to finda) the remaining two currents in the circuit, andb) the unknown voltageWeb Link: Building circuits
107Capacitors in Circuits dRecall:C AC 1/dCapacitors in Series:C1VC2C1VC2Capacitors in Parallel:CP = C1 + C2
108a) Find the total capacitance of the circuit Ex:8.0 F5 V4.0 F6.0 Fa) Find the total capacitance of the circuitb) Find the total charge stored on the capacitors
109RC Circuits Charging a Capacitor: Web Link: RC Circuit I At t = 0: close the switchFirst instant: I = V0/RThen: I decreases as the capacitor fills with chargeWeb Link: RC Circuit IIFinally: I = 0, and Vcap = Vbattery = V0q0 = CV0full capacitor chargeCharge on capacitortimeRC = time constant =
110Discharging a Capacitor: Web Link: RC Circuit IThe capacitor starts out fully charged to voltage V0At t = 0: close the switchFirst instant: I = V0/RThen: I decreases as the capacitor loses its chargeFinally: I = 0, and Vcap = 0Web Link: RC Circuit IICharge on capacitortime
111Magnetic Field (B) points from “North” to “South” poles Recall: Electric Field (E) points from + to - chargeMagnetic Field (B) points from “North” to “South” polesopposite poles attract like poles repelMagnetic Field LinesB is tangent to the field lines at any pointThe density of the lines represents the strength of the magnetic fieldWeb Links: Magnetic Field D Magnetic Field
112Facts about Magnetic Fields (B-fields) 1) North and South poles cannot be isolated2) All B-fields are caused by moving electric charge3) The Earth has a Magnetic Field:Web Links: Northern Lights4) B-fields exert a force on moving, charged particles:+Force is out of the screenBunaffected++unaffected+Force is into of the screen
113Magnetic Force = F = qvBsin What is the direction of this force?q = chargev = speed of chargeRight Hand Rule (RHR) (For a positive charge)B = magnetic field = angle between v and BFingers point with vBvFThen curl toward BThumb points with FSI unit for B-field is a Tesla (T)(F is in opposite direction for a negative charge)Other unit: Gauss = 10-4 T
114x’s indicate a B-field into the page Since it’s difficult to draw in 3-D, we’ll adopt the following symbols:xx’s indicate a B-field into the pagedots indicate a B-field out of the page(hint: just think of arrows: )Web Links: Charged particles in a Magnetic Field Deflection of a moving electron
115In the following examples, is the charge + or - ?
116Work done by the Magnetic Force x+vFsFFssWork = (Fcos)s = ?The work done by the Magnetic Force is equal to _____The speed of a charge in a Magnetic Field is ______
117Circulating Charged Particle When the charge moves perpendicular to the B-field, we can show that:Web Link: Charge in 2 Magnetic FieldsWhat path does the charge follow if v is not perpendicular to B?Web Link: Helix
118Ex:-An electron in a magnetic field moves at a speed of 1.3 x 106 m/s in a circle of radius .35 m. Find the magnitude and direction of the magnetic field.
119- Crossed () Electric and Magnetic Fields B E x v As the electron enters the crossed fields:The Electric Field deflects it in what direction?The Magnetic Field deflects it in what direction?If E and B are adjusted so that the electron continues in a straight line…Web Links: Magnetism inside a TV, TV Screens
120Another example of Magnetic and Electric fields working together: A Particle Accelerator The Large Hadron Collider (LHC), on the border of France and Switzerland, has a circumference of 16.7 miles. It accelerates particles to near the speed of light, so that high energy collisions can be used to further study the structure of matter. (Web Link: LHC News)
121F = I L B sin What happens to a current-carrying wire in a B-field? Remember: current is just moving chargeBWhat is the direction of force on this wire?ILWe can derive an equation for the magnitude of this force…F = I L B sin = angle between B and current
122Ex:xxB = .440 TL = 62.0 cmm = 13.0 gxxLFind the magnitude and direction of the current that must flow through the red bar in order to remove the tension from the springs.
123Make sure you don’t confuse these two separate effects: 1) A Magnetic Field exerts a force on a Current2) A Current produces its own Magnetic Field
124r Magnetic Field due to a long straight current: Right Hand Rule #2 B Thumb points with IIFingers curl with BThe magnitude of B depends on the distance r from the current:r0 = 4 x 10-7 Tm/AWeblink: Right Hand Rulepermeability of free space
125(roughly the value of earth’s magnetic field) Ex:If a wire carries a current of 480 A, how far from the wire will the magnetic field have a value of 5.0 x 10-5 T ?(roughly the value of earth’s magnetic field)
126Current I1 produces a B-field Parallel CurrentsdLCurrent I1 produces a B-fieldI1I2B1xxxxThis B-field exerts a force on current I2(and vice versa)What is the direction of force on I2 due to I1 ? (hint: use both right hand rules)What is the magnitude of force on I2 due to I1 ? (hint: use both equations)
127Consider a circular current… and use RHR #2 to determine the direction of the magnetic field at the center of the loop:IBIBBBBxorBBAt the center of the loop:Radius of loop
129If there are many circular loops: N = number of loopsWeb Link: Compass in loops of current
130Magnetic Fields add as vectors At the center of the loop:Do these fields add or subtract?The straight section creates a B-fieldThe circular section creates a B-fieldIDo the B-fields add or subtract in this case?
131I Solenoid inside: x x x x x x x x x x x x B For a long, ideal solenoid:B = 0n In = turns/lengthWeb Link: Solenoid Factors
133What are solenoids used for? doorbellscar starterselectric door locksWeb Link: How doorbells work
134Ex:20 cmThe solenoid has 100 turns. If a current of 23 A runs through it, what is the magnitude of the magnetic field in its core?
135In video games, what does it mean to play in a “toroidal world” AsteroidsIn video games, what does it mean to play in a “toroidal world”Web Link: Asteroids
136Magnetic Flux () is related to the number of magnetic field lines passing through a surface From aboveBWeb Link: Flux
137Magnetic Flux = = B A cos SI unit = 1 Weber = T·m2B = magnetic fieldA = surface area = angle between B and the Normal to the surface
138Ex:square loop2.0 mB = 5.0 x 10-4 Ta) What is the angle in this example?b) Calculate the magnetic flux through the loopc) What happens to the flux if the normal is rotated by 30° ?d) What happens to the flux if the normal is rotated by 90° ?
139Here’s a quicker way to do this: Recall: An emf is anything that produces a voltage difference (and therefore causes current flow)Recall: For a current loop, we can determine the direction of the B-field at its center:IBHere’s a quicker way to do this:Loop Right Hand Rule Fingers curl with I Thumb points with BBIIBx
140Faraday’s Law of Electromagnetic Induction An emf is induced in a conducting loop whenever the magnetic flux () is changing.Notes:Web Links: Induction, Faraday’s Experiment1) /t = rate of change of flux2) Induced emf causes induced current in the loop3) Induced current causes its own magnetic field4) This new B-field direction opposes the change in the original one. This part is called Lenz’s Law.Web Link: Lenz’s Law
1415) If there are multiple loops: (N = number of turns)
142Can you think of 3 different ways to induce a current in this loop? BAHere is a conducting loop in a magnetic fieldMagnetic Flux = = B A cos Can you think of 3 different ways to induce a current in this loop?
143Ex:BNSAs the loop moves to the left, what is the direction of the current that is induced in it?
147Notice in the previous examples: If the magnetic flux is increasing, the induced B-field is in the opposite direction as the original B-fieldBIf the magnetic flux is decreasing, the induced B-field is in the same direction as the original B-fieldBWeb Link: Lenz’s Law
148Find the direction of current in the loop when: Ex:BNSFind the direction of current in the loop when:a) The magnet moves to the leftb) The loop moves to the leftc) Both the magnet and loop are stationary
149Ex:20 cmB = 2.0 Tx20 cmThe wire loop has a resistance of 20 m. If its area is reduced to zero in a time of .20 s, find the magnitude and direction of the induced current.
150Web Link: Lenz’s Law Pipe Finally…why does it take so long for a magnet to fall through an aluminum pipe??Web Link: Lenz’s Law Pipe
151There are many familiar examples of induction all around us…
156What happens to the positive charge on the conductor? Motional emfxBWhat happens to the positive charge on the conductor?conductorLWhat about the negative charge?speed vPotential difference between the top and bottom =Motional emf = vBL
157Could we have found the current direction using Lenz’s Law instead? Ex:If the conducting bar is moved along conducting rails as shown below, we can see that there will be a current in the direction indicated:Could we have found the current direction using Lenz’s Law instead?
158a) Which side of the car is positive, the driver’s or passenger’s? Near San Francisco, where the vertically downward component of the earth’s magnetic field is 4.8 x 10-5 T, a car is traveling forward at 25 m/s. An emf of 2.4 x 10-3 V is induced between the sides of the car.a) Which side of the car is positive, the driver’s or passenger’s?b) What is the width of the car?
159SI unit = Henry(H) = Wb/A CircuitsDC voltage sourceAC voltage sourceResistorCapacitorE-field insideInductorB-field inside(Solenoid)Inductance =If N = number of turnsSI unit = Henry(H) = Wb/AI = current = magnetic flux
160The inductance (L) of a solenoid is not determined by the current or flux through it at a particular moment.L is a fixed property of each inductor:ARecall:n = turns / lengthL = 0 n2 A ℓInductors store energy in their B-fields:Energy stored in an inductor = ½ L I2
161How do inductors behave in circuits? L +-BConstant IIConstant Bvery boringChanging IChanging BChanging Induced emfvoltage across inductorOpposes change in ISince there is only one inductor, this is called Self-Induction
162When two inductors affect each other, it is called Mutual-Induction +-122If I1 changesB1I1B1 changesN2 turns2 changesemf2 induced in circuit 2Mutual Inductance =
163Secondary Circuit Primary Circuit During a 72-ms interval, a change in the current in a primary coil occurs. This change leads to the appearance of a 6.0-mA current in a nearby secondary coil The secondary coil is part of a circuit in which the resistance is 12 . The mutual inductance between the two coils is 3.2 mH. What is the change in the primary current?
164IV Recall : Power = I V Current is reduced to minimize power loss Voltage is reduced to household levelsIVIV
165How is the power line voltage raised and lowered? Transformer Station
166Web Link: Faraday’s Transformer Transformer increases (steps up) or decreases (steps down) ac voltage using inductionWeb Link: Faraday’s Transformer
168Find the output voltage and current. Ex:120 V 3.0 A?Find the output voltage and current.
169Recall the difference between AC and DC: Web Link: AC vs. DCDC ( ) :VoltagetimeEx:AC ( ) :VoltagetimeEx:V0-V0V = V0 sin ( 2 f t )Voltage amplitudefrequencytime
170Before we study AC circuits, let’s prepare by reviewing how the circuit components behave in a DC circuit:RVII = V/RRVCI = V/R at the first instant, then it decreases until I = 0IAt this point, the capacitor is fully charged, and acts like a break in the circuitRVLInduced emf across L slows current increase until I = V/RIAt this point the flux is no longer changing, and the inductor acts like a wire.
171Resistor in an AC Circuit V = V0sin(2ft)RThese are all average valuesWhat about the instantaneous values?Web Link: AC CircuitsVtVoltage and Current are in phase in a purely resistive circuit.It
173Capacitor in an AC Circuit Acts like a resistor:CVrms fR =Capacitive ReactanceSI unit = Ohms ()What happens to XC when the frequency is very large ??What happens to XC when the frequency is very small ??
184Non-Series RCL Circuits Vrms , fa) Find Irms for a very large frequencyb) Find Irms for a very small frequency
185Resonance in AC Circuits Oscillating systems:Mass on a springPEKEPEAC CircuitIWeb Link: Electromagnetic Oscillating Circuit++++E-fieldB-field
186This circuit has a natural frequency L C Resonant frequency for an RCL circuit(independent of R)Ex: Tuning a RadioWeb Link: Radio Tuning
187Mutually perpendicular and oscillating Electric and Magnetic fields Electromagnetic WaveMutually perpendicular and oscillating Electric and Magnetic fieldsWeb Link: Electromagnetic WaveElectromagnetic waves are transverse wavesElectromagnetic waves travel at the speed of light in a vacuum: c = 3.00 x 108 m/s
188This is how to make an electromagnetic wave BRecall these facts:1) A changing B-field produces an E-field-+atom2) A changing E-field produces a B-fieldE-fieldB-fieldE-fieldB-fieldIt could go on forever!This is how to make an electromagnetic waveWeb Links: Propagation of an electromagnetic waveVibrating Charges
189The Electromagnetic (e/m) Spectrum c = f wavelengthWeb Link: Wavelengthsspeed of lightfrequency
1900= permittivity of free space 0= permeability of free space Remember these constants?Fundamental constants of nature0= permittivity of free space0= permeability of free spaceIn 1865, Scottish physicist James Clerk Maxwell hypothesized electromagnetic waves and calculated that they would have to travel at a specific speed in a vacuum:Do the calculation. What do you get?This is the measured speed of light! Electromagnetic Waves do exist, and light must be one of them!
191Our Reference Frame determines where and when we observe an event: const. velocityxyzxyzIn both cases, the Reference Frame is at rest with respect to the observer
192Non-Inertial Reference Frame For each of the cases below, what path does the observer see the ball follow after he throws it straight up?on the groundin a truck with constant velocityin a truck with constant accelerationInertial Reference Frames (constant velocity)Non-Inertial Reference Frame
193Special Relativity Postulates 1) The laws of physics are the same in any inertial reference frame.2) The speed of light in a vacuum (c) has the same value when measured in any inertial reference frame, even if the light source is moving relative to it.speed of truckspeed of lightResult
194For speeds far less than c, relativity is barely noticeable For greater speeds, observers in different reference frames experience:a) Time Dilation (time slows down)b) Length Contraction (things shrink)
195Imagine a “light clock” Time DilationImagine a “light clock”Now imagine putting it on a spaceship.To an observer on the ground, what path does the light follow?
197Time Dilation Equation t0 = proper time (measured in the same reference frame as the events are occurring)t = time measured by an observer in a different reference framev = relative speed between the two reference framesc = 3.00 x 108 m/sSo what does this all mean ???
198Web Link: Time Dilation t > t0<1<1Time slows down in a reference frame that is moving relative to the observer !Web Link: Time DilationProof:1) Atomic clocks on jets slow by precisely this amount2) GPS and airplane navigation must use it in their calculations!3) Muons arrive at earth’s surface Web Link: Muon Time Dilation
199Ex:An observer on the ground is monitoring an astronaut in a spacecraft that is traveling at a speed of 5 x 107 m/s .On average, a human heart beats 70 times per minute. Calculate the time between heartbeats and the number of heartbeats per day fora) the person on earth (this part is easy)b) the space traveler, as monitored from earth
200So the guy on the ground sees the guy on the spaceship aging more slowly. What does the guy on the spaceship see when he looks at the guy on the ground ??
201Upon his return he will be 8 years younger than his twin! The Twin ParadoxOne twin travels at a speed of .80c to a galaxy 8 light years away and and then travels back to earth at the same speed.Upon his return he will be 8 years younger than his twin!How is this different from the previous example ??
202Understanding Time Dilation xyMore y-motion, less x-motionConstant speed in x-directiontimespaceMore motion through space, less motion through timeSitting still (not moving through space)Just think of time as the 4th dimension
203Length ContractionObserver (t)(t0)vL0v = relative speedL0 = proper length (measured by observer at rest with respect to object/distance)L = length measured from a different reference framec = 3.00 x 108 m/s
204Length Contraction Equation <1Distances/lengths appear shorter when moving relative to the observer.*Only in the direction of motion:Web Link: Length Contractionv
206Both have a proper length of 8.5 m. Ex: Passing spaceshipsspaceship (2.0 x 108 m/s)spaceship 2 (at rest)Both have a proper length of 8.5 m.How long does spaceship 1 look to spaceship 2 ?How long does spaceship 2 look to spaceship 1 ?
207Recall: momentum = p = mv Conservation of Momentum:m1v1 + m2v2 = constantWhen things are moving close to the speed of light, this equation is way off !We need to consider…
208Relativistic Momentum >mvRelativistic Momentum<1If we calculate momentum this way for high speeds, conservation of momentum is obeyed.What happens if we use this equation when v is very small ?Are there any situations in which things move so fast that we have to use this equation?
209Momentum is 40,000 times greater than mv ! Stanford Linear Particle AcceleratorElectrons accelerate to % speed of light !Momentum is 40,000 times greater than mv !
210E = mc2 Mass-Energy Equivalence E = mc2 Mass conserved together Energy Total Energy of an Object =If v=0 :E = mc2= rest energyThis much energyThis much massis equivalent to
211E0 = mc2 A huge amount of energy A small mass The rest energy of a 46 gram golf ball could be used to operate a 75-Watt light bulb for 1.7 million years!
212Ex:Our country uses about 3.3 trillion kWhrs of energy per year. Find the amount of mass that is equivalent to this much energy.
213Why don’t we notice this ? E0 = mc2If energy changesMass must change alsoWhy don’t we notice this ?When a 1 kg ball falls 200 m and lands on the ground, by how much does its mass change?
214e- e+ More examples of Mass-Energy Equivalence… Ex: Matter meets antimattere-electrone+positron+=gamma rays2 (9.11x10-31 kg)mass = 0pure energyPeople used to wonder if the moon was made of antimatter
215Ex: Nuclear Power (Fission) Big nucleus2 smaller nuclei(less total mass, less energy)Web Link: Fission
216(less total mass, less energy) Ex: The Sun (Fusion)Two small nucleiLarger nucleus(less total mass, less energy)Web Link: Fusion
217The sun loses over 4 billion kg per second due to fusion (Don’t worry, it will last for another 5 billion years or so)
218Relativistic Kinetic Energy We can solve for KE… Recall:E0 = mc2 = rest energyIf an object is moving, its total energy is the sum of its rest energy and its kinetic energy:E = E0 + KERelativistic Kinetic EnergyWe can solve for KE…What happens to this equation if an object is traveling at the speed of light?Objects with mass cannot reach the speed of light
219Let’s try to get an idea of how fast light really is… Recall that all these effects of Special Relativity would only become noticeable to us as speeds approach the speed of light.Let’s try to get an idea of how fast light really is…Traveling at the speed of light, just how far around the earth could you go in 1 second?
220When they are headed for the same place at the same time… Particles experience:Waves experience:CollisionsInterference
221Electrons are… Particles: and Waves: - Interference Web Links: Electron InterferenceDouble Slit Experiment
222Wave-Particle Duality Light is…a Wave:Wave-Particle Dualityand a Particle:Photoelectric Effectlightmetalcollisions-
223E = h f Light (any electromagnetic wave) is composed of … Photons – massless energy particlesE = h fE = Energy of 1 photonh = Planck’s constant = x Jsf = frequency of light wave
224Ex:How many photons are emitted in 1 hour by a 25 Watt red light bulb ? ( For red, use =750 nm)
225Ex:Which type of electromagnetic wave is represented by photons with the following energies ?E = 3.3 x Ja)E = 1.3 x Jb)
226The Photoelectric Effect Web Link: Photoelectric EffectPhoton E=hfW0 = Work Function = minimum work required to eject an electron from the metal-Electron with maximum KEConservation of Energy:hf = W0 + KEmaxNo electrons are ejected if the frequency is too lowMore light does not result in electrons with more KEEnergy is being absorbed in packets (like particles)
229More Photoelectric Effect Applications Automatic DoorsPhotographer’s light meterDigital CameraWeb Link: Digital CameraWeb Link: Solar Energy
230White Light (all colors) = 380-750 nm Ex:White Light (all colors) = nmSodium (W0=2.28 eV)--Find the maximum kinetic energy of the ejected electrons (in electron-Volts).
231Web Link: Compton Effect The electron now has some Kinetic Energy The Compton EffectWeb Link: Compton EffectThe electron now has some Kinetic EnergyDoes the photon have more or less energy after the collision?(Energy=hf)(Energy=hf’)
232What is the change in wavelength if =0°? =180°? ’Conservation of Energy & Conservation of Momentum…h = Planck’s constantm = electron massc = speed of light= Compton wavelength = 2.43 x mWhat is the change in wavelength if =0°? =180°?
233Now take a few minutes to discuss these with your group: Conceptual Example in the textbook (p.905)Solar SailCheck Your Understanding #10(p.906)Radiometer
234OK, so we’ve accepted the fact that waves act like particles (have momentum, collisions, etc.) In 1923 Prince Louis de Broglie suggested for the first time that maybe particles act like waves:De Broglie WavelengthWhen they finally tried it out with electrons, the interference pattern corresponded perfectly to this wavelength!
235Ex:Find the de Broglie wavelength of a car with a mass of 1000 kg traveling at a speed of 30 m/s.
236It’s a Probability Wave: So what does this wavelength really mean for particles??It’s a Probability Wave:100 electrons3000 electrons70000 electrons
237Does the universe exist if we’re not looking??? Web Link:Does the universe exist if we’re not looking???
238The Heisenberg Uncertainty Principle “The more precisely the position is determined, the less precisely the momentum is known” Heisenberg, Uncertainty paper, 1927If x = uncertainty in position,and p = uncertainty in momentum,then
239Find the uncertainty in the electron’s speed. Ex:Within an atom, the uncertainty in an electron’s position is m (the size of the atom).Find the uncertainty in the electron’s speed.
240Ex:10 cmThe marble (m=25 g) is somewhere within the box. Find the uncertainty in the marble’s speed.
241Heisenberg says “No, but I know where I am.” Heisenberg is out for a drive when he’s stopped by a traffic cop. The cop says “Do you know how fast you were going?”Heisenberg says “No, but I know where I am.”
242This leads to “Quantum Tunneling” There is another form of Heisenberg’s Uncertainty Principle that involves Energy and Time:If E = uncertainty in a particle’s energy,and t = the time it has that energy,thenThis leads to “Quantum Tunneling”Web Links: Scanning Tunneling Microscope Animated STMSTM images
243The best part about knowing all this physics, is that now you will get the jokes……
244A Party of Famous Physicists Let’s see how many of the following physicists you can guess…
245Everyone was attracted to his magnetic personality.
246He was under too much pressure to enjoy himself.
247He may or may not have been there. ???He may or may not have been there.
248He went back to the buffet table several times a minute.