Presentation on theme: "BELLRINGER Compare and explain in complete sentences and formulas what is the unit for nuclear force."— Presentation transcript:
BELLRINGER Compare and explain in complete sentences and formulas what is the unit for nuclear force.
Homework due tomorrow WHAT IS THE LAW OF CONSERVATION OF ENERGY? GIVE EXAMPLES.
There are Four Fundamental Forces: 1) The Electromagnetic Force 3) The Strong Nuclear Force 4) The Weak Nuclear Force (We’ll study it this term) These act over a very small range These are responsible for all we see accelerate 2) The Gravitational Force
The 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 CosmosSuperstring TheoryThe Elegant Universe The Fabric of the Cosmos Recent Physics Discovery!
Now let’s review the gravitational force… Any two masses are attracted by equal and opposite gravitational forces: m1m1 m2m2 r F-F Newton’s Universal Law of Gravitation where…… G=Universal Gravitation Constant = 6.67x Nm 2 /kg 2 This is an Inverse-Square force Gravity is a very weak force
atom If an atom has the same amount of + and - charge Neutral (no net charge) If it’s missing electrons net + charge If it has extra electrons net - charge
silk glass (rub) fur plastic - - Web Links: Static DusterStatic Duster New Carpet
Ex: If you rub a balloon against your hair, which ends up with more electrons, the balloon or your hair?
Opposites Charges Attract Like Charges Repel
Insulators (like plastic, rubber, pure water, and glass) will not conduct away extra charge. Conductors (such as metals, tap or salt water, and the human body) are good at conducting away any extra charge. Metal: “free electrons” Touching it with your hand will discharge it Use rubber gloves in the lab
Grounding - - The earth is a huge reservoir of positive and negative charge Object is discharged or “grounded”
Induced 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 2Charging by Induction 1 Charging by Induction 2
Electric Current wire electrons Current Electric current is in the direction that positive charge carriers “would” move why? ask Ben Franklin Current = Charge per Time I Amperes (A) Coulombs (C) seconds (s) SI units q t
Remember, opposite charges attract: and like charges repel: q 1 and q 2 may represent lots of extra or missing electrons How much force do q 1 and q 2 exert on each other? Coulomb’s Law k = electrostatic constant = 8.99 x 10 9 Nm 2 /C 2 Web Link: Orbiting electron Orbiting electron
Notes on Coulomb’s Law 1) It has the same form as the Law of Gravitation: Inverse-Square Force 2) 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 C 2 /Nm 2 4) Coulomb’s Law obeys the principle of superposition Web Links: Coulomb force, Releasing a test chargeCoulomb forceReleasing a test charge
Ex: +q -q rr What 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?
Ex: q1q1 q2q2 q3q3.15 m.10 m 73° q 1 = +4.0 C q 2 = -6.0 C q 3 = -5.0 C Find the net force on charge q 1
Smallest possible amount of charge: 1 extra electron: q = x C 1 missing electron: q = x C For any charge q: q = ne, where n = 1, 2, 3, etc… … Charge is quantized Also: Charge is conserved = e = elementary charge
Ex: - + electronproton 1.0 cm Calculate both the gravitational force and the electrostatic force, and compare their magnitudes.
Electric Fields Field – A set of values that defines a given property at every point in space Temperature Field:Elevation Field: Both of these examples are scalar fields We need to look at a vector field
Wind Notice that the wind vectors each have magnitude and direction This is an example of a vector field Here is an animated example: Wind MapWind Map
Electric Field (E) – A vector field surrounding a fixed, charged object that indicates the force on a positive test charge (q 0 ) placed nearby Draw 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. fixed, charged object test charge Web Link: Force FieldsForce Fields The Electric Field is defined as the Force per unit Charge at that point
Notes on E-field 1) The E-field points in the direction of force on a positive test charge 2) 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 vectors 5) Given the E-field value at a certain point, we can calculate the force F on any charge q 0 placed there: F = q 0 E
Ex: + q = 2.0 C (fixed charge) + q 0 = 1.0 C (test charge) a) Find the force on the test charge using Coulomb’s Law b) Find the electric field at the position of the test charge c) Could you have answered part b without knowing the value of the test charge?.10 m
Electric Field at a distance r from a point charge q r E = ? q
+ Electric Field Lines -represent symmetric paths of a positive test charge The number of lines is arbitrary, as long as they are symmetric The density of lines represents the strength of the Electric field What would the Electric field lines look like if there was a negative charge at the center?
What do you think the Electric Field lines would look like for… A charged, non-conducting sheet that is not infinite? A large (), charged, non-conducting sheet? Two oppositely charged plates? (called a parallel plate capacitor)
The Electric Field Lines for 2 Equal Charges:
The Electric Field Lines for 2 Opposite Charges (called an Electric Dipole): Web Links: Electric Field Lines, Releasing a test chargeElectric Field LinesReleasing a test charge
Charged Conductors Any excess charge ends up on the surface of a conductor, independent of its shape Why do you think this happens?
What happens to a neutral conductor placed in an external electric field? “Shielding” E = 0 At equilibrium, the Electric Field at any point within a conducting material is zero.
Faraday Cage: an example of shielding
Consider 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? a) b) c) f) d) e)
Recall… Gravitational Potential Energy or Elastic Potential Energy Now… Electric Potential Energy (EPE) Only Conservative Forces have an associated PE
Recall: PE grav = mg(h) = -(Work done by gravity) Similarly: EPE = -(Work done by electrostatic force) = - (Fcos)s Forcedisplacement angle between F and s EPE = -W = -(Fcos)s
Ex: Uniform Electric Field +proton E = 4.0 N/C a) 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 m
Work is Path Independent for conservative forces: path 1 path 2 Work done by gravity on path 1 = Work done by gravity on path 2 Ex: Electric Field path 1 path 2 Work done by electrostatic force on path 1 = Work done by electrostatic force on path 2 Ex: Gravity
EPE is a type of mechanical energy, like… Kinetic Energy (KE) = ½ mv 2 Rotational Kinetic Energy (KE R ) = ½ I 2 Gravitational Potential Energy (PE grav ) = mgh Elastic Potential Energy(PE elast ) = ½ kx 2 = Total Mechanical Energy (E) is conserved if there are no non-conservative forces present (ie friction)
Ex: Uniform Electric Field E = 150 N/C A proton released from rest into this electric field will be going how fast after traveling a distance of 1.0 m ? +proton Can you think of two different methods to use in solving this problem? Do they yield the same answers? m
In both previous examples, we saw that… EPE q E q 2q Twice the charge has twice the EPE We 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 charge Also called Potential or Voltage SI Unit = J/C = 1 Volt
From the definition of Electric Potential, we can show that when a charge is moved from one point to another in an electric field: Work done by the Electric Field = - Charge that was moved Difference in Potential between its old and new positions E 1 2 W = -q 0 (V)
Let’s make sure that we understand the difference between Potential and Electric Potential Energy: V (in Volts) = Potential a property of a certain position in an Electric Field with or without charges placed there E - EPE (in Joules) = Electric Potential Energy a property of charges placed at a certain position in an external Electric Field + - E Web Link: EPE vs Potential
We now have a new SI unit for Electric Field: Volts / meter There is a force of 3 Newtons on each 1 Coulomb of charge in the field The Potential changes by 3 Volts for every 1 meter of distance We 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 E = 3 N/C = 3 V/m Ex - 1 V -
Equipotential Surfaces adjacent points at the same electric potential E-field Equipotential Surface
Web Link: Equipotential surfacesEquipotential surfaces Equipotential Surface E-Field
Equipotential Surfaces are 3-dimensional:
Equipotential Surface E-Field Notes on Equipotential Surfaces 1) Equipotential surfaces are always perpendicular to Electric Field lines Web Link: Electric Field LinesElectric Field Lines 2) If a charge moves on an equipotential surface, the work done by the Electric Field is zero: + s F Web Link: Equipotential surfacesEquipotential surfaces
In the case of a Uniform Electric Field, it is especially easy to calculate the potential difference between equipotential surfaces: E Potential gets higher in this direction Potential gets lower in this direction E is in Volts/meter E = V/s V = E(s)
Ex:.30 m E = 5.0 V/m Find the potential difference between the plates.
In the lab, we could use a Voltmeter to simply measure the potential difference:
This means there is a potential difference (V) of 12 Volts between the terminals of the battery
Calculating the Potential due to a Point Charge q r What is the Potential at this point? k = electrostatic constant = 8.99 x 10 9 Nm 2 /C 2 Notes: 1) Include the sign of q in your calculation! (+ or -) 3) The equation can also be used for a charged sphere: rTotal charge Distance from center 2) Potential Difference can also be calculated: V = V 2 – V 1
Van de Graff generator
Ex: - electron a) 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?
Calculating 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 vector V = V 1 + V 2 + V 3 + … (an algebraic sum, not a vector sum)
Ex: +q -q-q-q-qP Find the potential V at point P due to the four charges. d d d d Web Link: Complex Electric FieldComplex Electric Field
Capacitor a device that stores energy by maintaining a separation between positive and negative charge (Symbol: )
Circuit Board Capacitor Resistors
Parallel Plate Capacitor - - +q -q-q This is called “charging a capacitor” q = charge of the capacitor VV V = potential difference of the capacitor q and V are proportional: q = C V C = Capacitance (a fixed property of each capacitor) SI unit = 1 Farad (F) = 1 Coulomb / Volt
Dielectrics electrically insulating materials Capacitor without a dielectric Capacitor with a dielectric What happens to the Electric Field? The Electric Field magnitude is less in a dielectric How much less depends on the dielectric constant () of the material
Calculating the Capacitance (C) of a parallel plate capacitor A A = plate area d d = plate separation = dielectric constant ( 0 = 8.85 x C 2 /Nm 2 ) Notice: Capacitance is independent of both charge and voltage Adding a dielectric increases the Capacitance Web Links: Capacitance Factors, LightningCapacitance FactorsLightning
How much Energy is stored by a capacitor? Energy = ½CV 2 VoltageCapacitance What’s the energy density in an Electric Field? * For any electric field
+q d -q +q D -q Consider 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 now 1. greater than before 2. the same as before 3. less than before
Here’s a Web Link about a huge capacitor and what can be done with all that stored energy: Pulse Discharge Machine
Imagine a wire: V +- E Web Link: DC ElectricityDC Electricity Now imagine bending the same wire into a loop: + - V Battery or other emf source emf – electromotive “force” – the potential difference between the terminals of an electric power source Ex: emf = 9 V
+ - + The current arrow points with the “positive charge carriers” Web Link: Conventional CurrentConventional Current Notes on Current: 1) Remember: charge is conserved SI unit = Ampere(A) = 1 C/s 2) Current is a scalar, not a vector 3) There are two types of current: DC (direct current) charge moves the same direction at all times AC (alternating current) charge motion alternates back and forth Web Link: AC vs. DCAC vs. DC I +
Ex: I A DC current of 5.0 A flows through this wire: How much charge flows past this point in 4.0 minutes?
Will the bird on the high voltage wire be shocked?
applied voltage resulting current SI unit: Ohm () = 1 V/A (Resistor symbol: ) Resistor – a circuit component designed to provide a specific amount of resistance to current flow. Web Link: ResistanceResistance
9 V 1000 Ex: Draw the circuit diagram, and calculate the current in this circuit.
Building Resistors Resistance = R = a property of a given resistor (Ex: 20 , 400 , etc.) Resistivity = = a property of a material used in making resistors A L ( : SI unit = ·m)
Ex: Aluminum Power Lines Consider an aluminum power line with a cross sectional area of 4.9 x m 2. Find the resistance of 10.0 km of this wire.
Ex: Incandescent Light Bulb 120 V I = 12.4 A Tungsten wire radius.045 mm What is the length of the tungsten wire inside the light bulb? Web Link: Light bulbLight bulb
V = I R ( I V ) I V Is it really a law ? “Ohm’s Law” It works for resistors: What about other devices? Diode I V Light Bulb I V “Ohm’s Law” is not really a Law! ( I V )
Power = P = IV SI Unit = 1 Watt (W) = 1 J/s Rate of energy transfer If the device is a resistor: P = I V V=IR = I 2 R P = I V I=V/R = V 2 /R Energy dissipated by the resistor as thermal energy
Ex: Space Heater 1500 W Heater 120 V Find: a) The resistance of the heater b) The current through the heater c) The amount of heat produced in 1 hour
…back to the difference between AC and DC: Web Link: AC vs. DCAC vs. DC DC ( ) : Voltage timeEx: AC ( ) : Voltage time Ex: V = V 0 sin ( 2 f t ) Voltage amplitude frequencytime radians
So what does AC current look like? Typical household outlet: V 0 = 170 V f = 60 Hz Light bulb: Resistance R = I 0 = current amplitude I = I 0 sin ( 2 f t ) I t
Ex: Alarm Clock How many times a day does the current change direction? V 0 = 170 V f = 60 Hz
look familiar?? AC Power P = I V = ? peak values These are the values that matter P = I rms V rms P = (I rms ) 2 R P = (V rms ) 2 / R Ex: V 0 = 170 V What is the rms voltage?
Ex: Speaker If the power rating of the speaker is 55 Watts, and its resistance is 4.0 , what is the peak voltage?
Heating element of resistance R AC generator
Resistors in Series R1R1 R2R2 R S = R 1 + R 2 (R S > R 1, R 2 ) Resistors in Parallel R1R1 R2R2 (R P < R 1, R 2 )
RR Consider two identical resistors wired in series. If there is an electric current through the combination, the current in the second resistor is 1. 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.
A B As more resistors are added to the parallel circuit shown here, the total resistance between points A and B 1. increases 2. remains the same 3. decreases
Ex: 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 ?
Basic Circuit: R V I = V/R I I R1R1 Series Circuit: V R2R2 Current (I) has the same value everywhere in the circuit current is like a parade V R1 + V R2 = V Battery voltage is like money RSRS V I I = V/R S R S = R 1 + R 2
RPRP V I1I1 Parallel Circuit: I2I2 R1R1 V R2R2 I3I3 I1I1 ? I 1 = I 2 + I 3 V Batt = V R1 = V R2 Web Link: Parallel Current Parallel Current I 1 = V/R P I 2 = V/R 1 I 3 = V/R 2
Ex: 44 16 V 44 What is the series resistance? Calculate the current in this circuit.
16 V 4444 What is the parallel resistance? Calculate the current in all branches of this circuit.
47 V 28 Ex: The current through the 47 resistor is.12 A Calculate the voltage V of the battery.
Ex: V 47 28 The current through the 47 resistor is.12 A Calculate the current through the 28 resistor.
R1R1 V R2R2 In a series circuit, the current is the same through each resistor R1R1 V R2R2 In a parallel circuit, the voltage is the same across each resistor Notice that the terminology will help us remember how to measure current and voltage
Measure the voltage across a resistor:
Measure the current through a resistor: You must break the circuit to measure current!
How to calculate the equivalent resistance for a group of resistors:
Ex: Find the equivalent resistance of this circuit:
Kirchoff’s Rules I) The Junction Rule The sum of the currents entering any junction is equal to the sum of the currents leaving that junction. Web Link: Kirchoff’s 1 st LawKirchoff’s 1 st Law I1I1 I2I2 I3I3 I4I4 I 1 + I 2 + I 3 = I 4 Ex:
II) The Loop Rule The potential differences around any closed loop sum to zero. Web Link: Kirchoff’s 2 nd LawKirchoff’s 2 nd Law I2I2 I1I1 I3I V = I R V R1 = I 2 R 1 V R2 = I 2 R 2 V R3 = ? +V - I 2 R 1 - I 2 R 2 = 0 This loop (clockwise): Write out the equations for this loop and the outer loop Ex: R1R1 V R2R2 R3R3
Here 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 I 1, I 2, I 3, 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 loop Step 5) Solve the equations for the unknown quantities
Ex: 8.0 VV 3.0 4.0 5.0 Use Kirchoff’s rules to find a) the remaining two currents in the circuit, and b) the unknown voltage Web Link: Building circuitsBuilding circuits 1.7 A
Capacitors in Circuits A d Recall: C A C 1/d C1C1 V C2C2 Capacitors in Parallel: C P = C 1 + C 2 Capacitors in Series: C1C1 V C2C2
Ex: 8.0 F 5 V 6.0 F 4.0 F a) Find the total capacitance of the circuit b) Find the total charge stored on the capacitors
Charging a Capacitor: Web Link: RC Circuit IRC Circuit I At t = 0: close the switch First instant: I = V 0 /R Then: I decreases as the capacitor fills with charge Finally: I = 0, and V cap = V battery = V 0 Web Link: RC Circuit II RC Circuit II Charge on capacitor time q 0 = CV 0 full capacitor charge RC = time constant = RC Circuits
Discharging a Capacitor: At t = 0: close the switch First instant: I = V 0 /R Then: I decreases as the capacitor loses its charge Finally: I = 0, and V cap = 0 Web Link: RC Circuit IRC Circuit I The capacitor starts out fully charged to voltage V 0 Charge on capacitor time Web Link: RC Circuit IIRC Circuit II
Magnetic Field (B) points from “North” to “South” poles Recall: Electric Field (E) points from + to - charge opposite poles attract like poles repel Magnetic Field Lines B is tangent to the field lines at any point The density of the lines represents the strength of the magnetic field Web Links: Magnetic Field 3-D Magnetic FieldMagnetic Field 3-D Magnetic Field
Facts about Magnetic Fields (B-fields) 1) North and South poles cannot be isolated 2) All B-fields are caused by moving electric charge 3) The Earth has a Magnetic Field: Web Links: Northern LightsNorthern Lights 4) B-fields exert a force on moving, charged particles: Force is out of the screen B + Force is into of the screen + unaffected + +
Magnetic Force = F = qvBsin v = speed of charge B = magnetic field = angle between v and B q = charge What is the direction of this force? Fingers point with v Then curl toward B Thumb points with F SI unit for B-field is a Tesla (T) (F is in opposite direction for a negative charge) Other unit: 1 Gauss = T Right Hand Rule (RHR) (For a positive charge) B v F
Since it’s difficult to draw in 3-D, we’ll adopt the following symbols: dots indicate a B-field out of the page xxxx xxxx xxxx xxx x x’s indicate a B-field into the page (hint: just think of arrows: ) Web Links: Charged particles in a Magnetic Field Deflection of a moving electronCharged particles in a Magnetic Field Deflection of a moving electron
In the following examples, is the charge + or - ? xxxx xxxx xxxx xxx x ? ? ?
Work done by the Magnetic Force xxxx xxxx xxxx xxx x + v s s s F F F Work = (Fcos)s = ? The work done by the Magnetic Force is equal to _____ The speed of a charge in a Magnetic Field is ______
Circulating Charged Particle When the charge moves perpendicular to the B-field, we can show that: Web Link: Charge in 2 Magnetic FieldsCharge in 2 Magnetic Fields What path does the charge follow if v is not perpendicular to B? Web Link: HelixHelix
Ex: - An electron in a magnetic field moves at a speed of 1.3 x 10 6 m/s in a circle of radius.35 m. Find the magnitude and direction of the magnetic field.
Crossed () Electric and Magnetic Fields xxxx xxxx x x B E - 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 ScreensMagnetism inside a TVTV Screens
Another 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)LHC News
What happens to a current-carrying wire in a B-field? Remember: current is just moving charge B I L What is the direction of force on this wire? We can derive an equation for the magnitude of this force… F = I L B sin = angle between B and current
xxxx xxxx xxxx xxx x Ex: x x x x xx B =.440 T L L = 62.0 cm m = 13.0 g Find the magnitude and direction of the current that must flow through the red bar in order to remove the tension from the springs.
Make sure you don’t confuse these two separate effects: 1) A Magnetic Field exerts a force on a Current 2) A Current produces its own Magnetic Field
r Magnetic Field due to a long straight current: I B Thumb points with I Fingers curl with B Right Hand Rule #2 The magnitude of B depends on the distance r from the current: 0 = 4 x Tm/A permeability of free space Weblink: Right Hand Rule Right Hand Rule
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 T ? (roughly the value of earth’s magnetic field)
Parallel Currents I1I1 I2I2 B1B1 xxxxxxxx d L Current I 1 produces a B-field This B-field exerts a force on current I 2 (and vice versa) What is the direction of force on I 2 due to I 1 ? (hint: use both right hand rules) What is the magnitude of force on I 2 due to I 1 ? (hint: use both equations)
Consider a circular current… I I I I B x B B B B B B and use RHR #2 to determine the direction of the magnetic field at the center of the loop: At the center of the loop: Radius of loop or
I I I If there are many circular loops: N = number of loops Web Link: Compass in loops of currentCompass in loops of current
Magnetic Fields add as vectors I I I The straight section creates a B-field The circular section creates a B-field Do these fields add or subtract? I I I At the center of the loop: Do the B-fields add or subtract in this case?
Solenoid x x x x x x B inside: I I For a long, ideal solenoid: B = 0 n I n = turns/length Web Link: Solenoid FactorsSolenoid Factors
What are solenoids used for? doorbells Web Link: How doorbells work How doorbells work car starters electric door locks
Ex: The solenoid has 100 turns. If a current of 23 A runs through it, what is the magnitude of the magnetic field in its core? 20 cm
Toroid Asteroids In video games, what does it mean to play in a “toroidal world” Web Link: AsteroidsAsteroids
From above B Magnetic Flux () is related to the number of magnetic field lines passing through a surface B NS B Web Link: FluxFlux
Magnetic Flux = = B A cos B = magnetic field A = surface area = angle between B and the Normal to the surface SI unit = 1 Weber = T·m 2
Ex:square loop 2.0 m B = 5.0 x T b) Calculate the magnetic flux through the loop c) What happens to the flux if the normal is rotated by 30° ? a) What is the angle in this example? d) What happens to the flux if the normal is rotated by 90° ?
Recall: An emf is anything that produces a voltage difference (and therefore causes current flow) I I I I B x B Recall: For a current loop, we can determine the direction of the B-field at its center: Here’s a quicker way to do this: Loop Right Hand Rule Fingers curl with I Thumb points with B B I
Faraday’s Law of Electromagnetic Induction An emf is induced in a conducting loop whenever the magnetic flux () is changing. Web Links: Induction, Faraday’s ExperimentInductionFaraday’s Experiment Notes: 1) /t = rate of change of flux 2) Induced emf causes induced current in the loop 3) Induced current causes its own magnetic field 4) This new B-field direction opposes the change in the original one. This part is called Lenz’s Law. Web Link: Lenz’s LawLenz’s Law
5) If there are multiple loops: (N = number of turns)
B A Here is a conducting loop in a magnetic field Magnetic Flux = = B A cos Can you think of 3 different ways to induce a current in this loop?
Ex: NS B As the loop moves to the left, what is the direction of the current that is induced in it?
As loop moves left:
Ex: xxxx xxxx xxxx xxx x As the loop is pulled and its area is decreased, what is the direction of the current that is induced in it? Web Link: Induced currentInduced current
Notice in the previous examples: If the magnetic flux is increasing, the induced B-field is in the opposite direction as the original B-field B If the magnetic flux is decreasing, the induced B-field is in the same direction as the original B-field B Web Link: Lenz’s LawLenz’s Law
NS Ex: Find the direction of current in the loop when: a) The magnet moves to the left b) The loop moves to the left c) Both the magnet and loop are stationary B
Ex: xxxx xxxx xxxx xxx x B = 2.0 T 20 cm The 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.
Finally… why does it take so long for a magnet to fall through an aluminum pipe?? Web Link: Lenz’s Law PipeLenz’s Law Pipe
There are many familiar examples of induction all around us…
Web Link: GeneratorGenerator
Web Link: Dynamic MicrophoneDynamic Microphone
Speakers Web Link: How a speaker worksHow a speaker works
Electric Guitar Web Link: Electric Guitar Electric Guitar
Motional emf speed vconductor What happens to the positive charge on the conductor? What about the negative charge? Potential difference between the top and bottom = xxxx xxxx xxxx xxx x B L Motional emf = vBL
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?
Near San Francisco, where the vertically downward component of the earth’s magnetic field is 4.8 x T, a car is traveling forward at 25 m/s. An emf of 2.4 x 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?
Circuits DC voltage source AC voltage source Resistor Capacitor Inductor (Solenoid) E-field inside B-field inside If N = number of turns I = current = magnetic flux Inductance = SI unit = Henry(H) = Wb/A
The inductance (L) of a solenoid is not determined by the current or flux through it at a particular moment. A Recall: n = turns / length L = 0 n 2 A ℓ Inductors store energy in their B-fields: Energy stored in an inductor = ½ L I 2 L is a fixed property of each inductor:
How do inductors behave in circuits? B L +- II Constant Bvery boring Constant I Changing I Changing B Changing Induced emf voltage across inductor Opposes change in I Since there is only one inductor, this is called Self-Induction
When two inductors affect each other, it is called Mutual-Induction I1I1 B1B1 22 N 2 turns If I 1 changes B 1 changes 2 changes emf 2 induced in circuit 2 Mutual Inductance =
Primary Circuit Secondary 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?
Recall : Power = I V IVIV IVIV Current is reduced to minimize power loss Voltage is reduced to household levels
How is the power line voltage raised and lowered? Transformer Station
Transformer - increases (steps up) or decreases (steps down) ac voltage using induction Web Link: Faraday’s TransformerFaraday’s Transformer
Iron generatorPrimary Coil Voltage V P N P turns Secondary Coil Voltage V s N S turns Transformer Equation Web Link: Transformer Transformer Transformer:
Ex: ? 120 V 3.0 A Find the output voltage and current.
Recall the difference between AC and DC: Web Link: AC vs. DCAC vs. DC DC ( ) : Voltage timeEx: AC ( ) : Voltage time Ex: V = V 0 sin ( 2 f t ) Voltage amplitude frequencytime V0V0 -V 0
Before we study AC circuits, let’s prepare by reviewing how the circuit components behave in a DC circuit: I = V/R I R V C I I = V/R at the first instant, then it decreases until I = 0 R V At this point, the capacitor is fully charged, and acts like a break in the circuit I R VL Induced emf across L slows current increase until I = V/R At this point the flux is no longer changing, and the inductor acts like a wire.
Resistor in an AC Circuit V = V 0 sin(2ft) R These are all average values What about the instantaneous values? Web Link: AC CircuitsAC Circuits I t V t Voltage and Current are in phase in a purely resistive circuit.
Capacitor in an AC Circuit Acts like a resistor: R = Capacitive Reactance SI unit = Ohms () What happens to X C when the frequency is very large ?? What happens to X C when the frequency is very small ?? C V rms f
Instantaneous Values for a Capacitor in an AC Circuit Web Link: AC CircuitsAC Circuits V t I (q/t) t Capacitor is full here: q=0 Capacitor is charging fastest when empty
Current leads Voltage by 90° in a purely capacitive AC circuit Power = I V one is maximum when the other is zero Average Power ( P ) = 0 for a capacitor in an AC circuit
L Inductor in an AC Circuit Acts like a resistor: R = Inductive Reactance SI unit = Ohms () What happens to X L when the frequency is very small ?? What happens to X L when the frequency is very large ??
Instantaneous Values for an Inductor in an AC Circuit Web Link: AC CircuitsAC Circuits L I t V ( I/t) t I is not changing: V=0 I decreasing fastest: V is minimum I increasing fastest: V is maximum
Current lags Voltage by 90° in a purely inductive AC circuit Power = I V one is maximum when the other is zero Average Power ( P ) = 0 for an inductor in an AC circuit
Series RCL Circuits Acts like a resistor: R = Phase Angle between I & V = = cos = power factor Impedance () Average Power ( P ) = I rms V rms cos
Ex: 16.0 4.10 F 5.30 mH a) Find I rms b) Find the voltage across each circuit element c) Find the average power dissipated in the circuit 15.0 V 1350 Hz
Non-Series RCL Circuits V rms, f a) Find I rms for a very large frequency b) Find I rms for a very small frequency
I I Mass on a spring Resonance in AC Circuits Oscillating systems: KEPE AC Circuit B-field E-field Web Link: Electromagnetic Oscillating Circuit Electromagnetic Oscillating Circuit
L CThis circuit has a natural frequency Resonant frequency for an RCL circuit (independent of R) Ex: Tuning a Radio Web Link: Radio TuningRadio Tuning
Electromagnetic Wave Mutually perpendicular and oscillating Electric and Magnetic fields Web Link: Electromagnetic WaveElectromagnetic Wave Electromagnetic waves travel at the speed of light in a vacuum: c = 3.00 x 10 8 m/s Electromagnetic waves are transverse waves
Recall these facts: 1) A changing B-field produces an E-field 2) A changing E-field produces a B-field - + atom E-fieldB-fieldE-fieldB-field It could go on forever! This is how to make an electromagnetic wave Web Links: Propagation of an electromagnetic wavePropagation of an electromagnetic wave Vibrating Charges B
The Electromagnetic (e/m) Spectrum c = f speed of lightfrequency wavelength Web Link: Wavelengths Wavelengths
Remember these constants? 0 = permittivity of free space 0 = permeability of free space Fundamental constants of nature In 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!
const. velocity Our Reference Frame determines where and when we observe an event: x y z x y z In both cases, the Reference Frame is at rest with respect to the observer
For each of the cases below, what path does the observer see the ball follow after he throws it straight up? on the ground in a truck with constant velocity in a truck with constant acceleration Inertial Reference Frames (constant velocity) Non-Inertial Reference Frame
Special 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 truck speed of light Result
For speeds far less than c, relativity is barely noticeable b) Length Contraction (things shrink) a) Time Dilation (time slows down) For greater speeds, observers in different reference frames experience:
Time Dilation To an observer on the ground, what path does the light follow? Now imagine putting it on a spaceship. Imagine a “light clock”
Time Dilation Equation t 0 = proper time (measured in the same reference frame as the events are occurring) t = time measured by an observer in a different reference frame v = relative speed between the two reference frames c = 3.00 x 10 8 m/s So what does this all mean ???
<1 t > t 0 Web Link: Time DilationTime Dilation Proof: 2) GPS and airplane navigation must use it in their calculations! 1) Atomic clocks on jets slow by precisely this amount 3) Muons arrive at earth’s surface Web Link: Muon Time DilationMuon Time Dilation Time slows down in a reference frame that is moving relative to the observer !
Ex: An observer on the ground is monitoring an astronaut in a spacecraft that is traveling at a speed of 5 x 10 7 m/s. On average, a human heart beats 70 times per minute. Calculate the time between heartbeats and the number of heartbeats per day for a) the person on earth (this part is easy) b) the space traveler, as monitored from earth
So 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 ??
The Twin Paradox One 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 ??
Understanding Time Dilation x y Constant speed in x-direction More y-motion, less x-motion time space Sitting still (not moving through space) More motion through space, less motion through time Just think of time as the 4 th dimension
Length Contraction L0L0 Observer (t) (t0)(t0) v v = relative speed L 0 = proper length (measured by observer at rest with respect to object/distance) L = length measured from a different reference frame c = 3.00 x 10 8 m/s
Length Contraction Equation <1 Web Link: Length ContractionLength Contraction *Only in the direction of motion: Distances/lengths appear shorter when moving relative to the observer. v
Ex: Passing spaceships spaceship 1 (2.0 x 10 8 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 ?
Recall: momentum = p = mv m1m1 v1v1 m2m2 v2v2 m 1 v 1 + m 2 v 2 = constant Conservation of Momentum: When things are moving close to the speed of light, this equation is way off ! We need to consider…
Relativistic Momentum <1 >mv 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? If we calculate momentum this way for high speeds, conservation of momentum is obeyed.
Stanford Linear Particle Accelerator Electrons accelerate to % speed of light ! Momentum is 40,000 times greater than mv !
Total Energy of an Object = E = mc 2 Mass-Energy Equivalence Mass Energy conserved together If v=0 : E = mc 2 0 = rest energy This much energy is equivalent to This much mass
E 0 = mc 2 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!
Our country uses about 3.3 trillion kWhrs of energy per year. Find the amount of mass that is equivalent to this much energy. Ex:
E 0 = mc 2 If energy changes Mass must change also When a 1 kg ball falls 200 m and lands on the ground, by how much does its mass change? Why don’t we notice this ?
More examples of Mass-Energy Equivalence… Ex: Matter meets antimatter e-e- electron e+e+ positron + = gamma rays 2 (9.11x kg) mass = 0 pure energy People used to wonder if the moon was made of antimatter
Ex: Nuclear Power (Fission) Big nucleus 2 smaller nuclei (less total mass, less energy) Web Link: FissionFission
Ex: The Sun (Fusion) Two small nuclei (less total mass, less energy) Larger nucleus Web Link: FusionFusion
The sun loses over 4 billion kg per second due to fusion (Don’t worry, it will last for another 5 billion years or so)
Recall:E 0 = mc 2 = rest energy If an object is moving, its total energy is the sum of its rest energy and its kinetic energy: E = E 0 + KE We can solve for KE… Relativistic Kinetic Energy What happens to this equation if an object is traveling at the speed of light? Objects with mass cannot reach the speed of light
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?
Particles experience: Collisions Waves experience: Interference When they are headed for the same place at the same time…
Electrons are… Particles: and Waves: Interference Web Links: Electron Interference Double Slit Experiment
collisions Light is…a Wave: and a Particle: light metal - - Photoelectric Effect Wave-Particle Duality
Light (any electromagnetic wave) is composed of … Photons – massless energy particles E = h f E = Energy of 1 photon h = Planck’s constant = x Js f = frequency of light wave
Ex: How many photons are emitted in 1 hour by a 25 Watt red light bulb ? ( For red, use =750 nm)
Ex: Which type of electromagnetic wave is represented by photons with the following energies ? E = 3.3 x J a) E = 1.3 x J b)
The Photoelectric Effect W 0 = Work Function = minimum work required to eject an electron from the metal Photon E=hf - Electron with maximum KE Web Link: Photoelectric EffectPhotoelectric Effect Conservation of Energy: hf = W 0 + KE max More light does not result in electrons with more KE Energy is being absorbed in packets (like particles) No electrons are ejected if the frequency is too low
The Photoelectric Effect in the garage…
More Photoelectric Effect Applications Photographer’s light meter Digital Camera Web Link: Digital Camera Digital Camera Automatic Doors Web Link: Solar EnergySolar Energy
Ex: Sodium (W 0 =2.28 eV) White Light (all colors) = nm - - Find the maximum kinetic energy of the ejected electrons (in electron-Volts).
(Energy=hf) (Energy=hf’) The Compton Effect Web Link: Compton EffectCompton Effect Does the photon have more or less energy after the collision? The electron now has some Kinetic Energy
e ’ e Conservation of Energy & Conservation of Momentum… m = electron mass h = Planck’s constant c = speed of light = Compton wavelength = 2.43 x m What is the change in wavelength if =0°? =180°?
Now take a few minutes to discuss these with your group: Conceptual Example 4 in the textbook (p.905) Solar Sail Check Your Understanding #10 (p.906) Radiometer
When they finally tried it out with electrons, the interference pattern corresponded perfectly to this wavelength! OK, 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 Wavelength
Ex: Find the de Broglie wavelength of a car with a mass of 1000 kg traveling at a speed of 30 m/s.
So what does this wavelength really mean for particles?? It’s a Probability Wave: 100 electrons 3000 electrons electrons
Does the universe exist if we’re not looking??? Web Link:
The Heisenberg Uncertainty Principle “The more precisely the position is determined, the less precisely the momentum is known” - Heisenberg, Uncertainty paper, 1927 If x = uncertainty in position, and p = uncertainty in momentum, then
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.
Ex: The marble (m=25 g) is somewhere within the box. Find the uncertainty in the marble’s speed. 10 cm
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.”
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, then Web Links: Scanning Tunneling Microscope Animated STMScanning Tunneling Microscope Animated STM STM images This leads to “Quantum Tunneling”
The best part about knowing all this physics, is that now you will get the jokes……
A Party of Famous Physicists Let’s see how many of the following physicists you can guess…
Everyone was attracted to his magnetic personality.
He was under too much pressure to enjoy himself.
He may or may not have been there. ? ? ?
He went back to the buffet table several times a minute.