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**BELLRINGER Compare and explain in complete sentences and formulas**

what is the unit for nuclear force.

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**CONSERVATION OF ENERGY?**

Homework due tomorrow WHAT IS THE LAW OF CONSERVATION OF ENERGY? GIVE EXAMPLES.

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**There are Four Fundamental Forces:**

These are responsible for all we see accelerate 1) The Electromagnetic Force (We’ll study it this term) 2) The Gravitational Force These act over a very small range 3) The Strong Nuclear Force 4) The Weak Nuclear Force

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**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 Cosmos Recent Physics Discovery!

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**Now let’s review the gravitational force…**

Any two masses are attracted by equal and opposite gravitational forces: F -F m1 m2 r Newton’s Universal Law of Gravitation where…… G=Universal Gravitation Constant = 6.67x10-11 Nm2/kg2 This is an Inverse-Square force Gravity is a very weak force

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**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 atom

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**- - - - - - - - - - + + + + glass (rub) silk plastic (rub) fur**

Web Links: Static Duster New Carpet

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Ex: If you rub a balloon against your hair, which ends up with more electrons, the balloon or your hair?

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**Opposites Charges Attract**

Like Charges Repel

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**Use 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 lab Touching it with your hand will discharge it

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**- - - - - - Grounding Object is discharged or “grounded” +**

The earth is a huge reservoir of positive and negative charge + -

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**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 2

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**Current = Charge per Time**

Electric Current wire - electrons Current ask Ben Franklin Electric current is in the direction that positive charge carriers “would” move why? Current = Charge per Time I q t Amperes (A) seconds (s) Coulombs (C) SI units

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**Remember, opposite charges attract:**

q1 and q2 may represent lots of extra or missing electrons and like charges repel: How much force do q1 and q2 exert on each other? Coulomb’s Law k = electrostatic constant = 8.99 x 109 Nm2/C2 Web Link: Orbiting electron

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**0= permittivity of free space = 8.85 x 10-12 C2/Nm2**

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 C2/Nm2 4) Coulomb’s Law obeys the principle of superposition Web Links: Coulomb force, Releasing a test charge

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**What is the direction of the net force on the charge in the middle ?**

Ex: +q -q +q r r 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?

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**Find the net force on charge q1**

Ex: q2 q1= +4.0 C q2= -6.0 C q3= -5.0 C .15 m 73° q1 q3 .10 m Find the net force on charge q1

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**Smallest possible amount of charge:**

1 extra electron: q = x C 1 missing electron: q = x C = e = elementary charge … For any charge q: q = ne , where n = 1, 2, 3, etc… Charge is quantized Also: Charge is conserved

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**- Ex: 1.0 cm + electron proton**

Calculate both the gravitational force and the electrostatic force, and compare their magnitudes.

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**Both of these examples are scalar fields**

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

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**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 Map

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Electric Field (E) – A vector field surrounding a fixed, charged object that indicates the force on a positive test charge (q0) placed nearby fixed, charged object + test charge 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. Web Link: Force Fields The Electric Field is defined as the Force per unit Charge at that point

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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 q0 placed there: F = q0E

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Ex: .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 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?

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**Electric Field at a distance r from a point charge q**

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**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?

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**What 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)

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**The Electric Field Lines for 2 Equal Charges:**

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**Web Links: Electric Field Lines, Releasing a test charge**

The Electric Field Lines for 2 Opposite Charges (called an Electric Dipole): Web Links: Electric Field Lines, Releasing a test charge

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**Why do you think this happens?**

Charged Conductors Any excess charge ends up on the surface of a conductor, independent of its shape Why do you think this happens?

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**What happens to a neutral conductor placed in an external electric field?**

“Shielding” At equilibrium, the Electric Field at any point within a conducting material is zero.

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**Faraday Cage: an example of shielding**

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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? d) a) + + e) b) + + c) f) + +

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**- Recall… Gravitational Potential Energy or Elastic Potential Energy**

Now… - + Electric Potential Energy (EPE) Only Conservative Forces have an associated PE

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**EPE = -W = -(Fcos)s Recall:**

PEgrav = mg(h) = -(Work done by gravity) + - Similarly: EPE = -(Work done by electrostatic force) = - (Fcos)s angle between F and s Force displacement EPE = -W = -(Fcos)s

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**Uniform Electric Field**

Ex: + 2.0 m proton + Uniform Electric Field 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.

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**Work is Path Independent for conservative forces:**

Ex: Gravity Ex: Electric Field path 1 path 2 path 1 path 2 Work done by electrostatic force on path = Work done by electrostatic force on path 2 Work done by gravity on path = Work done by gravity on path 2

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**= Total Mechanical Energy (E)**

+ = Total Mechanical Energy (E) EPE is a type of mechanical energy, like… +++ Kinetic Energy (KE) = ½ mv2 Rotational Kinetic Energy (KER) = ½ I2 Gravitational Potential Energy (PEgrav) = mgh Elastic Potential Energy(PEelast) = ½ kx2 is conserved if there are no non-conservative forces present (ie friction).

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**Uniform Electric Field E = 150 N/C**

Ex: + 1.0 m proton + 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 ? Can you think of two different methods to use in solving this problem? Do they yield the same answers?

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**EPE q E In both previous examples, we saw that… 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

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From the definition of Electric Potential, we can show that when a charge is moved from one point to another in an electric field: 1 2 E Work done by the Electric Field = - Charge that was moved Difference in Potential between its old and new positions W = -q0(V)

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**V (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) = 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

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**We now have a new SI unit for Electric Field: Volts / meter**

E = 3 N/C = 3 V/m Ex 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 - - 1 V

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**Equipotential Surfaces adjacent points at the same electric potential**

E-field Equipotential Surface

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**Equipotential Surface**

E-Field Web Link: Equipotential surfaces

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**Equipotential Surfaces are 3-dimensional:**

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**Notes on Equipotential Surfaces**

1) Equipotential surfaces are always perpendicular to Electric Field lines Web Link: Electric Field Lines 2) If a charge moves on an equipotential surface, the work done by the Electric Field is zero: F Equipotential Surface E-Field + s Web Link: Equipotential surfaces

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**Potential 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: ++++ ---- E Potential gets higher in this direction Potential gets lower in this direction E is in Volts/meter E = V/s V = E(s)

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**Find the potential difference between the plates.**

Ex: E = 5.0 V/m .30 m Find the potential difference between the plates.

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**In the lab, we could use a Voltmeter to simply measure the potential difference:**

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**This means there is a potential difference (V) of 12 Volts between the terminals of the battery**

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**Calculating the Potential due to a Point Charge**

What is the Potential at this point? k = electrostatic constant = 8.99 x 109 Nm2/C2 q Notes: 1) Include the sign of q in your calculation! (+ or -) 2) Potential Difference can also be calculated: V = V2 – V1 3) The equation can also be used for a charged sphere: + r Total charge Distance from center

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Van de Graff generator

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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?

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**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 = V1 + V2 + V3 + … (an algebraic sum, not a vector sum)

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Ex: +q d d d P -q -q d +q Find the potential V at point P due to the four charges. Web Link: Complex Electric Field

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Capacitor a device that stores energy by maintaining a separation between positive and negative charge (Symbol: )

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Circuit Board Capacitor Resistors

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**+q - -q q = C V Parallel Plate Capacitor**

This is called “charging a capacitor” +q - V -q V = potential difference of the capacitor q = charge 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

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**Dielectrics electrically insulating materials**

What happens to the Electric Field? Capacitor without a dielectric Capacitor with a dielectric The Electric Field magnitude is less in a dielectric How much less depends on the dielectric constant () of the material

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**Calculating the Capacitance (C) of a parallel plate capacitor**

A = plate area d d = plate separation = dielectric constant Notice: Capacitance is independent of both charge and voltage (0= 8.85 x C2/Nm2) Adding a dielectric increases the Capacitance Web Links: Capacitance Factors, Lightning

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**Energy = ½CV2 How much Energy is stored by a capacitor? Capacitance**

Voltage What’s the energy density in an Electric Field? * For any electric field

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+q -q -q +q d D 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

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**Pulse Discharge Machine**

Here’s a Web Link about a huge capacitor and what can be done with all that stored energy: Pulse Discharge Machine

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**Battery or other emf source**

Web Link: DC Electricity V + - Imagine a wire: - E - Now imagine bending the same wire into a loop: + - V Battery or other emf source Ex: emf = 9 V emf – electromotive “force” – the potential difference between the terminals of an electric power source

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**The current arrow points with the “positive charge carriers” I**

+ Web Link: Conventional Current + - + SI unit = Ampere(A) = 1 C/s Notes on Current: 1) Remember: charge is conserved 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. DC

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**A DC current of 5.0 A flows through this wire:**

Ex: A DC current of 5.0 A flows through this wire: I How much charge flows past this point in 4.0 minutes?

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**Will the bird on the high voltage wire be shocked?**

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applied voltage resulting current SI unit: Ohm () = 1 V/A Web Link: Resistance Resistor – a circuit component designed to provide a specific amount of resistance to current flow. (Resistor symbol: )

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**Draw the circuit diagram, and calculate the current in this circuit.**

Ex: 1000 9 V Draw the circuit diagram, and calculate the current in this circuit.

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**Resistivity = = 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 resistors Building Resistors L A (: SI unit = ·m)

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**Ex: 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.

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**Ex: Incandescent Light Bulb**

120 V Tungsten wire radius .045 mm I = 12.4 A What is the length of the tungsten wire inside the light bulb? Web Link: Light bulb

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**V = I R “Ohm’s Law” Is it really a law ? ( I V )**

It works for resistors: I V ( I V ) What about other devices? Light Bulb I V ( I V ) Diode I V “Ohm’s Law” is not really a Law!

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**If the device is a resistor:**

Power = P = IV Rate of energy transfer SI Unit = 1 Watt (W) = 1 J/s If the device is a resistor: V=IR Energy dissipated by the resistor as thermal energy P = I V = I2R P = I V = V2/R I=V/R

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Ex: Space Heater 120 V 1500 W Heater Find: a) The resistance of the heater b) The current through the heater c) The amount of heat produced in 1 hour

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**…back to the difference between AC and DC:**

Web Link: AC vs. DC DC ( ) : Voltage time Ex: AC ( ) : Voltage time Ex: V = V0 sin ( 2 f t ) radians Voltage amplitude frequency time

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**I = I0 sin ( 2 f t ) So what does AC current look like?**

Light bulb: Resistance R Typical household outlet: V0 = 170 V f = 60 Hz I = I0 sin ( 2 f t ) = I0 = current amplitude I t

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**How many times a day does the current change direction?**

Ex: Alarm Clock V0 = 170 V f = 60 Hz How many times a day does the current change direction?

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**These are the values that matter**

AC Power P = I V = ? peak values Ex: V0 = 170 V What is the rms voltage? These are the values that matter look familiar?? P = Irms Vrms P = (Irms)2 R P = (Vrms)2 / R

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Ex: Speaker If the power rating of the speaker is 55 Watts, and its resistance is 4.0 , what is the peak voltage?

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**Heating element of resistance R**

AC generator

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**Resistors in Series RS = R1 + R2 Resistors in Parallel R1 R2**

(RP < R1 , R2)

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R R 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.

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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

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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 ?

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**current is like a parade**

I = V/R Basic Circuit: V R R1 Series Circuit: V R2 Current (I) has the same value everywhere in the circuit RS = R1 + R2 I current is like a parade VR1 + VR2 = VBattery voltage is like money RS V I I = V/RS

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**Web Link: Parallel Current**

Parallel Circuit: I1 = I2 + I3 I1 Web Link: Parallel Current R1 V R2 I2 I3 ? VBatt = VR1 = VR2 I2 = V/R1 I3 = V/R2 RP V I1 I1 = V/RP

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**What is the series resistance?**

Ex: 4 16 V 4 What is the series resistance? Calculate the current in this circuit.

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**What is the parallel resistance?**

16 V 4 4 What is the parallel resistance? Calculate the current in all branches of this circuit.

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Ex: 47 V 28 The current through the 47 resistor is .12 A Calculate the voltage V of the battery.

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Ex: V 47 28 The current through the 47 resistor is .12 A Calculate the current through the 28 resistor.

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**In a series circuit, the current is the same through each resistor**

V R2 In a series circuit, the current is the same through each resistor R1 V R2 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

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**Measure the voltage across a resistor:**

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**Measure the current through a resistor:**

You must break the circuit to measure current!

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**How to calculate the equivalent resistance for a group of resistors:**

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**Find the equivalent resistance of this circuit:**

Ex: Find the equivalent resistance of this circuit:

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**Web Link: Kirchoff’s 1st Law**

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. Ex: I1+ I2+ I3= I4 I2 I3 I1 I4 Web Link: Kirchoff’s 1st Law

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**The potential differences around any closed loop sum to zero.**

II) The Loop Rule The potential differences around any closed loop sum to zero. Web Link: Kirchoff’s 2nd Law Ex: R1 V R2 R3 V = I R + - I2 I3 I1 + - + - VR1 = I2R1 + - VR2 = I2R2 VR3 = ? This loop (clockwise): Write out the equations for this loop and the outer loop +V - I2R1 - I2R2 = 0

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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 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 loop Step 5) Solve the equations for the unknown quantities

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**Use Kirchoff’s rules to find **

Ex: 3.0 8.0 V 4.0 V 1.7 A 5.0 Use Kirchoff’s rules to find a) the remaining two currents in the circuit, and b) the unknown voltage Web Link: Building circuits

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**Capacitors in Circuits**

d Recall: C A C 1/d Capacitors in Series: C1 V C2 C1 V C2 Capacitors in Parallel: CP = C1 + C2

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**a) Find the total capacitance of the circuit**

Ex: 8.0 F 5 V 4.0 F 6.0 F a) Find the total capacitance of the circuit b) Find the total charge stored on the capacitors

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**RC Circuits Charging a Capacitor: Web Link: RC Circuit I**

At t = 0: close the switch First instant: I = V0/R Then: I decreases as the capacitor fills with charge Web Link: RC Circuit II Finally: I = 0, and Vcap = Vbattery = V0 q0 = CV0 full capacitor charge Charge on capacitor time RC = time constant =

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**Discharging a Capacitor:**

Web Link: RC Circuit I The capacitor starts out fully charged to voltage V0 At t = 0: close the switch First instant: I = V0/R Then: I decreases as the capacitor loses its charge Finally: I = 0, and Vcap = 0 Web Link: RC Circuit II Charge on capacitor time

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**Magnetic Field (B) points from “North” to “South” poles**

Recall: Electric Field (E) points from + to - charge Magnetic Field (B) points from “North” to “South” poles 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 D Magnetic Field

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**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 Lights 4) B-fields exert a force on moving, charged particles: + Force is out of the screen B unaffected + + unaffected + Force is into of the screen

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**Magnetic Force = F = qvBsin**

What is the direction of this force? q = charge v = speed of charge Right Hand Rule (RHR) (For a positive charge) B = magnetic field = angle between v and B Fingers point with v B v F 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: Gauss = 10-4 T

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**x’s indicate a B-field into the page **

Since it’s difficult to draw in 3-D, we’ll adopt the following symbols: x x’s indicate a B-field into the page dots 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

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**In the following examples, is the charge + or - ?**

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**Work done by the Magnetic Force**

x + v F s F F s s Work = (Fcos)s = ? The work done by the Magnetic Force is equal to _____ The speed of a charge in a Magnetic Field is ______

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**Circulating Charged Particle**

When the charge moves perpendicular to the B-field, we can show that: Web Link: Charge in 2 Magnetic Fields What path does the charge follow if v is not perpendicular to B? Web Link: Helix

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Ex: - 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.

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**- 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

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**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)

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**F = I L B sin What happens to a current-carrying wire in a B-field?**

Remember: current is just moving charge B What is the direction of force on this wire? I L We can derive an equation for the magnitude of this force… F = I L B sin = angle between B and current

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Ex: x x B = .440 T L = 62.0 cm m = 13.0 g x x L Find the magnitude and direction of the current that must flow through the red bar in order to remove the tension from the springs.

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**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

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**r Magnetic Field due to a long straight current: Right Hand Rule #2 B**

Thumb points with I I Fingers curl with B The magnitude of B depends on the distance r from the current: r 0 = 4 x 10-7 Tm/A Weblink: Right Hand Rule permeability of free space

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**(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)

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**Current I1 produces a B-field**

Parallel Currents d L Current I1 produces a B-field I1 I2 B1 xxxx This 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)

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**Consider a circular current…**

and use RHR #2 to determine the direction of the magnetic field at the center of the loop: I B I B B B B x or B B At the center of the loop: Radius of loop

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**If there are many circular loops:**

N = number of loops Web Link: Compass in loops of current

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**Magnetic Fields add as vectors**

At the center of the loop: Do these fields add or subtract? The straight section creates a B-field The circular section creates a B-field I Do the B-fields add or subtract in this case?

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**I Solenoid inside: x x x x x x x x x x x x B**

For a long, ideal solenoid: B = 0n I n = turns/length Web Link: Solenoid Factors

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**What are solenoids used for?**

doorbells car starters electric door locks Web Link: How doorbells work

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Ex: 20 cm 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?

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**In video games, what does it mean to play in a “toroidal world”**

Asteroids In video games, what does it mean to play in a “toroidal world” Web Link: Asteroids

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**Magnetic Flux () is related to the number of magnetic field lines passing through a surface**

From above B Web Link: Flux

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**Magnetic Flux = = B A cos **

SI unit = 1 Weber = T·m2 B = magnetic field A = surface area = angle between B and the Normal to the surface

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Ex: square loop 2.0 m B = 5.0 x 10-4 T a) What is the angle in this example? b) Calculate the magnetic flux through the loop c) 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° ?

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**Here’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: I B Here’s a quicker way to do this: Loop Right Hand Rule Fingers curl with I Thumb points with B B I I B x

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**Faraday’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 Experiment 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 Law

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**5) If there are multiple loops:**

(N = number of turns)

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**Can you think of 3 different ways to induce a current in this loop?**

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?

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Ex: B N S As the loop moves to the left, what is the direction of the current that is induced in it?

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As loop moves left:

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**Web Link: Induced current**

Ex: 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 current

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**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 Law

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**Find the direction of current in the loop when:**

Ex: B N S 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

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Ex: 20 cm B = 2.0 T x 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.

150
**Web 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

151
**There are many familiar examples of induction all around us…**

152
Generator Web Link: Generator

153
**Web Link: Dynamic Microphone**

154
**Web Link: How a speaker works**

Speakers Web Link: How a speaker works

155
**Web Link: Electric Guitar**

156
**What happens to the positive charge on the conductor?**

Motional emf x B What happens to the positive charge on the conductor? conductor L What about the negative charge? speed v Potential difference between the top and bottom = Motional emf = vBL

157
**Could 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?

158
**a) 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?

159
**SI unit = Henry(H) = Wb/A**

Circuits DC voltage source AC voltage source Resistor Capacitor E-field inside Inductor B-field inside (Solenoid) Inductance = If N = number of turns SI unit = Henry(H) = Wb/A I = current = magnetic flux

160
The 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: A Recall: n = turns / length L = 0 n2 A ℓ Inductors store energy in their B-fields: Energy stored in an inductor = ½ L I2

161
**How do inductors behave in circuits? L**

+ - B Constant I I Constant B very boring 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

162
**When two inductors affect each other, it is called Mutual-Induction**

+ - 1 2 2 If I1 changes B1 I1 B1 changes N2 turns 2 changes emf2 induced in circuit 2 Mutual Inductance =

163
**Secondary 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?

164
**IV Recall : Power = I V Current is reduced to minimize power loss**

Voltage is reduced to household levels IV IV

165
**How is the power line voltage raised and lowered?**

Transformer Station

166
**Web Link: Faraday’s Transformer**

Transformer increases (steps up) or decreases (steps down) ac voltage using induction Web Link: Faraday’s Transformer

167
Transformer: Iron generator Primary Coil Voltage VP NP turns Secondary Coil Voltage Vs NS turns Transformer Equation Web Link: Transformer

168
**Find the output voltage and current.**

Ex: 120 V 3.0 A ? Find the output voltage and current.

169
**Recall the difference between AC and DC:**

Web Link: AC vs. DC DC ( ) : Voltage time Ex: AC ( ) : Voltage time Ex: V0 -V0 V = V0 sin ( 2 f t ) Voltage amplitude frequency time

170
Before we study AC circuits, let’s prepare by reviewing how the circuit components behave in a DC circuit: R V I I = V/R R V C I = V/R at the first instant, then it decreases until I = 0 I At this point, the capacitor is fully charged, and acts like a break in the circuit R V L Induced emf across L slows current increase until I = V/R I At this point the flux is no longer changing, and the inductor acts like a wire.

171
**Resistor in an AC Circuit**

V = V0sin(2ft) R These are all average values What about the instantaneous values? Web Link: AC Circuits V t Voltage and Current are in phase in a purely resistive circuit. I t

173
**Capacitor in an AC Circuit**

Acts like a resistor: C Vrms f R = Capacitive Reactance SI unit = Ohms () What happens to XC when the frequency is very large ?? What happens to XC when the frequency is very small ??

175
**Instantaneous Values for a Capacitor in an AC Circuit**

Web Link: AC Circuits Capacitor is full here: q=0 Capacitor is charging fastest when empty V t I (q/t) t

176
**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

177
**Inductor in an AC Circuit**

L Acts like a resistor: R = Inductive Reactance SI unit = Ohms () What happens to XL when the frequency is very small ?? What happens to XL when the frequency is very large ??

179
**Instantaneous Values for an Inductor in an AC Circuit**

Web Link: AC Circuits I decreasing fastest: V is minimum I is not changing: V=0 I increasing fastest: V is maximum I t V ( I/t) t

180
**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

181
**Average Power ( P ) = Irms Vrms cos **

Series RCL Circuits Acts like a resistor: R = Impedance () Phase Angle between I & V = = Average Power ( P ) = Irms Vrms cos cos = power factor

182
Ex: 16.0 4.10 F 5.30 mH 15.0 V Hz a) Find Irms b) Find the voltage across each circuit element c) Find the average power dissipated in the circuit

184
**Non-Series RCL Circuits**

Vrms , f a) Find Irms for a very large frequency b) Find Irms for a very small frequency

185
**Resonance in AC Circuits**

Oscillating systems: Mass on a spring PE KE PE AC Circuit I Web Link: Electromagnetic Oscillating Circuit ++++ E-field B-field

186
**This circuit has a natural frequency L C**

Resonant frequency for an RCL circuit (independent of R) Ex: Tuning a Radio Web Link: Radio Tuning

187
**Mutually perpendicular and oscillating Electric and Magnetic fields**

Electromagnetic Wave Mutually perpendicular and oscillating Electric and Magnetic fields Web Link: Electromagnetic Wave Electromagnetic waves are transverse waves Electromagnetic waves travel at the speed of light in a vacuum: c = 3.00 x 108 m/s

188
**This is how to make an electromagnetic wave**

B Recall these facts: 1) A changing B-field produces an E-field - + atom 2) A changing E-field produces a B-field E-field B-field E-field B-field It could go on forever! This is how to make an electromagnetic wave Web Links: Propagation of an electromagnetic wave Vibrating Charges

189
**The Electromagnetic (e/m) Spectrum**

c = f wavelength Web Link: Wavelengths speed of light frequency

190
**0= permittivity of free space 0= permeability of free space**

Remember these constants? Fundamental constants of nature 0= permittivity of free space 0= permeability of free space 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!

191
**Our Reference Frame determines where and when we observe an event:**

const. velocity x y z x y z In both cases, the Reference Frame is at rest with respect to the observer

192
**Non-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 ground in a truck with constant velocity in a truck with constant acceleration Inertial Reference Frames (constant velocity) Non-Inertial Reference Frame

193
**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

194
**For 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)

195
**Imagine a “light clock”**

Time Dilation Imagine a “light clock” Now imagine putting it on a spaceship. To an observer on the ground, what path does the light follow?

197
**Time 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 frame v = relative speed between the two reference frames c = 3.00 x 108 m/s So what does this all mean ???

198
**Web Link: Time Dilation**

t > t0 <1 <1 Time slows down in a reference frame that is moving relative to the observer ! Web Link: Time Dilation Proof: 1) Atomic clocks on jets slow by precisely this amount 2) GPS and airplane navigation must use it in their calculations! 3) Muons arrive at earth’s surface Web Link: Muon Time Dilation

199
Ex: 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 for a) the person on earth (this part is easy) b) the space traveler, as monitored from earth

200
**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 ??

201
**Upon his return he will be 8 years younger than his twin!**

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 ??

202
**Understanding Time Dilation**

x y More y-motion, less x-motion Constant speed in x-direction time space More motion through space, less motion through time Sitting still (not moving through space) Just think of time as the 4th dimension

203
Length Contraction Observer (t) (t0) v L0 v = relative speed L0 = proper length (measured by observer at rest with respect to object/distance) L = length measured from a different reference frame c = 3.00 x 108 m/s

204
**Length Contraction Equation**

<1 Distances/lengths appear shorter when moving relative to the observer. *Only in the direction of motion: Web Link: Length Contraction v

206
**Both have a proper length of 8.5 m.**

Ex: Passing spaceships spaceship (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 ?

207
**Recall: momentum = p = mv**

Conservation of Momentum: m1v1 + m2v2 = constant When things are moving close to the speed of light, this equation is way off ! We need to consider…

208
**Relativistic Momentum**

>mv Relativistic Momentum <1 If 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?

209
**Momentum is 40,000 times greater than mv !**

Stanford Linear Particle Accelerator Electrons accelerate to % speed of light ! Momentum is 40,000 times greater than mv !

210
**E = mc2 Mass-Energy Equivalence E = mc2 Mass conserved together Energy**

Total Energy of an Object = If v=0 : E = mc2 = rest energy This much energy This much mass is equivalent to

211
**E0 = 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!

212
Ex: Our country uses about 3.3 trillion kWhrs of energy per year. Find the amount of mass that is equivalent to this much energy.

213
**Why don’t we notice this ?**

E0 = mc2 If energy changes Mass must change also Why 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?

214
**e- e+ More examples of Mass-Energy Equivalence…**

Ex: Matter meets antimatter e- electron e+ positron + = gamma rays 2 (9.11x10-31 kg) mass = 0 pure energy People used to wonder if the moon was made of antimatter

215
**Ex: Nuclear Power (Fission)**

Big nucleus 2 smaller nuclei (less total mass, less energy) Web Link: Fission

216
**(less total mass, less energy)**

Ex: The Sun (Fusion) Two small nuclei Larger nucleus (less total mass, less energy) Web Link: Fusion

217
**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)

218
**Relativistic Kinetic Energy We can solve for KE…**

Recall: E0 = mc2 = rest energy If an object is moving, its total energy is the sum of its rest energy and its kinetic energy: E = E0 + KE Relativistic Kinetic Energy We 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

219
**Let’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?

220
**When they are headed for the same place at the same time…**

Particles experience: Waves experience: Collisions Interference

221
**Electrons are… Particles: and Waves: - Interference Web Links:**

Electron Interference Double Slit Experiment

222
**Wave-Particle Duality**

Light is… a Wave: Wave-Particle Duality and a Particle: Photoelectric Effect light metal collisions -

223
**E = h f 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

224
Ex: How many photons are emitted in 1 hour by a 25 Watt red light bulb ? ( For red, use =750 nm)

225
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)

226
**The Photoelectric Effect**

Web Link: Photoelectric Effect Photon E=hf W0 = Work Function = minimum work required to eject an electron from the metal - Electron with maximum KE Conservation of Energy: hf = W0 + KEmax No electrons are ejected if the frequency is too low More light does not result in electrons with more KE Energy is being absorbed in packets (like particles)

228
**The Photoelectric Effect in the garage…**

229
**More Photoelectric Effect Applications**

Automatic Doors Photographer’s light meter Digital Camera Web Link: Digital Camera Web Link: Solar Energy

230
**White Light (all colors) = 380-750 nm**

Ex: White Light (all colors) = nm Sodium (W0=2.28 eV) - - Find the maximum kinetic energy of the ejected electrons (in electron-Volts).

231
**Web Link: Compton Effect The electron now has some Kinetic Energy**

The Compton Effect Web Link: Compton Effect The electron now has some Kinetic Energy Does the photon have more or less energy after the collision? (Energy=hf) (Energy=hf’)

232
**What is the change in wavelength if =0°? =180°?**

’ Conservation of Energy & Conservation of Momentum… h = Planck’s constant m = electron mass c = speed of light = Compton wavelength = 2.43 x m What is the change in wavelength if =0°? =180°?

233
**Now take a few minutes to discuss these with your group:**

Conceptual Example in the textbook (p.905) Solar Sail Check Your Understanding #10 (p.906) Radiometer

234
**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 When they finally tried it out with electrons, the interference pattern corresponded perfectly to this wavelength!

235
Ex: Find the de Broglie wavelength of a car with a mass of 1000 kg traveling at a speed of 30 m/s.

236
**It’s a Probability Wave:**

So what does this wavelength really mean for particles?? It’s a Probability Wave: 100 electrons 3000 electrons 70000 electrons

237
**Does the universe exist if we’re not looking???**

Web Link: Does the universe exist if we’re not looking???

238
**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

239
**Find 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.

240
Ex: 10 cm The marble (m=25 g) is somewhere within the box. Find the uncertainty in the marble’s speed.

241
**Heisenberg 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.”

242
**This 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, then This leads to “Quantum Tunneling” Web Links: Scanning Tunneling Microscope Animated STM STM images

243
**The best part about knowing all this physics, is that now you will get the jokes……**

244
**A Party of Famous Physicists**

Let’s see how many of the following physicists you can guess…

245
**Everyone was attracted to his magnetic personality.**

246
**He was under too much pressure to enjoy himself.**

247
**He may or may not have been there.**

? ? ? He may or may not have been there.

248
**He went back to the buffet table several times a minute.**

249
**He turned out to be a powerful speaker.**

250
**He got a real charge out of the whole thing.**

251
**He thought it was a relatively good time.**

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Electric Energy and Capacitance

Electric Energy and Capacitance

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