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ELECTRIC CHARGE Chapter 16 Just as the mass of the earth exerts an invisible force on you because of your mass. Any two objects which have an electric charge also exert a force on each other. The electron on the comb is not moving so it is called: STATIC ELECTRICITY the study of stationary charges is called: ELECTROSTATICS Gravity Which type of force is generally stronger? Electrical Force little comb paper BIG EARTH If I had two 1 kg piles of electrons separated by 1 m 1m 1 kg e- 1 kg e- Their masses would attract each other due to gravity with a force of: .000000000067 N Their Charges would repel each other with an Electrical force of: 270,000,000,000,000,000,000,000,000,000,000 N In Mechanics, a fundamental concept was MASS. We never really said what it is, just how it behaves. Gravity Inertia Momentum Energy With Electrostatics, a fundamental concept is CHARGE We won’t define what it is or why it acts as it does, just how it behaves. There are ONLY 2 types of charges Positive (+) Negative (-) LIKE CHARGES REPEL + + - - OPPOSITE CHARGES ATTRACT - + Charge maze game applet All charge in the universe comes from two particles Electrons (-) Protons(+) How can an atom be neutral? + + - Neutral + + 2 protons & 2 electrons How does an atom become a positive ion? - positive 2 protons & 1 electrons + + CATION Negative? - - + + ANION - negative 2 protons & 3 electrons The charge of an electron is equal & opposite the charge on a proton - + if an electron is -1 a proton is exactly +1 The smallest amount of charge possible is the charge on 1 electron or 1 proton the charge on any object is a multiple of this amount - + Our charge cannot not be split into a smaller piece of charge Conservation of Charge Charge is not created or destroyed, but it can move from 1 object to another Some materials are very good at holding onto their own electrons or stealing them from other objects. Like: Plastics and Rubber Others don’t hold on to their electrons well and tend to lose them. Like: hair or glass They start When two out materials with NO areNET rubbed, CHARGE. usually electrons get stolenare Why bythey one the neutral? of the objects. cloth glass + + - - - + + + + - After the electrons move. What it the charge on each object? cloth glass + + + - - - + + + - Negative Positive If a piece of Plastic is rubbed on the same cloth (neutral again) cloth rubber + + - - + - + + + - If a piece of Plastic is rubbed on the same cloth (neutral again) cloth rubber + + + + + - - + - They both end up charged cloth rubber + + + + - + + - Positive Negative CHARGE IS NOT CREATED It is only transferred between OBJECTS 2+ 0 + + - - - + + - + + 0 + + + 0+0=0 e-s 2+ + + 2+ + 2- = 0 2e-s thus CHARGE IS CONSERVED 0+0=0 (2+) + (2-) = 0 0=0 Initial = Final RECAP How does an object become negatively charged It GAINS Electrons positively charged It LOSES Electrons An object DOES NOT gain protons to become positively charged. This would be a NUCLEAR REACTION. John Travoltage applet BEN FRANKLIN FOUND THAT + + + Repel + + - - + -+ + - + + Repel -+ + - + + - + Attract + + + - - So he knew that the charges were different + + + I dub thou charge on the glass rod POSITIVE. and Rubber rod shall be NEGATIVE - + -+ + - This were arbitrary 1- 1+ - + - The smallest charge an object can have is 1 electron + charge is QUANTIFIED (comes in chunks) The SI unit of CHARGE is a COULOMB (C) The smallest possible AMOUNT charge is (the charge on 1 electron) e = 1.60 x -19 10 C All Net charge is a multiple of this amount In other words charge is quantized, it only come in discrete packets or quantities. How many electrons do I need to have 1 full coulomb of charge? e = 1.60 x -19 10 C Millikan oil drop video clip ( in folder) Video via you tube The force exerted between two charged objects is Charge on object #1 (C) F12 = F21 (N) k Q1 Q2 F= 2 r r Q1 Q2 Charge on object #2 (C) distance between (m) Coulomb’s Constant= 8.988 109 N m2 C2 k Q1 Q2 F= 2 r This equation is known as COULOMB’S LAW k Q1 Q2 F= 2 r 1 k = 4pe 0 A fundamental constant known as THE PERMITTIVITY OF FREE SPACE = 8.85 10-12 C2/N m2 So in some cases you will see Coulomb’s law written like this. If so I would think that you will be given eo Q Q 1 1 2 F = 4pe r2 0 You generally will need a direction for the force. I typically use a picture to determine direction and simply put in the charges without their signs. k Q1 Q2 F= 2 r Force of Gravity 6.667 10-11 (little) Coulombic Force 8.988 109(BIG) k Q1 Q2 G m1 m2 F= F = 2 2 r r Proportional to mass Proportional to charge BOTH FOLLOW INVERSE SQUARE LAW Force of Gravity Coulombic Force k Q1 Q2 G m1 m2 F= F = 2 2 r r Always attractive Mass is always positive Can be attractive or repulsive Charge can be positive or negative What is the magnitude of electrostatic force on a 1s electron in a helium atom due to the nucleus. The distance from electron to the nucleus is .53 x 10-10 m What is the direction of the force on the electron? What is the magnitude and direction of the force on the nucleus? How would the force change if the radius was doubled? How would the force change if the nucleus had two protons? What if the charge on both were doubled? A fixed proton and an electron are separated by some distance. When the electron is released released the ...... The force on the e- them will_______ increase increase The acceleration of the e- will_______ increase The velocity of the e- will_______ A fixed electron and another electron are separated by some distance. When the electron is released released the ...... The force on the e- them will_______ decrease decrease The acceleration of the e- will_______ increase The velocity of the e- will_______ Page 497: 1, 2, 5 2.7 N http://www.colorado.edu/physics/2000/waves_particles/wavpart2.html Coulomb’s Law only gives us the force between two particles. If more than 2 are present the forces just add or subtract Find the Resultant Force on Particle #2 Q3 = -21.5 mC Q1 = -15.4 mC - .50 m + .65 m Q2 = +80.6 mC F2,1 = 44.6 N FNET = 7.7 N + + F2,3 = 36.9 N - F= k Q1 Q2 r2 If the particles are not in a line, you can still add the forces together. Remember adding vectors? + 1 + 2 3 - Let’s look at the direction of the forces on PARTICLE #2 How would we find the Total Force on #2? + 1 + 2 3 - F2,3 F2,1 How would we find the Total Force on #2? Resultant Force F21 F23 Find the Resultant Force on Particle #2 - Q1 = -2.5 x 10-5 C .65 m Q3 = +1.4 x 10-5 C + .50 m + Q2 = +8.6 x 10-5 C Problems: Honors Physics Page 497: 11, 14 2.96 x 105 N Electrons can travel easily through some materials but are STUCK in place in others Conductor- electrons travel easily Insulator- electrons are tightly bound Electricity will travel hundreds of miles through metal wire (conductor) rather than a few centimeters of glass (insulator). If a charge is placed on a conductor, the like charges repel each other and excess charge migrates to the surface of a conductor to get as far as possible - from other like charges. - - Negatively charged metal sphere + + + + + + Positively charged metal sphere --- - - - - - - - - - -- - - - - - - - - - -- If a charge is placed on a INSULATOR, electrons are stuck where they land. So charged patches can be seen. ---- -- -- -- ------- -- like your black slate desk top What would have happened to cause a positive patch your desk? Friction (rubbing) is not the only an object can be charged Starting with a negatively charged sphere and a neutral one separated by air Negative Metal Sphere - - - - Note: the extra electron on this sphere repel each other and spread out Neutral Metal Sphere They electrons If they are (repelling) brought into are contact able to spread out further, charging the other sphere! - - - - Note the spheres would now repel each other The second sphere was charged by CONDUCTION. CONDUCTION- Charging by contact. - - COPPER - - - The charge was CONDUCTED, through the copper - - Glass - - NO CONDUCTION THROUGH AN INSULATOR How would a neutral object become positively charged by conduction? positively charged, fewer electrons than protons Neutral + -+ + - + - +- -+ + - + -+ - + -+ How would a neutral object become positively charged by conduction? Neutral positive + -+ + - positive + - +- -+ +- + - + -+ + Electron leave the neutral object a negative object brought near (but notside touching) a neutralside. one TheIfneutral object will is end up with a positive and a negative Negative - - - Neutral + -+ + - + - +- -+ it is still neutral but now polar This movement of charge (without contact) is called induction The If neutral theIfsphere a negative object moves will object back, endisupthe brought with sphere a near positive is still a neutral side neutral and onebut a negative not polar side Negative Neutral - - - + + + - -+ -+ + The process of induction will cause a charged object to attract a neutral one - - + + -+ - - - + -+ - +- Attract - - - --- ++ + + + + Distance Why are the attractive forces stronger than the repulsive ones? Neutral objects are attracted to charged objects Charged comb attracts neutral bits of paper. Charged comb attracts neutral water molecules. Demo soda can- attraction by induction Here a sphere shows an induced polarity, they attract. Will they be attracted or repelled after they touch? Attract - - - + ++ +- ++ -++ ++ - + +- - NOW THEY BOTH HAVE A NET NEGATIVE CHARGE!!!! REPEL Two neutral metal spheres are in contact. If a negatively charged sphere is brought near….. What would happen if this sphere moved back away? - - - + -+ + - -+ ++ + - +- + - + - +- -+ INDUCTION can be used to create a “permanent” charge on an object 2 neutral metal spheres in contact, and a charged one is brought close. - - - + -+ + - -+ ++ + - +- + - + - +- -+ When the spheres are separated. They remain charged even if the left sphere is removed. WHY? Are the charges on the remaining spheres equal and opposite? - - + + + + + + + -+ -++ -+ - -+ - The earth is neutral (and really big). So it acts like a charge reservoir. If a negatively charged object touches a conductor which is “grounded”…. -- neutral Electrons will flow to the earth. The earth is so big it is still essentially neutral & so is the object --neutral If a positively charged object touches a conductor which is “grounded”…. + + + + + -+ neutral +- -+ -+ + + - - Electrons from the earth flow to the positive object. Again both objects are now neutral -+ + + e-’s neutral Charging by induction and grounding - + - + - + + + + - -+ + Charging by induction and grounding - + + + + + + -+--- + - - -- What would the charge be on the can if a positively charged rod was used instead? + + + + + + + - + - + + + + -- ++ - + -+ What would the charge be on the can if a positively charged rod was used instead? + + + + + + -+ -+ + - + -- ++ - + -+ + + The hand acts as a GROUND in this experiment Demo soda can- attraction by induction (rolling) Demo 2 soda cans & van de graaf) alligator clip alligator clip ground attraction by induction, repulsion after conduction, neutralization by grounding Charging an object by induction & grounding - - - - animation - --- ++ - - - - + + + + + + + + + + + + + the right sphere is grounded + + + Earth Ground both spheres are now charged neutral - - + + - Positive + + + -+ - - + - Negative + + neutral + + + + - - + + -+ - - + + + + + + + + + + + + - - + + + + - - These spheres have been charged by INDUCTION animation an ELECTROSCOPE is a device used to detect charge INSULATORS Metal ball & Rod Rubber Stopper Glass Flask Thin Metal Foil Strips It can start out neutral + -+ - -+ +-+ If a negatively charged object is brought near - - - -- - - -- - - + + Electrons are repelled down to the foil strips + -+ + - - The negatively charged foil strips repel each other (charged by induction) If the rod is taken away, electrons redistribute themselves again + -+ - -+ +-+ If a negatively charged object is brought near again. And then touches - - - -- - - -- - - + + + -+ + - - Electrons will move from the rod to the electroscope Now the electroscope is negatively charged by: contact or conduction - - + - -+ + -+ + - - Even if the rod is removed, the negative charge remains and the leaves STILL repel each other + - -+ + -+ + - - If a positively charged rod is brought near + + + + + + + + - -+ + -+ + - - If a positively charged rod is brought near Electrons migrate from the leaves toward the positive rod reducing their repulsion + + + + + + + --+--+- - + +-+ Powder Painting PHOTOCOPIERS Copy Machine (animation) LASERPRINTERS Electrostatic Precipitators Problems involving static charge Electronics lightning winter and door knobs Problems and Questions: 1.) At automobile toll-collecting stations a thin metal wire sticks up from the road and makes contact with cars before they reach the toll collector. What is the purpose of this wire? 2.) Why are the tires for trucks carrying gasoline and other flammable fluids manufactured to conducting electricity? 3.) Would it be necessary for a charged body to actually touch the ball of the electroscope for the leaves to diverge? Explain. 4.) Strictly speaking, when an object acquires a positive charge, what happens to its mass? If it acquires a negative charge? 5.) How can you charge an object negatively with only the help of a positively charged object? 6.) Which of the two would be safer: a house with no lightning rod , or , a house with a lightning rod not connected to the ground? Explain. 7.) Why is a good conductor of electricity also a good conductor of heat? 8.) If you rub an inflated balloon against your hair and place it against the wall, it will stick. Explain. 9.) How are electrically neutral atoms and molecules able to electrically attract each other? 10.) Five pith balls are tested against each other, Ball A attracts B and repels C. Ball D has no effect on E. Are all the pith balls charged? What charges are on the pith balls? 11.) Describe the process of putting a negative charge on an electroscope by induction. Use diagrams as necessary and explain the motion of the electrons in the electroscope in terms of attractive and repulsive forces between the charges. Static Electricity Lab Triboelectric series Human Hands (if very dry) Leather Rabbit Fur Glass Human Hair Nylon Wool Fur Lead Silk Aluminum Paper Cotton Steel (neutral) Wood Amber Hard Rubber Nickel, Copper Brass, Silver Gold, Platinum Polyester Styrene (Styrofoam) Saran Wrap Polyurethane Polyethylene (scotch tape) Polypropylene Vinyl (PVC) Silicon Teflon ELECTRON GIVERS (Positive) ELECTRON STEALERS (Negative) WHAT 3 types of things can exert a force without physical contact with the other object Electric Charge Magnets Gravity(mass) Electric Charge Magnets Gravity(mass) Exert a force without contact through a vacuum That really bugs me. A charge creates a FIELD, and the field exerts a force on objects in it - + Electric Field Electric, Magnetic, and Gravitational Fields are FORCE FIELDS An ELECTRIC FIELD cannot be seen directly. But it can be felt. An electric field is mapped out by placing a POSITIVE “test particle” in it and measuring the force on the test particle. 2+ Compare the magnitude and direction of the force felt by the particles + 3 + 1 To show each Force vector at every possible location would be too messy. applet Electric Field Vector Map (applet) FIELD LINES are used to simplify the picture Arrows point in the direction of the force a positive test charge would feel at that location FIELD LINES are used to simplify the picture Lines are CLOSE where Field is STRONG and FURTHER where field is weaker Why do field line arrow point TOWARDS a negative CHARGE Compare the two sets of Field Lines Field around 2 positive charges + + what is the field midway between the two charges? applet Field around 2 opposite charges Field Lines are like a map. How does is a topography map show elevation changes They indicate the magnitude and direction of the Field (vector). The direction FIELD LINE is also the direction of the FORCE ON A POSITIVE TEST PARTICLE Electric Field applet Field Lines around charged parallel plates Note evenly placed field lines within between charged plates indicate a uniform strength electric field. I.e. same force but continuous force on a charge object in the field DO MORE HERE WITH INTERPRETING FIELD LINES See ActFF025-fieldlines in maloney file What would field lines look like outside of a charged metal ring? - - - - - - - - - - - - What about on the inside? Lets put a test charge in and see which way it is pulled. - - - - - - - - + No Electric Field on the inside - - - - Inside of a charge CONDUCTING object, there is no NET FORCE and NO FIELD (no matter the shape of the object) animation of hollow conductor An electric field does not affect the inside of a conductor. It is SHIELDED The rubber tires DO NOT PROTECT YOU in a car. The lightning just jumped over 1,000 ft through air (a few inches of rubber are no problem). You are surrounded by a conductor and so the electric field inside is ZERO. The person is shielded from the electric field, perfectly safe. This type of demo uses a Faraday Cage named for Michael Faraday. We’ll see him later with magnetism When determining the field around a charge, why should we use a small test charge? Object creating field to be measured - + small test charge BECAUSE the test charge creates its own field. The field generated by a charge must be found by using a test charge and looking for the force on it F= +q Q k Qq r2 What would happen to the force on the test particle if its charge was doubled? Did the electric Field from particle 1 change? The field generated by a charge must be found by using a test charge and looking for the force on it (Test Charge) +q Q F= k Qq r2 The force measured on the test particle depends on its own charge The ELECTRIC FIELD we are measuring DOES NOT depend on the test particle Electric Field (N/C) q(Test Charge) + Q Force on Test Charge E= F q Charge on Test Charge (C) So the charge of the test particle is divided out E= q Q F q Electric Field is 24 N/C here. What would be the direction and magnitude of force of a 2 C charge placed here? F= +q Q E= E= F q k Qq q r2 k Qq r2 + Q q kQ E= 2 r The Strength of an electric Field: Increases with the charge of the object creating it Decreases with the square of the distance from the object creating it a hammerhead shark biting at an electrode All living marine organisms generate an electric field around their body and some animals possess a sensory system (the Ampullae of Lorenzini) which enables them to detect weak electric fields and use them to orient to cryptic prey. What is the strength and direction of the electric field 2.5 x 10-9 m to the right of an electron? Electric Fields can add or subtract just like FORCES What is show is the “net” electric field Here Two electric Fields are affecting our Test Charge. What is the direction of each field at its location? Q1 - E1 E2 Q2 - + Test Charge Why is the field from particle 1 stronger at that point? Will the Forces on the test particle add or subtract + E1 + E2 = = What is the direction of the two electric fields at the test charge? Q1 - E1 E2 Q2 + + Test Charge Will the Forces on the test particle add or subtract + E1 + E2 = = 10-11 m 5x10-11 m Q2 + Q1 e- p+ What is the strength of the field at the blue point? And what is the force on a 1mC charge at that location? E1 + E2 Q2 - Q1 - What direction would the net electric field point at the test charge? Electric Field applet Electric Field Strength (at a given location) tells you the amount of FORCE per charge - + 2+ + + + + + + + + Both charges feel the same field strength but different forces Basic dialogue Energy was useful in mechanics Relate PE of charge and gravity Use test + test particle to show low and high PE’s Intro voltage, increase or decrease based on + particle + charges tend to go from high to low potentials, -charges tend to go from low to high potentials Voltage always based on differences, like energy Usually ground is considered zero-tie to GPE Similarly 2 masses on the surface of the earth experience the same gravitational field strength (9.8 m/s2) but the one with twice the mass, experiences twice the force Field strength and Potential energy are related but different.... What happens to the Potential Energy as What happens to the field strength the as object is lifted this case)? the object is (in lifted? Why does a rock lifted up on earth gain POTENTIAL ENERGY You sure do have potential, son!! The PE is the amount of Work done to lift the object against the force of gravity. PE = mgh = W = Fd h The FORCE of Gravity, can convert its height to Kinetic Energy ( it is in a gravitational field) Weeeee + Gravitational Potential Energy Electric Potential Energy - + Both can be converted to KE - Work must be done to move against a force to put them back in the same spot + - Does the Electric Potential Energy increase or decrease? 1 - + 2 - + Does the Electric Potential Energy increase or decrease? 1 + + 2 + + If 2 J of work was done to push them closer. Then 2 J of electric potential energy was gained 1 + + 2 + + The monkey does work to bring the charges closer. That energy can be converted to kinetic energy when released UE V= q electric potential energy electric potential (in Volts or V) electric potential is the Joules of energy per unit charge. So one way of expressing volts is J/C Remember if we say the rock has 9.8 J of Ug, We really mean, it has 9.8 J of Ug compared to… 1 kg 1m DUE DV = q We really mean than the difference in voltage is proportional to the difference in potential energy between two locations. Usually we consider one state to have an energy of zero. Which is… 1 kg 1m DUE DV = q We can only measure the voltage DIFFERENCE between two position. Usually a grounded wire is considered to be a a zero potential + + + + + + + + + + + + + + + + + + What happens to the potential energy of the particle as it is moved? + Potential energy increases _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ + Low Voltage + High Voltage + + + Where would voltage (electric potential) + be higher? + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ + Low Voltage + High Voltage + + + + CHANGES IN VOLTAGE are ALWAYS + based on a POSITIVE test charge. + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ + Low Voltage + High Voltage + + + + + + + + + + Positive charges naturally move + High to ______ Low potentials + from________ + + Know this + + + - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ + Low Voltage + High Voltage + + + + + + + + + + Negative charges naturally move + Low to ______ High potentials + from________ + + Know this + + + - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ + Low Voltage + High Voltage + + + + + + + + + + The two charges are moved from + + low to high potentials. Increases + The U of the + charge_________ E + Decreases The UE of the + charge_________ + + + - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ or work We say that the original position has no energy, so its voltage is Zero DUE DV = q or work We say that the original position has no energy, so its voltage is Zero DUE DV = q or work Since the voltage changed by 10 V, we did 30 J of work to move the charges DUE DV = q Gravitational potential energy Lifting a rock that has twice the mass Requires twice the work. Moving a particle that has twice the charge also requires twice the work, because it has twice the force. UE V= q Electric Potential or Voltage is the electric potential energy per charge. This ONLY depends on the location / strength of the electric field not the “test charge” The more Voltage DIFFRENCE, the Greater the difference in ENERGY each electron has Electric Field = Voltage = electric potential Force q UE q electric potential energy This particle has twice the potential energy but the same electric potential (voltage). Energy per charge. This just depends on location and the source charge! - 2- + + + + + + + + + + + + + + + + + + + + Demo- Van de Graaff Generator Charges in electric field have energy Voltage is the energy per unit charge (basically it just depends on location) Electric Potential Energy (J) UE V= q Charge (C) Electric Potential (J/C or Volts) OUR Van de Graaf Generator creates a voltage of 50,000 V or 50,000 J/C WHY is there not that much energy discharged when you get ZAPPED?? There is not that much CHARGE!! Some Voltages (Potentials) Lightning Our VDG Residential Electric D battery 100,000,000 Volts 50,000 Volts 120 Volts 1.5 Volts How much electric potential energy does 2 coulombs of charge have at 120 V (standard household voltage). UE V= q Rearranging UE = V q and more correctly written DUE = qDV A common unit of measuring very small amounts of energy is an electron volt (eV) UE = qV 1 eV= 1.60x10-19 C 1V 1 eV= 1.60x10-19 J Potential Energy looks at a change in position. Usually one state is said to have zero potential DPE = mgDh DPE = qDV - - - -- - - -- - - DV - Dh + + + + + + + How much PE does an electron have in a lightning bolt about to strike? Assume the voltage is 100,000,000 (108)Volts. DUE = QDV charge on an electron: 1.6x10-19 C How fast is it moving when it strikes the ground? mass of an electron: 9.1 x10-31 kg A charge +2 C, is in a uniform electric field of 6 N/C between two parallel plates as indicated in the diagram below. If the charge is moved 3 meters -- how much work was done, --by how much did its energy change, --What is the change in electric potential (& increase or --decrease), --did it gain or lose electric potential energy? 3m + + E = 6 N/C A charge +2 C, is in a uniform electric field of 6 N/C between two parallel plates as indicated in the diagram below. If the charge is moved 3 meters how much work was done, by how much did its energy change, did it gain or lose electric potential energy.? + 3m + E = 6 N/C A charge +2 C, is in a uniform electric field of 6 N/C between two parallel plates as indicated in the diagram below. If the charge is moved 3 meters how much work was done, by how much did its energy change, did it gain or lose electric potential energy.? E = 6 N/C 3m + 45o + Solving this generically, a charge (q) in a uniform electric field (E) moved a distance (d) parallel with the field. F E= q Plugging in for F….. W=Fd Solving for F DUE = q E d F= q E E + W=qEd + And we all know work = the change in …. DUE = qEd The change in electric potential for a charge in a uniform Electric field. Uniform meaning that field strength is constant as is the case between parallel plates. DUE = qEd DUE =V q V = Ed And of course by V we really mean DV, a comparison between two states… One usually taken to be Zero. V=Ed + + + + + + E d - - - battery - - - The Field must be uniform for this to work V=Ed + + + + + + E .11 m - - - 12 V battery - - - What is the strength of the electric field between the plates More than one spot can have the same Potential (voltage) Meaning if an electron was place in anywhere along 1 dashed line it would have the same UE These are indicated by EQUIPOTENTIAL LINES Which electrons have the same electric potential? - - - Both electrons have the same potential energy. Because they are the same distance from the charge and the field strength is the same as well. - The voltage is the same along an equipotential line Equipotential lines must be perpendicular to field line… For the equipotential lines shown, draw an electric field line Voltage is based on energy per charge. To find the voltage “at a given location”, we compare it to a position where the voltage is considered to be zero. Where would a positive test charge have the least/Zero electric potential energy? At infinite distance + To find the voltage “at a given location”, the amount of work to bring a particle to that location from an infinite distance is calculated. from an infinite distance + k Qq F= 2 r Work = F d UE so F d V= V= q q ra= ∞ +Q rb q Fd V= q k Qq d = q r2 ra= ∞ +Q rb q k Q dr V= 2 r The distance is really r so... ra= ∞ +Q rb q kQ V= r The difference in voltage between the two locations k Q k Q DVab = Vb - Va = rb ra ra= ∞ +Q rb q The change in voltage of a particle brought from infinite distance (and zero force) to a distance r from the charge. kQ V= r ra= ∞ +Q rb q kQ V= r r This equation yields the change in voltage of a particle brought from infinite distance to a distance r from the charge. It can be thought of as just the voltage at that location. Or Voltage can be figured out by calculus kQ V= r An electron is brought from an infinite distance to a distance of 1 nm from a proton. What is the voltage at that location? Does the voltage depend on the electron being there? How much work was done? If a particle is moved from one location to another, just find the voltage at both locations and subtract them. If the charge moved was 3 C, how much work was done? V1 = 4 V V2= 9 V What happens to the electric field as the test particle is brought on an approaching equidistant path. + + - A side note, electric potentials do have signs based on the source charge. Consider the test + charge brought in from infinity and brought to the location below. As it got closer to the two charges, the red positive object caused its PE and V to.... the blue negative object caused its PE and V to.... + + - What is the electric potential at a location 10 meters from the two charges below? How much work was done to bring and electron to this location? 2C -3C Common Misconceptions Electric Potential Energy is not the same as Electrical Potential. Electrical Potential can also be described by the terms, potential difference, voltage, potential drop, potential rise. The variable we use for potential difference is V and the unit for potential difference is also V (volts). Don't let that confuse you when you see V = 1.5V The electron volt is not a smaller unit of the volt, it's a smaller unit of the Joule. The Electric Field inside of a conductor (charged or not) must be 0. Why? - - - - - - - - - - - - Why excess charge distributes itself out until the net force on any excess charge is zero. - - - - - - - --- - - - - The electric field inside of a conductor is always zero, EVEN if… the conductor isn’t round or a charge is placed inside a hollow conductor Because the excess charge on a conductor can move and will do so until there is no net force on them even in a charge is placed inside a hollow conductor. If there is no net force on the excess charge on the outside of a hollow conductor due to charge inside…. (Newton’s 3rd law says). F E= q In order to accomplish this, excess charge tends to concentrate on the “sharper” parts of a hollow conductor. (probably not that important). But the electric field inside each is still zero. Is there an electric field outside the conductor? This is an AP objective so copy this down R r kQ E = R2 (At the surface) kQ E = r2 (away from the surface) Inside the conductor the electric field is zero Back to electric potential (voltage). A change in voltage occurs when work changes the electric energy of a charged particle. How would I calculate the work involved to move a charge particle in a hollow conductor? + + E=0 + + + + + + + F=0 + W=0 + DV = 0 + + + + + + The electric potential in a hollow conductor is constant Would there be work to bring a charged particle from a distance away from the conductor to inside of it? YES + + + + + + + + + + + + + + + + + Also an AP objective R r kQ (At the surface and inside) V= R kQ Outside of the V= r sphere Going back to conductors connected by wires - - COPPER - - - When equilibrium is established (this is assumed)… The net force on any excess charge is zero which means anywhere on or in a conductor means…. Zero The net force on a charge particle is___________ Zero The electric field is ____________ Constant The electric potential is___________ AP objective Explain why a conductor must be an equipotential, and apply this principle in analyzing what happens when conductors are connected by wires. Capacitors store energy in an electric field They come in all shapes and sizes Capacitors the energy for a camera flash the energy is stored slowly and released QUICKLY the capacitor from a camera being discharged by “shorting the circuit” BIG capacitors store energy to be used when you Air conditioner starts up. They are used in most electronic device like TV’s. They retain their energy even when the power is off. So be careful when digging around in one. Conducting plates are connected to a battery (or another power source) the plates do not touch and are separated by an insulator like air, capacitor animation When connected electrons flow building up charge on the plates The Voltage across the plates will eventually be the same as the battery 1.5 V - + + + + e- 1.5 V capacitor animation e- The total charge that can be stored in a capacitor is Q = CV voltage of power source Stored Charge (Coulombs) Capacitance (farads, F) a fudge factor based on the actual capacitor’s size and materials The greater the voltage source and capacitance the more charge can be stored The capacitance depends on the: dielectric constant of material between the plates (page 514) e0 =8.85x10-12 C2/Nm2 Ke0A C= d A (area) What will units on A and d be? d Table of dielectric constants Inserting a dielectric material between the capacitor plates reduces the electric field there Material Vacuum Air(1 atm) Air(100 atm) Teflon Polyethylene Benzene Mylar Polyvinyl chloride Plexiglas Neoprene Glass Germanium Liquid ammonia(-78°C Glycerin Water Strontiun titanate Dielectric Constant 1 1.00059 1.0548 2.1 2.25 2.284 3.1 3.18 3.4 6.7 7 16 25 42.5 80.4 310 Ke0A C= d Q = CV Inserting a dielectric material improves the capacitor by 1.) Increases the voltage you can apply before a spark jumps between the plates 2.) Allows the plates to be closer together without sparking. Reducing d increases C. 3.) By simply being there, increases the capacitance by the factor “K”. Ke0A C= d Q = CV Two metal plates are separated by some distance with air between them forming a capacitor. They are connected to a 12 V battery. If a dielectric material such as teflon is placed between them, what happens to the amount of charged stored on the plates? Good animation for this Ke0A C= d Q = CV For a given applied voltage..... As area of the plates increases the amount of charge that can be stored As distance between the plates increases the amount of charge that can be stored Capacitance DOES NOT depend on its voltage or charge, just its structure. (like a storage tank) Typical Capacitance ranges from mF = -6 10 F pF = 10-12 F To increase the area of the plates without making the capacitor huge, the “plates” are sandwiched between a dielectric material and rolled up. Capacitors are essentially parallel plates. What does the electric field look like between two charged electric plates. UNIFORM + + + + + + E d - - - battery - - - What is the relationship between electric field inside a parallel plate capacitor, the voltage, and plate separation. V=Ed + + + + + + E d - - - V V battery - - - So as Or… voltage___ electric field ____ V E= d + + distance___ electric field ____ + + + + E d - - - V battery - - - What is the capacitance of two sheets of aluminum foil, each .30 m x 1.5 m. Which are separated by paper (K = 5.0) which is .50 mm thick. What is the total charge, if connect to a 9.0 V battery? A capacitor stores energy What determines the amount of energy, for a given capacitor QV UE = 2 Energy (J) Charge on capacitor (C) Voltage between plates (V) Since Q = CV plugging in for V plugging in for Q 2 Q QV U= = = 2 2C 2 CV 2 How much energy was stored on our aluminum foil capacitor (C= 4.0 x 10-8 F) charged to 12 V? Capacitance Problems Honors Physics Page 524: 32, 33, 39