This Week Electric charge. What is it? Where is it? Voltage and energy What is a battery? Conductors and Insulators Bad idea to wave a golf club in a thunderstorm What is Lightning? Electrocution How does a microwave work? 10/5/2012 Physics 214 Fall 2012 1
Electric charge an atom has a central nucleus of protons and neutrons surrounded by electrons Each element in the periodic table has a different combination of protons and neutrons. Hydrogen just has one proton and one electron. Electrons and protons carry electric charge and it is the force between the charges that hold the atom together. Charge comes in both negative (electrons) and positive (protons) and each carry one unit of charge. Normally objects have zero net charge but it is possible for an object to have charge which is a multiple of the unit charge either positive or negative. It is quite easy to separate electrons from atoms. 10/5/2012 Physics 214 Fall 2012 2
Electromagnetism Almost every action in our everyday lives is due to the electromagnetic force caused by electric charges. Everything that is not due to gravity is electromagnetism. All transmission and use of electric power is due to the flow of electrons through wires. A camera flash is an example of separating positive and negative charge, which requires work. This work is then released as energy by letting the charges combine (lightning) If there is a separation of charge between two objects there will be a very strong attractive force which will transfer charge until the objects are neutral 10/5/2012 Physics 214 Fall 2012 3
Positive and negative Charge only occurs as a multiple of the unit charge on an electron or proton which is 1.6 x 10-19 coulombs So any charge q is an integer multiple And N can be positive or negative q = N x 1.6 x 10-19 coulombs Opposite charges attract Same sign charges repel 10/5/2012 Physics 214 Fall 2012 4
Coulomb s Law Coulomb s Law F = kq 1 q 2 /r 2 (k = 9 x 10 9 N.m 2 /C 2 ) F r F The force between two charges of one coulomb each separated by 1 meter is 9 x 10 9 Newtons (your weight ~ 1000N) The gravitational force between two 1 kg masses 1 meter apart is 6.67 x 10-11 Newtons a difference of ~ 10 20. F F To separate a negative charge from a positive charge requires work which is stored as potential energy. When the two charges are released this energy will be liberated as kinetic energy Held in place F ext 10/5/2012 Physics 214 Fall 2012 5
Everyday charge In order to separate electrons from atoms requires work and frictional forces are sufficient to do this. Simple actions like rubbing two objects together or walking across a carpet will often result in a transfer of charge. This transfer is caused by stripping electrons from the atom since every atom has a few electrons which are weakly bound. Electrons can also be more easily moved since (mass electron)/(mass proton) ~ 1/2000 10/5/2012 Physics 214 Fall 2012 6
Conductors and insulators There are two broad classes of substances related to electrical phenomena. Conductors electrons are free to move Insulators electrons are not free to move If we bring a charged object near a neutral object the electrons and the protons will feel the force and in a conductor the charges will separate. Water is a very good conductor so for example we usually only see static sparks in the winter when the air is very dry and objects can hold any excess charge that accumulates. 10/5/2012 Physics 214 Fall 2012 7
5A-01 Static Electricity Demonstration that positive and negative charge exists What information does the electroscope provide? ++++++++ Rubbing the hard rubber rod with fur produces a negative charge on the rod Rubbing the glass with silk produces a positive charge on the glass If we bring a charged rod close to the electroscope it will repel opposite charge and the moving arm will be displaced. If we touch the electroscope with a charged rod then charge will be transferred THE ELECTROSCOPE CAN T DETERMINE THE SIGN OF THE CHARGE BUT IT DOES SHOW CHARGE EXISTS IN TWO KINDS + AND - 10/5/2012 Physics 214 Fall 2012 8
5A-03 Two-by-Four Electroscope Showing the strength of the electromagnetic force. How does the charged ebonite rod move the board? ++++++++++ ------------- Rubbing the rod produces a surface charge. When it is brought close to the wood it attracts the opposite sign charge in the wood and there is an attractive force. This is the same effect as static cling THE GRAVITATIONAL FORCE IS MUCH WEAKER THAN THE ELECTRICAL FORCE. THE RATIO OF THE TWO FORCES IS ~10-39. 10/5/2012 Physics 214 Fall 2012 9
5 A 04 Conductors and insulators The difference between conductors and insulators What happens to the balls? The apparatus with the dome produces electric charge. If the rods connecting the balls are conducting the balls become charged and repel eachother If the rods are insulators the balls remain uncharged All materials contain equal amounts of positive and negative charge. In conductors charge, generally electrons, is free to move. In insulators the charges on the constituent atoms or molecules is tightly bound and does not move. Dry air is a very good insulator but water is a very good conductor and damp air is also a good conductor. Even insulators can break down for example lightning. 10/5/2012 Physics 214 Fall 2012 10
5 A 06 Static electric charge and induction Using an electroscope to see the effects of charge How do we see charge? --------- ++++++++ ++++++++++++ +++++++++ When the rod is brought close it attracts negative charge meaning the pivot rod becomes positively charged. If the top plate is now touched negative charge flows out and the whole electroscope becomes positively charged. The movement of charge, usually electrons, is called a current and all electrical systems work using currents. 10/5/2012 Physics 214 Fall 2012 11
Electric field Any distribution of charges will produce a force field. That is if a test charge q is placed anywhere it will feel a force. Electric field E = F/q 0 or F = q 0 E By definition the test charge is positive and both the electric field and the force are in the same direction The electric field at a point tells you what force a charge +q would feel both in magnitude and direction. 10/5/2012 Physics 214 Fall 2012 12
Electric potential Electric potential difference is the change in potential energy per positive charge. That is it is the work done or energy released in moving unit charge in an electric field. The unit is V = PE/q (joules/coulomb = volt) In a battery charge is separated and potential energy is stored. When it is connected in a circuit charge flows and the energy is released. 10/5/2012 Physics 214 Fall 2012 13
Voltage In a uniform field the work done in moving a charge q a distance d W = qed = PE and the voltage difference is V = PE/q = Ed So if a positive charge q is moved toward the positive plate the voltage increases. 10/5/2012 Physics 214 Fall 2012 14
Basic Force Two point particles with electric charge feel a force and the force between two charges q 1 q 2 is F r F F = kq 1 q 2 /r 2 (k = 9 x 10 9 N.m 2 /C 2 ) F F 10/5/2012 Physics 214 Fall 2012 15
Work and Energy Objects with electric charge also have mass and everything we have done on work and energy is the same. In fact when I push an object across the floor the force is electromagnetic. F d F =ma W =Fd KE = 1/2mv 2 10/5/2012 Physics 214 Fall 2012 16
Electric Fields If there is some distribution of charge that exists and I place a charged object anywhere it will feel a force that will depend on location and what the value of q is. If I move the charge around I can map out the force field and we define the force field by using q = 1coulomb and we define electric field E = F/q So if I know E then we can determine the force at any point for any charge. q F The charge q we use to map out the electric field is always positive So E is always in the direction of the force a plus charge feels 10/5/2012 Physics 214 Fall 2012 17
5A-10 Motion in an Electric Field The effects of transferring charge + - + - What is the movement of the balls? THE BALL IS ATTRACTED TO ONE TERMINAL THEN RECEIVES A CHARGE AND THEN IS REPELLED TO THE OTHER TERMINAL, WHERE IT PICKS UP THE OPPOSITE CHARGE AND IS REPELLED. 10/5/2012 Physics 214 Fall 2012 18
5A-23 Electric Wind The emittance of electrically charged particles from highly charged object What causes the arms to turn? The metal arms are charged by an electrostatic generator and the forces are greatest at the tips so charged particles are driven off by repulsion. Conservation of momentum makes the arms turn in the electric wind The wind can be indirectly seen by the extinguishing of a candle. Before lighting strikes there is charge build up and lightning conductors have sharp tips to attract the lightning. The sun also has large electric and magnetic fields and emits the solar wind 10/5/2012 Physics 214 Fall 2012 19
Simple fields and potential energy The field lines show the direction of the force a positive charge feels. If I place a charge anywhere in the field it has potential energy. That is if I release it will be accelerated and gain kinetic energy. v F F Or if I start it with velocity v it will come to rest and KE PE v 10/5/2012 Physics 214 Fall 2012 20
Voltage and potential energy Electric potential difference (voltage)is the change in potential energy per unit positive charge. That is it is the work done or energy released in moving unit charge in an electric field. V = PE/q (joules/coulomb = volt) Uniform electric field E then force on charge q is Eq and work done in moving the charge a distance d is Eqd so V = PE/q = Ed When you are going against the direction of the electric field the voltage increases 10/5/2012 Physics 214 Fall 2012 21
Conduction and Induction A conducting solid contains electrons which can move and if they are in an electric field they will move opposite to the direction of E If I rub two insulators together electrons will be removed from one insulator and the other will get an excess. If I bring an insulator with negative charge near a conductor then the charge in the conductor will separate. If I now touch the conductor where there is excess electrons they will repel the electrons on the skin and electrons will flow into me. If I now remove my finger the original conductor will be positively charged. If I had touched the conductor where there was excess positive charge electrons would have flowed from me into the conductor. This is Induction There is always charge conservation 10/5/2012 Physics 214 Fall 2012 22
Summary of Chapter 12 Electric charge can be + or F r F q = N x 1.6 x 10-19 coulombs F = kq 1 q 2 /r 2 (k = 9 x 10 9 N.m 2 /C 2 ) F F Charge is carried by particles the most common are electrons - light which can move easily positive nuclei - more than 2000 times as massive Conductors electrons are free to move Insulators electrons are not free to move 10/5/2012 Physics 214 Fall 2012 23
Fields and voltages Electric field E = F/q or F = qe V = PE/q (joules/coulomb = volt) uniform field W = qed = PE voltage difference is V = PE/q = Ed So if a + charge q is moved toward the + plate the voltage increases. 10/5/2012 Physics 214 Fall 2012 24
Positive charge In an atom the positive charge is carried by the protons in the nucleus. For a conductor it is the nuclei which form the structure of the solid and give it properties so in an electric field it is only the electrons which flow. In the case of a gas electrons which are stripped from atoms can move and in an electric field both the electrons and positive ions can move, but F = ma so electrons are accelerated > 2000 times more than ions In the case of the atmosphere strong updrafts and downdrafts cause separation of charge with the bottom of clouds being negative and the top positive. The negative cloud charge pushes negative charge away from the earths surface and then there is lightning. The electric field is highest at objects with sharp ends hence lightning conductors to attract the lightning +++++++++++++++ top of cloud -------------------------- bottom of cloud lightning +++++++++++++++ earth 10/5/2012 Physics 214 Fall 2012 25
Lightning The air around a lightning bolt is superheated to about 54,000 degrees Fahrenheit (five times hotter than the sun!). This sudden heating causes the air to expand faster than the speed of sound, which compresses the air and forms a shock wave; we hear it as thunder. Since the bolt is actually several short bursts strung together, multiple shock waves are created at different altitudes; this is why thunder seems to rumble -- each shock wave takes a different amount of time to reach your ear. Every minute, there are more than a thousand thunderstorms around the Earth causing some 6,000 flashes of lightning. A lightning charge ~ 30 million volts at 100,000 amperes. Insurance for being hit by lightning is a better bet than the lottery but the downside is you can t enjoy it. http://www.space.com/scienceastronomy/101_earth_facts_030722-1.html 10/5/2012 Physics 214 Fall 2012 26
Voltage and Current Voltage is defined by the potential energy stored or released as charge moves in an electric field. If I separate charge as in a battery then there is a voltage across the terminals but charge only flows if a conductor connects the two terminals. As far as your body is concerned it can have excess charge e.g. Static electricity or it can be part of a circuit and charge would flow through the body. Since it is charge and currents responsible for all muscle contractions including the heart significant currents can cause death and higher voltages give higher currents. If you touch a high voltage source but there is no conducting path current will not flow but if you are not insulated e.g. touching metal connected to earth or in a wet environment you can be electrocuted 10/5/2012 Physics 214 Fall 2012 27
Microwave oven A microwave oven generates electromagnetic radiation which contains strong electric fields which change direction 2450 x 10 6 times per second. These electric fields exert a force on charge. The charge in a H 2 O molecule is separated like a tylenol tablet so the water molecules are shaken and the friction between molecules causes the water to heat. In conductors charge can move freely so the charge will move and there will be large currents and sparking and it acts like a short circuit. Ice is not heated because of it s crystalline structure and the water molecules in air are not dense enough to heat. The electric fields and therefore the heating is not uniform in the oven which is why there is a rotating turntable or mechanism which swirls the electric field http://www.youtube.com/watch?v=8wmbxh_mcdw&mode=related&search= http://apache.airnet.com.au/~fastinfo/microwave/ 10/5/2012 Physics 214 Fall 2012 28
Questions Chapter 12 Q2 Two pith balls are both charged by contact with a plastic rod that has been rubbed by cat fur, A. What sign will the charges on the pith balls have? Explain. B. Will the two pith balls attract or repel one another? Explain. A.The sign of the charge is negative. B. They will repel Q3 Two pith balls are charged by touching one to a glass rod that has been rubbed with a nylon cloth and the other to the cloth itself, A. What sign will the charge on each pith ball have? Explain. B. Will the two pith balls attract or repel one another? Explain. A. The first ball will have positive charge the second negative charge B. The two balls will attract each other 10/5/2012 Physics 214 Fall 2012 29
Q13 Will bits of paper be attracted to a charged rod even if they have no net charge? Yes because the charge will attract the opposite charge in the paper Q14 Why are pith balls initially attracted to a charged rod and later repelled by the same rod, even though they have not touched any other charged object? Because once they touch the charged rod they pick up some of the charge and the ball is repelled 10/5/2012 Physics 214 Fall 2012 30
Q18 If two charges are both doubled in magnitude without changing the distance between them, will the force that one charge exerts on the other also be doubled? The force varies as q 1 q 2 /r 2 so the force will increase by a factor of 4 Q19 Can both the electrostatic force and the gravitational force be either attractive or repulsive? No, the gravitational force is always attractive. 10/5/2012 Physics 214 Fall 2012 31
Q20 Is it possible for an electric field to exist at some point in space at which there is no charge? Yes. Electric fields are created by charge but extend to infinity Q21 Two charges, of equal magnitude but opposite sign, lie along a line as shown in the diagram. Using arrows, indicate the directions of the electric field at points A, B, C, and D shown on the diagram. C -q q A - + D B 10/5/2012 Physics 214 Fall 2012 32
Q22 If we change the negative charge in the diagram for question 21 to a positive charge of the same magnitude, what are the directions of the electric field at points A, B, C, and D? (Indicate with arrows.) C q q A + + D B 10/5/2012 Physics 214 Fall 2012 33
Q23 Three equal positive charges are located at the corners of a square, as in the diagram. Using arrows, indicate the direction of the electric field at points A and B on the diagram. q + A + q q + B Q25 If we move a positive charge toward a negative charge, does the potential energy of the positive charge increase or decrease? The potential energy decreases 10/5/2012 Physics 214 Fall 2012 34
Q26 If we move a negative charge toward a second negative charge, does the potential energy of the first charge increase or decrease? It increases because they repel each other it means as you get closer the force gets larger. You have to do work to bring them closer Q32 Would you be more likely to be struck by lightning if you stood on a platform made from a good electrical insulator than if you stood on the ground? Standing on an insulator is the safest which is why the safest place in inside a car because the tires are insulators. It s also the same with fallen power lines 10/5/2012 Physics 214 Fall 2012 35
Ch 12 E 8 Electron and proton have charges of equal magnitude, 1.6 10-19 C, but opposite signs. If the electron and proton are separated by R=5 10-11 m, what is the electrostatic (vector) force b/w them? e - P + F = kq 1 q 2 / r 2 = - (9 10 9 )(1.6 10-19 ) 2 / (5 10-11 m) 2 F = 9.22 10-8 N towards proton r 10/5/2012 Physics 214 Fall 2012 36
CH 12 E14 Charge q = -4 10-6 c placed in Electric field of E = 8.5 10 4 N/C Towards right. What is the electrostatic (vector) force on charge q? E 9m F = qe = (4 10-6 )(8.5 10 4 ) F = 0.34 N Since positive charge moves with field lines and q is negative, q moves to the left F = 0.34 N to left 10/5/2012 Physics 214 Fall 2012 37
CH 12 CP 2 2 equal charges (positive) are near one another (see diagram). a) Using small arrows indicate the direction of the electric field at labeled points on diagram. (Think about what a positive test charge would do!) b) Sketch electric field lines D E F A B + + C G H I 10/5/2012 Physics 214 Fall 2012 38
Ch 12 CP2 (cont) a) D E F D E F A + + C A B + + C G H I G H I b) 10/5/2012 Physics 214 Fall 2012 39
Ch 12 CP 4 4 equal positive charges located at corners of the square (see diagram) a) Use small arrows to indicate direction of electric field at each labeled point b) Would the magnitude of electric field be equal to zero at any labeled point? a) + + + + B E A C + + + + D b) Electric Field is equal to zero at the center of the square (A). 10/5/2012 Physics 214 Fall 2012 40
Summary of Chapter 7 Impulse equation p = F t = mv f mv i F 2 F 1 Collision F 1 = -F 2 and p 1 + p 2 = 0 Total momentum is conserved p = F t = mv f mv i If we choose positive down p will be negative If we choose positive up p will be positive 10/5/2012 Physics 214 Fall 2012 41
Isolated systems In each case m 1 v 1 = - m 2 v 2 anim0010.mov 10/5/2012 Physics 214 Fall 2012 42
Collisions Elastic m 1 v = m 1 v f + m 2 v f 1/2m 1 v 2 = ½ mv 1f2 + 1/2mv 2f 2 Pool balls Bowling ball/tennis ball v v v Tennis ball/bowling ball Inelelastic only momentum is conserved mv i = 3mv final and v final = v i /3 Kinetic Energy before = 1/2mv i 2 Kinetic energy after = ½ x 3mv 2 final So KE before /KE final = 3 10/5/2012 Physics 214 Fall 2012 43
Summary of Chapter 8 Rotational motion Angular velocity ω = θ/ t Angular acceleration α = ω/ t One full circle = 3600 = 2π radians Circumference = 2πR Time for one revolution = 2πR/v 2πr/v = 2π/ω then v = rω v R 57.3 0 Displacement d θ Velocity v = d/ t ω = θ/ t Acceleration a = v/ t α = ω/ t Constant v = v 0 + at ω = ω 0 + αt d = v 0 t + 1/2at 2 θ = ω 0 t + 1/2αt 2 v 2 = v 02 + 2ad ω 2 = ω 02 +2αθ 10/5/2012 Physics 214 Fall 2012 44
Torques Torque = Fl where where l is the perpendicular distance to the line of action of the force + is counterclockwise and is clockwise net torque is sum of all torques For the boy on the plank he will fall when W p d p > W c d c Torque = Fl = Iα I plays the role of mass for rotation Kinetic energy = 1/2Iω 2 Work = Tθ ( full circle T2π = Fr2π Angular momentum L = Iω There is a point in the geometry of a body at which all the mass appears to act and one can balance the body with a single force (center of mass/gravity) g 10/5/2012 Physics 214 Fall 2012 45
Conservation of angular momentum In a closed system L = Iω we can change I and ω will change like a skater. We can invert the bicycle wheel and ω will change to keep L constant 10/5/2012 Physics 214 Fall 2012 46
Conservation of angular momentum In a closed system L = Iω and we can change ω by changing I since L is constant in both magnitude and direction. If we change L for one object in a system the rest of the system changes to keep L constant. 10/5/2012 Physics 214 Fall 2012 47
Summary of Chapter 9 P = F/A Pascals F 1 /A 1 = F 2 /A 2 Work done = F 1 h 1 = F 2 h 2 1 Atmosphere = 1.013 10 5 Pa and will support 76cm of mercury 32 feet of water No Air g 10/5/2012 Physics 214 Fall 2012 48
Liquids P = W/A = ρgh Water is 1 gram/cc 1 gram/cm 3 = 1000kg/m 3 T buoyant force = the weight of liquid displaced T + F B = W = mg For a floating object T = 0 F b mg g 10/5/2012 Physics 214 Fall 2012 49
Summary Chapters 10 and 11 W = P V for the piston shown W external = + W system = - U = Q W system or U = Q + W external Work done on gas = Fd = PAd V = Ad W = P V Work done by gas is -W Temperature scales Celsius, Fahrenheit Kelvin Mixture of ice and water 0 0 C 32 0 F 273 0 K Boiling point of water 100 0 C 212 0 F 373 0 K T c = 5/9(T f 32) T f = 9/5T c + 32 T K = T c + 273 c = is the quantity of heat required to raise unit mass of a substance by one degree. Q = mc T 1 calorie = heat required to raise 1 gram of water 1 0 C = 4.186 joules Change of state (internal energy changes temperature is constant) 80 cals/gm is the latent heat of fusion 540 cals/gm is the latent heat of vaporization 10/5/2012 Physics 214 Fall 2012 50
Gases Work done by gas = -Fd = -PAd V = Ad W = -P V External work done = W =P V Energy conservation U = Q W gas Ideal gas law PV = NkT (T in degrees Kelvin) Adiabatic no heat in or out Q = 0 Compression work is + ( U, T increase) Expansion work is ( U, T decrease) Isothermal T does not change U = 0 Q = W = P V put in heat gas expands take out heat gas must be compressed Isobaric pressure is kept constant Put in heat T increases gas expands (hot air balloon) 10/5/2012 Physics 214 Fall 2012 51
Heat engines Efficiency = ε = W/Q H Change in internal energy in one cycle is zero W = Q H Q c (c = environment) 2 nd law No engine working in a continuous cycle can take heat at a single temperature and convert that heat completely to work. 10/5/2012 Physics 214 Fall 2012 52
Summary of Chapter 12 Electric charge can be + or F r F q = N x 1.6 x 10-19 coulombs F = kq 1 q 2 /r 2 (k = 9 x 10 9 N.m 2 /C 2 ) F F Charge is carried by particles the most common are electrons - light which can move easily positive nuclei - more than 2000 times as massive Conductors electrons are free to move Insulators electrons are not free to move 10/5/2012 Physics 214 Fall 2012 53
Fields and voltages Electric field E = F/q or F = qe V = PE/q (joules/coulomb = volt) uniform field W = qed = PE voltage difference is V = PE/q = Ed So if a + charge q is moved toward the + plate the voltage increases. 10/5/2012 Physics 214 Fall 2012 54