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Electrostatics Essential Knowledge 1.B.2: There are only two kinds of electric charge. Neutral objects or systems contain equal quantities of positive and negative charge, with the exception of some fundamental particles that have no electric charge. Like-charged objects and systems repel and unlike-charged objects and systems attract. Charged objects or systems may attract neutral systems by changing the distributions of charge in neutral systems. 1.B.3: The smallest observed unit of charge that can be isolated is the electron charge, also known as the elementary charge. The magnitude of the elementary charge is equal to1.6 x1 10-19 Coulombs. Electrons have a negative elementary charge of equal magnitude, although the mass of the proton is much larger than the mass of an electron. 3.C.2: Electric force results from the interaction of one object that has an electric charge with another object that has an electric charge. Electric force dominates the properties of the objects in our everyday experiences. However, the large number of particles interaction that occur make it more convenient to treat everyday forces, such as normal force, friction, and tension. Electric force may be attractive or repulsive, depending upon the charges on the objects involved. 5.A.1: A system is an object or collection of objects. The objects are treated as having no internal structure. Learning Objectives 1.B.2.1: The students is able to construct and explanation of the two charge models of electric charge based on evidence produced through scientific practices. 1.B.3.1: The student is able to challenge the claim that an electric charge smaller than elementary charge has been isolated. 3.C.2.1: The students is able to use Coulomb’s law qualitatively and quantitatively to make predictions about the interaction between two electric point charges (interaction between collections of electric point charges are not covered in Physics 1 and instead are restricted to Physics 2) 3.C.2.2: The student is able to connect concepts of gravitational forces and electric force to compare similarities and differences between the forces. Science Practices 1.5: The student can re-express key elements of natural phenomena across multiple representations in the domain. 2.2: The student can apply mathematical routines to quantities that describe natural phenomena. 6.1: The student can justify claims with evidence. 6.2: The students can construct explanations of phenomena based on evidence produced through scientific practices. 6.4: The student can make claims and predictions about natural phenomena based on scientific theories and models. 7.2: The students can connect concepts in and across domain(s) to generalize or extrapolate in and/or across enduring understanding and/or big ideas. Electric Charges 1. Two kinds of charges: Positive and Negative 2. Like charges repel, unlike charges attract 3. Charge is conserved 4. Charge is quantized LINK Law of Conservation of Charge The total charge in a closed system remains constant. Charges are transferred. The total charge in a closed system remains constant. Neutral objects have equal amounts of positive and negative charge. Only electrons are transferred in solids. Single charges may not be created nor destroyed. Pairs of opposite charges may be created or destroyed. Examples: Charge separation by friction Chemical equations Beta Decay Pair production / pair annihilation SI Unit for Charge Coulomb [C] is the SI unit for charge. Coulomb is a derived unit based on the fundamental unit for current, Ampere. Coulomb is a humongous amount of charge. Natural unit for charge On the atomic level, the unit of charge is the elementary charge, e. +e is the charge of a proton -e is the charge of an electron +2e is the charge of an alpha particle Balloon Charge Tester Item Attract Repel Natural unit for charge On the sub-atomic level, fractional charges exist. Quarks have + (1/3) e or + (2/3) e Charge is Quantized In 1909 Robert Millikan confirmed that electric charge always occurs in integral multiples of the fundamental unit of charge, e. q is the standard symbol for charge (units - Coulombs) QT N q Total Charge Number of fundamental charges Elementary Charge 1.6 x 10-19 C Money is quantized, the smallest unit of US currency is the penny! Fundamental particle properties Particle Mass electron 9.11 x 10 -31 kg proton 1.672 x 10 -27 kg neutron 1.674 x 10 -27 kg Charge -1.6 x 10 -19 C -1e +1.6 x 10 -19 C +1e 0 An object has a net charge of +3 Coulombs 1. How many more protons than electrons are on the object? 2. Can you determine the total number of protons on the object? QT N qe Ex: Find the total charge on the object in each case Object # of Excess Protons/Electrons Quantity of Charge (Q) in Coulombs (C) A 1 x 106 excess electrons - 1.6 x 10-13 C B 2 x 108 excess protons + 3.2 x 10-11C C 2 x 1010 excess electrons - 3.2 x 10-9 C QT N qe (1106 ) (1.6 1019 )C 1.6 1013 C QT N qe (2 108 ) (1.6 1019 )C 3.2 1011 C Conductors and Insulators Good conductors have many “free” electrons EX: Metals Insulators have few “free” electrons Ex: Rubber, wood Insulators and Conductors Electrical Conductibility Insulators Semi-conductors No movement of charges within the object Limited number of free carriers Wood, plastics, glass Silicon, Germanium Conductors Free movement of charges Metals (Cu, Ag, Al) Grounding: The “Earth” is considered an infinite sink of charges Ground (Earthing) Grounding: The “Earth” is considered an infinite source or sink for excess charge. Grounding prevents charge from building up on the chassis of appliances. Mutual grounding provides a common reference point. Coulomb’s Law In 1785 Charles Coulomb established a law of electric force between two stationary charged particles. 1. 2. 3. 4. 5. Force inversely proportional to square of distance Force along the line joining the particles Force proportional to the product of the charges Force attractive between opposite sign charges. Force repulsive between charges of the same sign k = Coulomb constant = 8.99 x 109 Nm2/C2 Direction of the Coulomb Force 1. Force can be attractive or repulsive 2. Equal in magnitude 3. Opposite in direction Ex: If q1 =-3uC, q2 = +4uC, and d = 2 m, find the electric force between the charges. F21 + d q2 F12 q1q2 F k 2 r - q1 6 6 ( 3 10 C )(4 10 C) 9 2 2 (8.99 10 N m / C ) 2 (2m) .027N q1q2 F k 2 r Coulomb Force is proportional to 1/r2 Hyperbolic relationship between force and distance 1 F 2 d link Analogy to Gravitational Force Coulomb Force Gravitational Force q1q2 Fe k 2 d m1m2 Fg G 2 d The gravitational force can only be attractive. Example: Compare the gravitational force in the hydrogen atom to the Coulomb (electric) force. Which is stronger? Atomic Radius: 10-10 meters Nuclear Diameter: 10-15 meters Mass of electron: me = 9.11 x 10-31 kg Mass of proton: mp = 1.67 x 10-27 kg Compare the gravitational force in the hydrogen atom to the Coulomb (electric) force. Which is stronger? How much stronger? m1m2 r2 (6.67 x1011 N m 2 / kg 2 )(1.67 X 1027 kg )(9.11x1031 kg ) (1010 m) 2 FG G k q1q2 (9 x109 N m2 C 2 )(1.6 x1019 C ) 2 FE 2 r (1010 m) 2 4.6 x1018 N Difference and Similarities between Electricity and Gravity Coulomb Law and Law of Gravitation similarities Gravitation is always attractive Electrical force can be attractive or repulsive Electric force dominates the atomic world Gravitational forces dominates the macroscopic scale: people, planets, galaxies Electric forces are stronger !!! A metal sphere is charged by losing 5.18 x 1013 electrons while a second sphere is charged by losing 15.54 x 1013 electrons. The two spheres are 25 cm apart. Determine the force between the two spheres. 1. Two charged objects have a repulsive force of .080 N. If the charge of one is doubled, and the distance separating them is doubled what is the new force? 2. Two charged objects have a repulsive force of .080 N. If the charge of both of the objects is doubled and the distance separating the objects is doubled what is the new force? 3. Two charged objects have an attractive force of .080 N. If the charge of one of the objects is quadrupled, and the distance separating the objects is doubled what is the new force? 4. Two charged objects have an attractive force of .080 N. If the charge of one is tripled and the distance separating the objects is tripled what is the new force? Two uniformly charged spheres are firmly fastened to and electrically insulated from a table. The charge on sphere 2 is three times the charge on sphere 1. Which diagram correctly shows the magnitude and direction of the electrostatic forces: Alternate Form of Coulomb’s law Coulomb’s constant k is often written in terms of the permittivity of free space e0 q1q2 F k 2 r 0 1 4 k 8.85 10 C /N m -12 2 2 Coulomb’s Law can then be written as: q1q2 F 2 4 0 d 1 Superposition Principle When more than two charges are present, the resultant force on any one of them is equal to the vector sum of the forces exerted by each of the individual charges. FT F12 F13 F14 Three point charges located at corners of triangle as shown. Find The resultant force on q3 q1 = q3 = 5 C q2 = -2 C a = .1 m F31 F32 Solution: 450 Note the direction of forces Resolve F32 and F31 into their x and y components Add the x and y components of F32 and F31 to find x and y components of F3 Find the magnitude and direction of F3 450 Two 2 gram balloons are suspended by strings that are 60 cm long. The two balloons establish equilibrium with an angle between the two strings of 250. Determine the charge on each balloon. Assume the same amount of charge is on each. Methods of Charging 1. Friction - Transfer of electrons between neutral objects. 2. Induction - A neutral object becomes charges without ever contacting the charged object. 3. Conduction - A charged body comes in contact with another body and charge is transferred between them. 1. Friction - When two neutral objects are rubbed together. One gives up its negative charges to the other. One becomes positively charged while the other becomes equally negative. Hair gives up electrons to the balloon. Frictional charging is a result of transfer of electrons Some materials are greedy and steal electrons, they have a high electroconductivity, while others are willing to give them up. 2. Induction - When an object is charged by the influence of a charged object near, but not in contact with it. The word induction means to influence without contact. 1. Positively charged object brought near, does not touch the electroscope. 2. Ground’s attached and electrons are drawn up. 3. Ground is removed trapping electrons on the electroscope. 4. Electroscope ends up oppositely charged to the object brought near. Temporary polarization by induction Electrons pushed by negative object toward the bottom of the electroscope. The foil leaves at the bottom have a negative charge so they repel each other. Electrons attracted by the positive object toward the top of the electroscope. The foil leaves at the bottom have a positive charge so they repel each other. Electrostatic Induction occurs only in conductors. Ground - Is an infinite source or sink for electrons. Induction Induction Polarization and Induction Induction A negatively charged rubber rod is brought near an uncharged sphere The charges in the sphere are redistributed. After the sphere is grounded they leave the sphere The positive charge on the sphere is evenly distributed Charging by induction requires no contact with the object inducing the charge 3. Conduction – Charging by contact When charging something by contact: 1. A charged objects must touch and transfer some electrons. 2. The objects become charged alike. 3. The original charged object becomes less charged. Conduction A charged object (the rod) is placed in contact with another object (the sphere) Some electrons on the rod can move to the sphere When the rod is removed, the sphere is left with a charge The object being charged is always left with a charge having the same sign as the object doing the charging Grounding neutralizes a charged object Polarization and charging by contact Polarization-Induced Attractions Attraction is more common than repulsion Charged objects can attract uncharged ones A charged rod attracts a neutral metal ball It redistributes the charge separation of charge in the uncharged object. The attractive force is then greater. Water faucet comb demo Conduction or Induction? After rubbing the balloon, why does balloon stick to wall? How do you know that this force is stronger than gravity? Negatively charged paint adheres to positively charged metal. Van def Graff generator and charging by contact Charge Distributions The excess charge on a conductor resides on the outer surface concentrating on rough edges and corners. Automobiles are a safe haven from lightening. Lightening rods and point discharge Gravitational Fields •Surround anything with mass •Vector fields (have magnitude and direction) •Weaken as you move away from a single mass •Magnitude of field can be calculated by: FG w g m m Electric Fields •Surround charged objects •Vector fields (magnitude and direction) •Direction depends on the charge •Weaken as you move away from isolated one charge •Magnitude of field calculated by: F E= q0 Unit : N/C q0 is the test charge Q is the charged object in the area E is the electric field experienced by q0 due to Q Electric Field Strength The Electric Field Strength at a point in an Electric Field is the Force per unit positive test charge exerted on a charge at that point. E = F/q *Vector Quantity *[N/C] Field of an isolated point charge q1q2 F k 2 r F E= q0 Unit : N/C q1q2 F 2 4 0 d 1 F E= q0 Unit : N/C q1 Ek 2 d q1 1 E 4o d 2 q1q2 F k 2 r Coulomb Force is proportional to 1/r2 Hyperbolic relationship between force and distance 1 F 2 d Calculate the force exerted by E = 4 N/C to the right(→) on each of the following: q1 = +1 C q2 = +4 C q3 = - 4 C q4 = + 1.5 C q5 = - 1.5 C q6 = 6 μC q7 = p + q8 = e- q9 = 2e- 1. What is the strength of the electric field 2 cm fron a +3uC charge? 6 Q (3 10 C) 9 2 2 E k 2 (8.99 10 N m / C ) r (.02m)2 2. If you double the distance from the charge what will be the new electric field strength at that point? 6.74 10 N / C 7 Ans: ¼ the original strength 1 (6.74 107 N / C ) 1.68 107 N / C 4 The number of lines per unit area through the surface is proportional to the magnitude of the electric field The closer the lines the stronger the field, ‘E’. Drawing Electric Field Lines Lines begin on positive and end on negative charges. No two field lines can cross. Number of field lines leaving is proportional to the charge. Strength of the field is proportional to the density of lines. Electric field lines are proportional to magnitude of the charge Electric field is tangent at any point If charges are not equal in magnitude the greater charge will have more field lines Twice the charge, twice the field lines Double the charge means double the field lines Field the same strength at every point along the circle The diagram below is a representation of the electric field arising from? a. a single negative charge b. two unlike charges c. a single positive charge d. a pair of positive charges e. a pair of negative charges Must Know what the electric fields looks like around 1. 2. 3. 4. 5. 6. 7. A positive point charge A negative point charge A positive and negative point charge Two positive point charges Two negative point charges Around and inside a conducting sphere Between 2 parallel plates NOTE: Point Charges have no dimensions Positive Point Charge + + 1. 2. 3. 4. Field emanates from positive charge Perpendicular to the surface Field lines never cross Field weakens as 1/r2 Negative Point Charge 1. Field terminates on it 2. Field perpendicular to the surface 3. Field lines never cross 4. Field weakens as the distance increases Positive Point Charge 1. Inverse square law: 1/r2 2. Double the distance the field is a ¼ the original strength. 3. Less field lines per unit area. One Positive and one Negative Point Charge 1. Out of the positive and into the negative 2. Strongest between the charges 3. Field lines are perpendicular to the surface 4. Field lines never cross Two Positive Point Charges 1. Field zero between the charges 2. Field lines diverge 3. Field lines never cross 4. Field lines perpendicular to surface Two Negative Point Charges Same as positive charge diagram except field lines go into the charges 1. Field 0 between the charges 2. Field lines diverge 3. Field lines never cross 4. Field lines perpendicular to surface Negatively Charged Conducting Sphere _ _ _ _ _ E=0 _ _ _ It’s NOT dimensionless 1. Field ends on the charge 2. Field ZERO inside the sphere 3. All excess charge is on the surface 4. More charge equals more field lines Field lines perpendicular to surface Double the distance, field is ¼ original strength. E=0 Everywhere inside Inverse square law Positively Charged Conducting Sphere 1. Field begins on the charge 2. Field ZERO inside the sphere 3. All excess charge is on the surface 4. More charge equals more field lines Edge effects- Electric field lines bulge out slightly around the edges of Parallel Plates – Field weaker All fields are vectors: 1. Magnitude - The force on a charge placed in the field divided by the charge itself. F N E q C 2. Direction - The direction that the force would be on a positive test charge placed at that point. The field lines for a large positively charged plate. The field lines flow away from the plate on both sides. (Note: this is a small section near the center of a large plate. This is why the field lines are not coming from the outside rim of the plate.) A uniform electric field is created between two parallel metal plates if the plates are connected to a battery. The way the terminals are connected determines the direction of the field Field around and between charged parallel plates 1. Field comes out of the positive plate goes into the negative plate 2. Field is UNIFORM, same strength everywhere 3. Field above and below the plates is zero. Positive plate Parallel Plate Capacitor + + + + + + + + + + + + + + + + + + E =const. Uniform field - - - - - - - - - - - - - - - - - - - - - - - - - Everywhere outside the plates the field is zero Negative Plate A charged particle introduced perpendicular to the electric field will follow a parabolic path Like a projectile in a gravitational field