Presentation on theme: "Charge and Polarization"— Presentation transcript:
1Charge and Polarization Monday, January 14, 2008Charge and Polarization
2Demonstration #1Demonstrate how you can pick up the tissue without touching it in any way with your body.What is occurring on the atomic level that lets you do this?
3The atomThe atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction.The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without all that much difficulty.
4QuestionYou charge the balloon by rubbing it on hair or on a sweater, and the balloon becomes negative. How can it pick up a neutral tissue?
5This is an electroscope PoleThe electroscope is made from a metal or other conductor, and may be contained within a flask.The vanes are free to move.Vanes
6Demonstration #2Rub the black rod with the fur. Bring the rod toward the pole of the electroscope. What happens to the vanes?Come up with an atomic-level explanation for your observations.
7Demonstration #3Rub the glass rod with the silk. Bring the rod toward the pole of the electroscope. What happens to the vanes?Come up with an atomic-level explanation for your observations.
8Demonstration #4What happens when your touch the electroscope with the glass rod?
9ChargeCharge comes in two forms, which Ben Franklin designated as positive (+) and negative(–).Charge is quantized.The smallest possible stable charge, which we designate as e, is the magnitude of the charge on 1 electron or 1 proton.We say a proton has charge of e, and an electron has a charge of –e.e is referred to as the “elementary” charge.e = Coulombs.The coulomb is the SI unit of charge.
10Sample ProblemA certain static discharge delivers -0.5 Coulombs of electrical charge. How many electrons are in this discharge?
11Sample ProblemHow much positive charge resides in two moles of hydrogen gas (H2)?How much negative charge?How much net charge?
12Sample ProblemThe total charge of a system composed of 1800 particles, all of which are protons or electrons, is 31x10-18 C.How many protons are in the system?How many electrons are in the system?
13Coulomb’s Law and Electrical Force Tuesday, January 15, 2008Coulomb’s Law and Electrical Force
14Electric Force Charges exert forces on each other. Like charges (two positives, or two negatives) repel each other, resulting in a repulsive force.Opposite charges (a positive and a negative) attract each other, resulting in an attractive force.
15Coulomb’s Law – form 1Coulomb’s law tells us how the magnitude of the force between two particles varies with their charge and with the distance between them.k = 8.99 109 N m2 / C2q1, q2 are charges (C)r is distance between the charges (m)F is force (N)Coulomb’s law applies directly only to spherically symmetric charges.
16Coulomb’s Law – form 2Sometimes you see Coulomb’s Law written in a slightly different formeo = 8.85 C2/ N m2q1, q2 are charges (C)r is distance between the charges (m)F is force (N)This version is theoretically derived and less practical that form 1
17Spherically Symmetric Forces Newton’s Law of GravityCoulomb’s Law
18Sample ProblemA point charge of positive 12.0 μC experiences an attractive force of 51 mN when it is placed 15 cm from another point charge. What is the other charge?
19Sample Problem qA = 1.50 nC A B qB = -0.50 nC 1.3 m Calculate the mass of ball B, which is suspended in midair.AqA = 1.50 nC1.3 mBqB = nC
20Superposition Electrical force, like all forces, is a vector quantity. If a charge is subjected to forces from more than one other charge, vector addition must be performed.Vector addition to find the resultant vector is sometimes called superposition.
21y (m) 2.0 1.0 -3 mC 2 mC 4 mC 1.0 2.0 x (m) Sample Problem What is the force on the 4 mC charge?y (m)2.01.0-3 mC2 mC4 mC1.02.0x (m)
22y (m) 2.0 -3 mC 1.0 2 mC 4 mC 1.0 2.0 x (m) Sample Problem What is the force on the 4 mC charge?y (m)2.0-3 mC1.02 mC4 mC1.02.0x (m)
24The Electric FieldThe presence of + or – charge modifies empty space. This enables the electrical force to act on charged particles without actually touching them.We say that an “electric field” is created in the space around a charged particle or a configuration of charges.If a charged particle is placed in an electric field created by other charges, it will experience a force as a result of the field.Sometimes we know about the electric field without knowing much about the charge configuration that created it.We can easily calculate the electric force from the electric field.
25Why use fields?Forces exist only when two or more particles are present.Fields exist even if no force is present.The field of one particle only can be calculated.
26Field around + chargeThe arrows in a field are not vectors, they are “lines of force”.The lines of force indicate the direction of the force on a positive charge placed in the field.Negative charges experience a force in the opposite direction.
29Field Vectors from Field Lines The electric field at a given point is not the field line itself, but can be determined from the field line.The electric field vectors is always tangent to the line of force at that point.Vectors of any kind are never curvy!
35Sample ProblemA proton traveling at 440 m/s in the +x direction enters an an electric field of magnitude 5400 N/C directed in the +y direction. Find the acceleration.
36For Spherical Electric Fields The Electric Field surrounding a point charge or a spherical charge can be calculated by:E = k q / r2E: Electric Field (N/C)k: 8.99 x 109 N m2/C2q: Charge (C)r: distance from center of charge q (m)Remember that k = 1/4peo
37Principle of Superposition When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges.Again, as with force vectors, this is referred to as superposition.
38Remember…Electric field lines are NOT VECTORS, but may be used to derive the direction of electric field vectors at given points.The resulting vector gives the direction of the electric force on a positive charge placed in the field.
39Sample ProblemA particle bearing -5.0 μC is placed at -2.0 cm, and a particle bearing 5.0 μC is placed at 2.0 cm. What is the field at the origin?
40Sample ProblemA particle bearing 10.0 mC is placed at the origin, and a particle bearing 5.0 mC is placed at 1.0 m. Where is the field zero?
41Sample Problem What is the charge on the bead? It’s mass is 32 mg. E = 5000 N/C40o
42Electric Potential and Potential Energy Friday, January 18, 2008Electric Potential and Potential Energy
43Electric Potential Energy Electrical potential energy is the energy contained in a configuration of charges. Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable.The unit is the Joule.
44Electric Potential Energy Electrical potential energy increases when charges are brought into less favorable configurationsΔU > 0++-+
45Electric Potential Energy Electrical potential energy decreases when charges are brought into more favorable configurations.ΔU < 0+-++
46Electric Potential Energy +–ΔU = ____ΔU = ____+++-Work must be done on the charge to increase the electric potential energy.
47Work and ChargeFor a positive test charge to be moved upward a distance d, the electric force does negative work.The electric potential energy has increased and ΔU is positive (U2 > U1)+d+EF
48Work and ChargeIf a negative charge is moved upward a distance d, the electric force does positive work.The change in the electric potential energy ΔU is negative (U2 < U1)-dF-E
49Electric PotentialElectric potential is hard to understand, but easy to measure.We commonly call it “voltage”, and its unit is the Volt.1 V = 1 J/CElectric potential is easily related to both the electric potential energy, and to the electric field.
50Electrical Potential and Potential Energy The change in potential energy is directly related to the change in voltage.U = qVU: change in electrical potential energy (J)q: charge moved (C)V: potential difference (V)All charges will spontaneously go to lower potential energies if they are allowed to move.
51Electrical Potential and Potential Energy Since all charges try to decrease UE, and DUE = qDV, this means that spontaneous movement of charges result in negative DU.ΔV = ΔU / qPositive charges like to DECREASE their potential (DV < 0)Negative charges like to INCREASE their potential. (DV > 0)
52Sample ProblemA 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change?
53Electrical Potential in Uniform Electric Fields The electric potential is related in a simple way to a uniform electric field.V = -EdV: change in electrical potential (V)E: Constant electric field strength (N/C or V/m)d: distance moved (m)dEDV
54Sample ProblemAn electric field is parallel to the x-axis. What is its magnitude and direction of the electric field if the potential difference between x =1.0 m and x = 2.5 m is found to be +900 V?
55Sample Problem y(m) C 1.0 A B 1.0 2.0 x(m) What is the voltmeter reading between A and B? Between A and C? Assume that the electric field has a magnitude of 400 N/C.y(m)C1.0AB1.02.0x(m)
56Sample Problem y(m) C 1.0 A B 1.0 2.0 x(m) How much work would be done BY THE ELECTRIC FIELD in moving a 2 mC charge from A to C? From A to B? from B to C?. How much work would be done by an external force in each case?y(m)C1.0AB1.02.0x(m)
57Electric Field Lines and Shielding Tuesday, January 22, 2008Electric Field Lines and Shielding
60Review: Electric Fields and Equipotential Lines Java Simulation
61Excess Charges on Conductors Excess charges reside on the surface of a charged conductor.If excess charges were found inside a conductor, they would repel one another until the charges were as far from each other as possible… the surface!+
62Electric Field and Lightning Rods Electric field lines are more dense near a sharp point, indicating the electric field is more intense in such regions.All lightning rods take advantage of this by having a sharply pointed tip.During an electrical storm, the electric field at the tip becomes so intense that charge is given off into the atmosphere, discharging the area near a house at a steady rate and preventing a sudden blast of lightning.
63Electric Field inside a Conductor The electric field inside a conductor must be zero.++++++E = 0++++++
64Conductor in an electric field If a conductor is placed in an electric field, then the charges polarize to nullify the external field.-+-+-+-E = 0++-+-+--+
65Energy Conservation in Electric Fields Wednesday, January 23, 2008Energy Conservation in Electric Fields
66Conservation of Energy Review In a conservative system, energy changes from one form of mechanical energy to another.When only the conservative electrostatic force is involved, a charged particle released from rest in an electric field will move so as to lose potential energy and gain an equivalent amount of kinetic energy.The change in electrical potential energy can be calculated byDUE = qDV.
67Sample ProblemIf a proton is accelerated through a potential difference of -2,000 V, what is its change in potential energy?How fast will this proton be moving if it started at rest?
68Sample ProblemA proton at rest is released in a uniform electric field. How fast is it moving after it travels through a potential difference of V? How far has it moved?
69Electric Potential Energy for Spherical Charges Electric potential energy is a scalar, like all forms of energy.U = kq1q2/rU: electrical potential energy (J)k: 8.99 109 N m2 / C2q1, q2 : charges (C)r: distance between centers (m)This formula only works for spherical charges or point charges.
71Sample Problem y (m) 2.0 1.0 2 mC 4 mC x (m) 1.0 2.0 What is the potential energy of the configuration shown below?y (m)2.01.02 mC4 mCx (m)1.02.0
72Sample Problem y (m) 2.0 -3 mC 1.0 2 mC 4 mC x (m) 1.0 2.0 How much work was done in assembling the charge configuration shown below?y (m)2.0-3 mC1.02 mC4 mCx (m)1.02.0
73Potential and Potential Energy of Configurations of Point Charges Wednesday, January 23, 2008Potential and Potential Energy of Configurations of Point Charges
74Absolute Electric Potential (spherical) For a spherical or point charge, the electric potential can be calculated by the following formulaV = kq/rV: potential (V)k: 8.99 x 109 N m2/C2q: charge (C)r: distance from the charge (m)Remember, k = 1/(4peo)
75Sample Problem y (m) 2.0 -3 mC 1.0 2 mC 4 mC x (m) 1.0 2.0 What is the electric potential at (2,2)?y (m)2.0-3 mC1.02 mC4 mCx (m)1.02.0
77Equipotential surfaces High potentialLow potential
78QuestionWhat can you say about the intersection between field lines and equipotential surfaces?
79+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Sample ProblemDraw field lines for the charge configuration below. The field is 600 V/m, and the plates are 2 m apart. Label each plate with its proper potential, and draw and label 3 equipotential surfaces between the plates. You may ignore edge effects.
80Sample ProblemDraw a negative point charge of -Q and its associated electric field. Draw 4 equipotential surfaces such that DV is the same between the surfaces, and draw them at the correct relative locations. What do you observe about the spacing between the equipotential surfaces?
81Fill in the following table for spherical charges ForcePotential EnergyFieldPotential
82What is magnitude and direction of electric field What is magnitude and direction of electric field? b) What is shortest distance one can go to undergo a change of 5.00 V?