* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download four slides per page
Survey
Document related concepts
Introduction to gauge theory wikipedia , lookup
Magnetic monopole wikipedia , lookup
Work (physics) wikipedia , lookup
Weightlessness wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Anti-gravity wikipedia , lookup
Speed of gravity wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Fundamental interaction wikipedia , lookup
Maxwell's equations wikipedia , lookup
Electromagnetism wikipedia , lookup
Field (physics) wikipedia , lookup
Lorentz force wikipedia , lookup
Transcript
Administrative Details Physics / Higher Physics 1B Electricity and Magnetism Michael Ashley, [email protected] Room 137, OMB My course website (linked from “lecturer’s notes” in Moodle): http://mcba11.phys.unsw.edu.au/~mcba/PHYS1231 Please ensure you have a “course pack” Please bring your lab book next week Moodle site for course information: http://moodle.telt.unsw.edu.au Lecture Notes Assessment Laboratory 20% Six quizzes 20% (due Sunday 11pm odd weeks; beginning week 3) End of Session exam 60% You must pass each component and complete all the labs Administration, syllabus, on-line study, academic honesty Syllabus (Physics for Scientists and Engineers with Modern Physics, Serway & Jewitt, 8th ed) ppt slides + movies Tutorial solutions Multiple choice quizzes Ancillary information Electrostatics (§23.1, 23.3-23.6) Gauss’s Law (§24.1-24.4) Electric Potential (§25.1-25.6, 25.8) Capacitance & Dielectrics (§26.1-26.5) Magnetic Fields & Magnetism (§29.1-29.4) Ampere’s & Biot-Savart Law (§30.1-30.5) Faraday’s Law, Induction, Inductance (§31.131.6, 32.1, 32.3) 1 Before we get started… just for fun… Chapter 23 What would happen if you could throw a ball at 0.9c? Electrostatics Electricity and Magnetism, Some Ancient History Many applications Chinese Macroscopic and microscopic Documents suggest that magnetism was observed as early as 2000 BC Greeks Electrical and magnetic phenomena as early as 700 BC Experiments with amber and magnetite 2 Electricity and Magnetism, Some History, 2 1785 There are two kinds of electric charges Michael Faraday and Joseph Henry showed that when a wire is moved near a magnet, an electric current is produced in the wire 1873 James Clerk Maxwell used observations and other experimental facts as a basis for formulating the laws of electromagnetism Unified electricity and magnetism Charges in matter: the atom EFA02AN1 Called positive and negative 1831 Hans Oersted found a compass needle deflected when near a wire carrying an electric current Electric Charges, 1 Charles Coulomb confirmed inverse square law form for electric forces 1819 Electricity and Magnetism, Some History, 3 Negative charges are the type possessed by electrons Positive charges are the type possessed by protons Charges of the same sign repel one another and charges with opposite signs attract one another 3 Demo EA3: Electrostatic forces Attraction of a stream of water by a charged rod Demo EA1: Electrostatic Charging by Friction – can move large objects Glass rubbed with silk will gain a positive charge and plastic rubbed with fur a negative charge. A metal rod will also acquire a charge if rubbed with rubber and held by an insulated handle. Electric Charges, 2 The rubber rod is negatively charged The glass rod is positively charged The two rods will attract Electric Charges, 3 The rubber rod is negatively charged The second rubber rod is also negatively charged The two rods will repel 4 More About Electric Charges Electric charge is always conserved in an isolated system For example, charge is not created in the process of rubbing two objects together The electrification is due to a transfer of charge from one object to another Conservation of Electric Charges Quantization of Electric Charges The electric charge, q, is said to be quantized q is the standard symbol used for charge Electric charge exists as discrete packets q = Ne N is an integer e is the fundamental unit of charge |e| = 1.6 x 10-19 C Electron: q = -e Proton: q = +e A glass rod is rubbed with silk Electrons are transferred from the glass to the silk Each electron adds a negative charge to the silk An equal positive charge is left on the rod Conductors Electrical conductors are materials in which some of the electrons are free electrons Free electrons are not bound to the atoms These electrons can move relatively freely through the material Examples of good conductors include copper, aluminum and silver When a good conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material 5 Insulators Electrical insulators are materials in which all of the electrons are bound to atoms These electrons cannot move freely through the material Examples of good insulators include glass, rubber and wood When a good insulator is charged in a small region, the charge is unable to move to other regions of the material Quick Quiz 23.2 Three objects are brought close to each other, two at a time. When objects A and B are brought together, they repel. When objects B and C are brought together, they also repel. Which of the following are true? (a) Objects A and C possess charges of the same sign. Semiconductors The electrical properties of semiconductors are somewhere between those of insulators and conductors Examples of semiconductor materials include silicon and germanium Quick Quiz 23.2 Answer: (a), (c), and (e). The experiment shows that A and B have charges of the same sign, as do objects B and C. Thus, all three objects have charges of the same sign. We cannot determine from this information, however, whether the charges are positive or negative. (b) Objects A and C possess charges of opposite sign. (c) All three of the objects possess charges of the same sign. (d) One of the objects is neutral. (e) We would need to perform additional experiments to determine the signs of the charges. 6 Conductors - charge distribution EFM03VD2 Coulomb’s Law Coulomb’s Law, Equation Mathematically, qq Fe k e 1 2 2 r The SI unit of charge is the Coulomb (C) ke is called the Coulomb constant 9 . 2 2 ke = 8.9875 x 10 N m /C = 1/(4πo) o is the permittivity of free space -12 C2 / N.m2 o = 8.8542 x 10 Charles Coulomb measured the magnitudes of electric forces between two small charged spheres He found the force depended on the charges and the distance between them Coulomb’s Law EFM04AN1 7 Coulomb’s Law Fe k e q1 q 2 r 2 Coulomb's Law, Notes The force is attractive if the charges are of opposite sign The force is repulsive if the charges are of like sign The electrical behavior of electrons and protons is well described by modelling them as point charges The electrical force is a “conservative” force Remember the charges need to be in Coulombs e is the smallest unit of charge e = 1.6 x 10-19 C So 1 C needs 1/e = 6.24 x 1018 electrons or protons! i.e. the same work is done whatever path is taken to move between two positions [except quarks….] Typical charges can be in the µC range Remember that force is a vector quantity Vector Nature of Electric Forces Demo Ea2: Electrostatic forces In vector form, F12 k e q1 q 2 r 2 rˆ rˆ is a unit vector directed from q1 to q2 Like charges produce a repulsive force between them 8 Vector Nature of Electrical Forces, 2 Electrical forces obey Newton’s Third Law The force on q1 is equal in magnitude and opposite in direction to the force on q2 F21 = -F12 With like signs for the charges, the product q1q2 is positive and the force is repulsive Vector Nature of Electrical Forces, 3 Two point charges are separated by a distance r With unlike signs for the charges, the product q1q2 is negative and the force is attractive Quick Quiz 23.4 Quick Quiz 23.4 Object A has a charge of +2 μC, and object B has a charge of +6 μC. Which statement is true about the electric forces on the objects? Answer: (e). From Newton's third law, the electric force exerted by object B on object A is equal in magnitude to the force exerted by object A on object B. (a) FAB = –3FBA (b) FAB = –FBA (c) 3FAB = –FBA (d) FAB = 3FBA (e) FAB = FBA (f) 3FAB = FBA 9 Quick Quiz 23.5 Quick Quiz 23.5 Object A has a charge of +2 μC, and object B has a charge of +6 μC. Which statement is true about the electric forces on the objects? Answer: (b). From Newton's third law, the electric force exerted by object B on object A is equal in magnitude to the force exerted by object A on object B and in the opposite direction. (a) FAB = –3FBA (b) FAB = –FBA (c) 3FAB = –FBA (d) FAB = 3FBA (e) FAB = FBA (f) 3FAB = FBA Hydrogen Atom Example The electrical force between the electron and proton is found from Coulomb’s law EFA04AN1 Fe = keq1q2 / r2 = 8.2 x 10-8 N (exercise….) This can be compared to the gravitational force between the electron and the proton The electric force is vastly stronger than the gravitational force! Strength Electrostatic Forces c.f. Gravity QuickTime™ and a Graphics decompressor are needed to see this picture. Fg = Gmemp / r2 = 3.6 x 10-47 N (exercise…) 10 Superposition Principle, Example The Superposition Principle The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges that are present The resultant force on q1 is the vector sum of all the forces exerted on it by other charges: F1 = F21 + F31 + F41 + … The force exerted by q1 on q3 is F13 The force exerted by q2 on q3 is F23 The resultant force exerted on q3 is the vector sum of F13 and F23 Electrical Force with Gravitational Force; example Example Calculate the force for charges +q, +Q and -Q, distributed at the vertices of an equilateral triangle. The spheres are in equilibrium Since they are separated, they exert a repulsive force on each other Like charges Equate the forces, since they are in equilibrium note that one force is an electrical force and the other is gravitational 11 Electrical Force with Gravitational Forces; example The free body diagram includes the components of the tension, the electrical force, and the weight Solve for |q| You cannot determine the sign of q, only that they both have same sign Electric Field – Definition An electric field is said to exist in the region of space around a charged object Demo EA5: Electrostatic field and lines of force the number of lines per unit area. Electric Field – Definition, cont This charged object is the source charge When another charged object, the test charge, enters this electric field, an electric force acts on it Paper strips attached to a van der Graaf generator show the electrostatic field lines; i.e. the direction of the electric field. Think about the inverse square law: The electric field is defined as the electric force on the test charge per unit charge The electric field vector, E, at a point in space is defined as the electric force F acting on a positive test charge, qo placed at that point divided by the test charge: E = Fe / qo. i.e. Fe = q0 E Strictly, only valid for a point charge 12 Electric Field Notes, Final The direction of E is that of the force on a positive test charge The SI units of E are N/C We can also say that an electric field exists at a point in space if a test charge at that point experiences an electric force E ke i ri 2 rˆi qq o r rˆ 2 Then, the electric field will be E At any point P, the total electric field due to a group of source charges equals the vector sum of electric fields of all the charges qi Remember Coulomb’s law, between the source and test charges, can be expressed as Fe k e Superposition with Electric Fields Electric Field, Vector Form Fe qo ke q r 2 rˆ Superposition Example Find the electric field at point P due to q1, E1 Find the electric field at point P due to q2, E2 E = E1 + E2 Remember, the fields add as vectors The direction of the individual fields is the direction of the force on a positive test charge 13 Electric Field – Continuous Charge Distribution Electric Field – Continuous Charge Distribution, equations Divide the charge distribution into small elements, each of which contains Δq Calculate the electric field due to one of these elements at point P Evaluate the total field by summing the contributions of all the charge elements Charge Densities Example – Charged Disk Volume charge density: when a charge is distributed evenly throughout a volume Surface charge density: when a charge is distributed evenly over a surface area Linear charge density: when a charge is distributed along a line E ke =Q/ℓ q r qi 0 2 rˆ Because the charge distribution is continuous E k e lim ρ=Q/V σ=Q/A For the individual charge elements i qi ri 2 rˆi k e dq r 2 rˆ The ring has a radius R and a uniform charge density σ Choose dq as a ring of radius r The ring has a surface area 2πr dr Calculate E-field at P a distance x away on axis Example 23.9 14 Electric Field Lines Field lines give us a means of representing the electric field pictorially The electric field vector E is tangent to the electric field line at each point The line has a direction that is the same as that of the electric field vector The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region Electric Field: van der Graaf generator Electric Field Lines, General EFM05VD1 The density of lines through surface A is greater than through surface B The magnitude of the electric field is greater on surface A than B The lines at different locations point in different directions This indicates the field is non-uniform Demo EA14: van der Graaf generator Electric field, and lines of force, shown in a hair-raising experiment! With clean hair, the subject’s hair will stand on end as it becomes charged. 15 Electric Field Lines, Positive Point Charge The field lines radiate outward in all directions In three dimensions, the distribution is spherical Electric Field Lines, Negative Point Charge The lines are directed away from the source charge A positive test charge would be repelled away from the positive source charge The charges are equal and opposite The number of field lines leaving the positive charge equals the number of lines terminating on the negative charge A positive test charge would be attracted toward the negative source charge Electric Field Lines – Like Charges Electric Field Lines – Dipole The field lines radiate inward in all directions The lines are directed toward the source charge The charges are equal and positive The same number of lines leave each charge since they are equal in magnitude At a great distance, the field is approximately equal to that of a single charge of 2q 16 Quick Quiz 23.7 Rank the magnitude of the electric field at points A, B, and C shown in this figure (greatest magnitude first). (a) A, B, C Quick Quiz 23.7 Answer: (a). The field is greatest at point A because this is where the field lines are closest together. The absence of lines near point C indicates that the electric field there is zero. (b) A, C, B (c) B, C, A (d) B, A, C (e) C, A, B (f) C, B, A Quick Quiz 23.8 Which of the following statements about electric field lines associated with electric charges is false? Quick Quiz 23.8 Answer: (b). Electric field lines begin and end on charges and cannot close on themselves to form loops. (a) Electric field lines can be either straight or curved. (b) Electric field lines can form closed loops. (c) Electric field lines begin on positive charges and end on negative charges. (d) Electric field lines can never intersect with one another. 17 Motion of Charged Particles When a charged particle is placed in an electric field, it experiences an electrical force If this is the only force on the particle, it must be the net force The net force will cause the particle to accelerate according to Newton’s second law Motion of Particles, cont Fe = qE = ma If E is uniform, then a is constant If the particle has a positive charge, its acceleration is in the direction of the field Electron in a Uniform Field, Example The electron is projected horizontally into a uniform electric field The electron undergoes a downward acceleration End of Chapter It is negative, so the acceleration is opposite E F=ma=qE so that a=qE/m Its motion is parabolic while between the plates c.f. projectile motion under gravity 18 Quick Quiz 23.1 If you rub an inflated balloon against your hair, the two materials attract each other, as shown in this figure. Fill in the blank: the amount of charge present in the system of the balloon and your hair after rubbing is _____ the amount of charge present before rubbing. Quick Quiz 23.1 Answer: (b). The amount of charge present in the isolated system after rubbing is the same as that before because charge is conserved; it is just distributed differently. (a) less than (b) the same as (c) more than Quick Quiz 23.6 Quick Quiz 23.6 A test charge of +3 μC is at a point P where an external electric field is directed to the right and has a magnitude of 4 × 106 N/C. If the test charge is replaced with another test charge of –3 μC, the external electric field at P Answer: (a). There is no effect on the electric field if we assume that the source charge producing the field is not disturbed by our actions. Remember that the electric field is created by source charge(s) (unseen in this case), not the test charge(s). (a) is unaffected (b) reverses direction (c) changes in a way that cannot be determined 19