Fundamental Physics II

PETROVIETNAM UNIVERSITY FUNDAMENTAL SCIENCES DEPARTMENT Fundamental Physics II • Pham Hong Quang • E-mail: quangph@pvu.edu.vn Vungtau, December 2012

Giớithiệumônhọc 1. Tênmônhọc:Vật lý 2 (Physics 2) 2. Sốtínchỉ: 03 (2 Lýthuyết + 1 Thínghiệm) 4. Phânbổthờigian: -Lênlớp: 30 tiết (6 tiết/tuần) + Lýthuyết: 24 tiết + Bàitập: 6 tiết -Thínghiệm: 30 tiết (2 tiết/tuần) - Kiểmtragiữakỳ: 2 tiết - Thikếtthúchọckỳ: 90 phút - Tự học: 60 giờ Pham Hong Quang

Tàiliệu Tàiliệuchính: [1] CơsởVậtlý, Tập IV, V, VI: ĐiệnvàTừhọc, Quanghọc, David Halliday, Robert Resnik, Jearl Walker, bảndịchtiếngViệt, NXBGiáodục (1999). Sáchthamkhảo: [2] Fundamentals of physics, 8th ed., Extended, David Halliday, Robert Resnick and Jearl Walker, John Wiley & Sons (2008). Pham Hong QuangFaculty of Fundamental Sciences

Đánhgiá điểm • Lý thuyết (hệ số 2) • Tham dự lớp đầy đủ: 5 % • Bài tập: 25 % • Điểm kiểm tra giữa kỳ: 20 % • Điểm thi kết thúc môn học: 50 % • Thí nghiệm (hệ số 1) • Thực hiện tất cả các bài thí nghiệm (bao gồm tóm tắt lý thuyết trước và xử lý số liệu sau thí nghiệm): 50% • Thi vấn đáp: 50% Pham Hong QuangFaculty of Fundamental Sciences

CHAPTER I Electric Charges, and Electric Fields • Pham Hong Quang5PetroVietnam University

Chapter 1 Electric Charges, and Electric Fields Electric Charge Insulators and Conductors Coulomb’s Law The Electric Field Electric Field Lines Shielding and Charging by Induction Electric Flux and Gauss’s Law Potentials Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge The effects of electric charge were first observed as static electricity: After being rubbed on a piece of fur, an amber rod acquires a charge and can attract small objects. Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge Charging both amber and glass rods shows that there are two types of electric charge; like charges repel and opposites attract. Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge All electrons have exactly the same charge; the charge on the proton (in the atomic nucleus) has the same magnitude but the opposite sign: Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge The electrons in an atom are in a cloud surrounding the nucleus, and can be separated from the atom with relative ease. Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge When an amber rod is rubbed with fur, some of the electrons on the atoms in the fur are transferred to the amber: Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge We find that the total electric charge of the universe is a constant: Electric charge is conserved. Also, electric charge is quantized in units of e. The atom that has lost an electron is now positively charged – it is a positive ion The atom that has gained an electron is now negatively charged – it is a negative ion Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge Insulators and Conductors Conductor: A material whose conduction electrons are free to move throughout. Most metals are conductors. Insulator: A material whose electrons seldom move from atom to atom. Most insulators are non-metals. Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge Insulators and Conductors If a conductor carries excess charge, the excess is distributed over the surface of the conductor. Pham Hong Quang Faculty of Fundamental Sciences

1.1 Electric Charge Insulators and Conductors Semiconductors have properties intermediate between conductors and insulators; their properties change with their chemical composition. Photoconductive materials become conductors when light shines on them. Pham Hong Quang Faculty of Fundamental Sciences

1.2 Coulomb’s Law Coulomb’s law gives the force between two point charges: The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if the charges are like. Pham Hong Quang Faculty of Fundamental Sciences

1.2 Coulomb’s Law The forces on the two charges are action-reaction forces. Pham Hong Quang Faculty of Fundamental Sciences

1.2 Coulomb’s Law If there are multiple point charges, the forces add by superposition. Pham Hong Quang Faculty of Fundamental Sciences

1.2 Coulomb’s Law Coulomb’s law is stated in terms of point charges, but it is also valid for spherically symmetric charge distributions, as long as the distance is measured from the center of the sphere. Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field Definition of the electric field: Here, q0 is a “test charge” – it serves to allow the electric force to be measured, but is not large enough to create a significant force on any other charges. Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field If we know the electric field, we can calculate the force on any charge: The direction of the force depends on the sign of the charge – in the direction of the field for a positive charge, opposite to it for a negative one. Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field The electric field of a point charge points radially away from a positive charge and towards a negative one. The electric field due to the point charge q at r isE = kq/r2 Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field Just as electric forces can be superposed, electric fields can as well. Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field Electric Field Lines • Electric field lines are a convenient way of visualizing the electric field. • Electric field lines: • Point in the direction of the field vector at every point • Start at positive charges or infinity • End at negative charges or infinity • Are more dense where the field is stronger Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field The charge on the right is twice the magnitude of the charge on the left (and opposite in sign), so there are twice as many field lines, and they point towards the charge rather than away from it. Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field Combinations of charges. Note that, while the lines are less dense where the field is weaker, the field is not zero where there are no lines. In fact, there is only one point within the figures below where the field is zero – can you find it? Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field A parallel-plate capacitor consists of two conducting plates with equal and opposite charges. Here is the electric field: Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field Shielding and Charge by Induction Since excess charge on a conductor is free to move, the charges will move so that they are as far apart as possible. This means that excess charge on a conductor resides on its surface, as in the upper diagram. Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field When electric charges are at rest, the electric field within a conductor is zero. Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field The electric field is always perpendicular to the surface of a conductor – if it weren’t, the charges would move along the surface. Pham Hong Quang Faculty of Fundamental Sciences

1.3 The Electric Field The electric field is stronger where the surface is more sharply curved. Pham Hong Quang Faculty of Fundamental Sciences

1.4 Electric field due to a continuous distribution • Instead of summing the charge we can imagine a continuous distribution and integrate it. This distribution may be over a volume, a surface or just a line. • E = ∫dE = ∫ kdqi/r2 Pham Hong Quang Faculty of Fundamental Sciences

1.4 Electric field due to a continuous distribution Electric field due to a line of uniform + charge of length L with linear charge density equal to λ Pham Hong Quang Faculty of Fundamental Sciences

1.4 Electric field due to a continuous distribution What is the electric field from an infinitely long wire with linear charge density of +100 nC/m at a point 10 cm away from it. What do the lines of flux look like? Pham Hong Quang Faculty of Fundamental Sciences

1.4 Electric field due to a continuous distribution The electric field on the axis of a uniformly charged ring with linear charge density l = Q/2pR. =0 at z=0 =0 at z=infinity =max at z=0.7R Pham Hong Quang Faculty of Fundamental Sciences

1.5 Electric Flux and Gauss’s Law Electric flux is a measure of the electric field perpendicular to a surface: Pham Hong Quang Faculty of Fundamental Sciences

1.5 Electric Flux and Gauss’s Law Gauss’s law states that the electric flux through a closed surface is proportional to the charge enclosed by the surface: Pham Hong Quang Faculty of Fundamental Sciences

1.5 Electric Flux and Gauss’s Law Gauss’s law can be used to find the electric field in systems with simple configurations. Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Gravitational force: F=Gm1m2/r2 • Electrostatic force: F=Gq1q2/r2 • One thing is in common: both of these forces are conservative What does it mean for a force or field to be conservative? The work done by the force is independent of path! Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Gravitational force Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Electrostaticforce We can assign the Reference Point of Electric Potential Energy where W is the work done by the electric force field. If we take U∞ = 0 then, U = - W∞ The potential energy of a charge at a point is equal to the negative of the work done by the field in bringing the charge from infinity to that point. Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Electric Potential is the potential energy per unit charge. V = U/q DV = DU/q = -W/q V = - W∞/q Note that the work you apply to a charge is the negative of the work that the field applies on the charge (when there is no change in kinetic energy). DV = Wapplied/q or Wapplied = q DV The units of J/C is defined to be the volt (V). Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Notes Electric field always points from higher electric potential to lower electric potential. A positive charge accelerates from a region of higher electric potential energy (or higher potential) toward a region of lower electric potential energy (or lower potential). A negative charge accelerates from a region of lower potential toward a region of higher potential. Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Equipotential Surfaces An equipotentialsurface is a surface on which the electric potential is the same everywhere. Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Equipotential Surfaces, Cont. • The net electric force does no work as a charge moves on an equipotential surface. • The electric field created by any charge or group of charges is everywhere perpendicular to the associated equipotential surfaces and points in the direction of decreasing potential. What will happen if the electric field E is not perpendicular to the equipotential surface? Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Calculating the Potential from the Field Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Calculating the Field from the Potential The potential gradient gives the component of the electric field along the displacement Δs Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Potential due to a Point Charge: With the understanding that V∞ = 0 Potential due to a Group of Point Charges: • Notice that: • V is a scalar (much easier to handle than a vector!) • V can be positive or negative! Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Potential Due to a Continuous Charge Distribution Pham Hong Quang Faculty of Fundamental Sciences

1.6 Electric Potential Line of Charge A thin nonconducting rod of length L has a positive charge of uniform linear density λ . Let us determine the electric potential V due to the rod at point P, a perpendicular distance d from the left end of the rod. Pham Hong Quang Faculty of Fundamental Sciences

Fundamental Physics II