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PHY127 Summer Session II Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY127-08 5 homework problems for each chapter are in general due a week later at 11:59 pm and are delivered through MasteringPhysics website at: http://www.masteringphysics.com. You need to open an account. In addition to homework problems, there is naturally a reading requirement of each chapter, which is very important. The website above is the point of contact outside the class for important messages, so regularly and frequently check the website. At the end of class a quiz is given for the previous chapter covered in the class. Bring a calculator (no wireless connection), a pencil, an eraser, and a copy of lecture note for the chapter. The lab session is an integrated part of the course and make sure that you will attend all the sessions. See the syllabus for the detailed information and the information (e.g. lab manuals) at the website above.

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Chapter 20: Electric Charge/Force/Field Electric charge Two opposite signed charges attract each other Two equally signed charges repel each other When a plastic rod is rubbed with a piece of fur, the rod is “negatively” charged When a glass rod is rubbed with a piece of silk, the rod is “positively” charged Electric charge is conserved

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Electric charge (cont’d)

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Particle Physics Model of Atoms electrons e - nucleus Old view Semi-modern view Modern view nucleus quarks proton What is the world made of? Electric charge (cont’d)

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Electron: Considered a point object with radius less than 10 -18 meters with electric charge e= -1.6 x 10 -19 Coulombs (SI units) and mass m e = 9.11 x 10 - 31 kg Proton: It has a finite size with charge +e, mass m p = 1.67 x 10 -27 kg and with radius –0.805 +/-0.011 x 10 -15 m scattering experiment –0.890 +/-0.014 x 10 -15 m Lamb shift experiment Neutron: Similar size as proton, but with total charge = 0 and mass m n = –Positive and negative charges exists inside the neutron Pions: Smaller than proton. Three types: + e, - e, 0 charge. –0.66 +/- 0.01 x 10 -15 m Quarks: Point objects. Confined to the proton and neutron, – Not free – Proton (uud) charge = 2/3e + 2/3e -1/3e = +e – Neutron (udd) charge = 2/3e -1/3e -1/3e = 0 – An isolated quark has never been found Electric charge (cont’d)

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Two kinds of charges: Positive and Negative Like charges repel - unlike charges attract Charge is conserved and quantized 1.Electric charge is always a multiple of the fundamental unit of charge, denoted by e. 2.In 1909 Robert Millikan was the first to measure e.Its value is e = 1.602 x 10 −19 C (coulombs). 3.Symbols Q or q are standard for charge. 4.Always Q = Ne where N is an integer 5.Charges: proton, + e ; electron, − e ; neutron, 0 ; omega, − 3e ; quarks, ± 1/3 e or ± 2/3 e – how come? – quarks always exist in groups with the N×e rule applying to the group as a whole.

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Charging by contact

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Charging by induction (cont’d)

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Conductors, insulators, and induced charges Conductors : material in which charges can freely move. metal Insulators : material in which charges are not readily transported. wood Semiconductors : material whose electric property is in between. silicon Induction : A process in which a donor material gives opposite signed charges to another material without losing any of donor’s charges

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Coulomb’s law Coulomb’s law - The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them r : distance between two charges q 1,q 2 : charges k : a proportionality constant - The directions of the forces the two charges exert on each other are always along the line joining them. - When two charges have the same sign, the forces are repulsive. - When two charges have opposite signs, the forces are attractive. ++ r q1q1 q2q2 -- r q1q1 q2q2 +- r q1q1 q2q2 F 2 on 1 F 1 on 2 F 2 on 1 F 1 on 2 F 2 on 1

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Coulomb’s law Coulomb’s law and units r : distance between two charges (m) q 1,q 2 : charges (C) k : a proportionality constant (=k e ) SI units Exact by definition charge of a proton

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Coulomb’s law Example: Electric forces vs. gravitational forces electric force gravitational force ++ r q q Gravitational force is tiny compared with electric force! ++ 0 0 proton neutron particle

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Coulomb’s law Example: Forces between two charges +- r F 1 on 2 F 2 on 1

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Coulomb’s law Superposition of forces Principle of superposition of kforces When two charges exert forces simultaneously on a third charge, the total force acting on that charge is the vector sum of the forces that the two charges would exert individually. Example: Vector addition of electric forces on a line +- 2.0 cm F 1 on 3 F 2 on 3 + q1q1 q2q2 q3q3 4.0 cm

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Coulomb’s law Example: Vector addition of electric forces in a plane + + + 0.50 m 0.40 m 0.30 m q 1 =2.0 C q 2 =2.0 C Q=4.0 C force due to q 2

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Electric field and electric forces Electric field and electric forces + + + + + + + + + A B + + + + + + + + A P remove body B Existence of a charged body A modifies property of space and produces an “electric field”. When a charged body B is removed, although the force exerted on the body B disappeared, the electric field by the body A remains. The electric force on a charged body is exerted by the electric field created by other charged bodies.

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Electric field and electric forces Electric field and electric forces (cont’d) + + + + + + + + A Test charge + + + + + + + + A P placing a test charge To find out experimentally whether there is an electric field at a particular point, we place a small charged body (test charge) at point. Electric field is defined by (N/C in SI units) The force on a charge q:

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Electric field and electric forces Electric field of a point charge +- P P q0q0 q0q0 qq S S + + P q0q0 q S P’

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Electric field and electric forces Electric field by a continuous charge distribution

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Electric field and electric forces Electric field by a continuous charge distribution (cont’d) These may be considered in 1, 2 or 3 dimensions. There are some usual conventions for the notation: Charge per unit length is λ ; units C/m i.e, dq = λ dl Charge per unit area is σ ; units C/m 2 i.e, dq = σ dA Charge per unit volume is ρ ; units C/m 3 i.e, dq = ρdV

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Electric field and electric forces Example : Electron in a uniform field y x O 1.0 cm - - + 100 V Two large parallel conducting plates connected to a battery produce uniform electric field Since the electric force is constant, the acceleration is constant too From the constant-acceleration formula: when The electron’s kinetic energy is: The time required is:

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Electric field lines An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric-field vector at that point. Electric field lines show the direction of at each point, and their spacing gives a general idea of the magnitude of at each point. Where is strong, electric field lines are drawn bunched closely together; where is weaker, they are farther apart. At any particular point, the electric field has a unique direction so that only one field line can pass through each point of the field. Field lines never intersect.

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Electric field lines E-field lines begin on + charges and end on - charges. (or infinity) They enter or leave charge symmetrically. The number of lines entering or leaving a charge is proportional to the charge. The density of lines indicates the strength of E at that point. At large distances from a system of charges, the lines become isotropic and radial as from a single point charge equal to the net charge of the system. No two field lines can cross. Field line drawing rules: Field line examples

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Electric field lines (cont’d) Field line examples (cont’d)

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Electric Dipoles An electric dipole is a pair of point charges with equal magnitude and opposite sign separated by a distance d. qd d electric dipole moment Water molecule and its electric dipole

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Electric Dipoles Force and torque on an electric dipole torque: electric dipole moment: work done by a torque during an infinitesimal displacement d

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Electric Dipoles Force and torque on an electric dipole (cont’d) potential energy for a dipole in an electric field

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Exercises Trajectory of a charged particle in a uniform electric field

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Exercises Cathode ray tube

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Exercises Electric field by finite line charge

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Exercises Electric field by a ring charge

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Exercises Electric field by a uniformly charged disk

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Exercises Electric field by infinite plate charge + + + + + + +

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Exercises Electric field by two oppositely charged parallel planes

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Exercises Far field by an electric dipole

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