Prozorov_01 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURE 1 Introduction. Electric charge. Coulomb’s law. Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 1 Physics Mechanics Thermal properties Electromagnetism •Electrostatic •Electric current •Magnetism Condensed Mater High energy Optics Atoms & particles •Geometrical optics •Wave optics Biophysics Classical physics Quantum physics Relativistic physics Quantum relativistic physics Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 2 Electromagnetism • deals with electric and magnetic phenomena • ELECTROSTATICS o studies stationary electric charges, forces between these charges and (electrostatic) fields produced by these charges. o electrostatics can be applied to slow moving charges. Slow means that all velocities involved are much less than the speed of light: v<<c o so it can be used for all practical purposes Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 3 electric charge • Benjamin Franklin proposed that with the rubbing, objects acquired some kind of “electric charge”. There are two types of electric charge, which he called positive and negative. rubbed off remains on the cat • charges manifest themselves via forces: o equal charges repel each other o opposite charges attract each other o the force gets weaker with the increase of the distance between the charges Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 4 triboelectric effect • Although the word comes from the Greek for "rubbing", τρίβω (τριβή: friction), the two materials only need to come into contact and then separate for electrons to be exchanged. • After coming into contact, a chemical bond is formed between some parts of the two surfaces, called adhesion, and charges move from one material to the other to equalize their electrochemical potential. This is what creates the net charge imbalance between the objects. • When separated, some of the bonded atoms have a tendency to keep extra electrons, and some a tendency to give them away. • In addition, some materials may exchange ions of differing mobility, or exchange charged fragments of larger molecules. Physics 222 - Prof. Ruslan Prozorov - Iowa State University + most positive Air Human skin Leather Rabbit's fur Glass Quartz Mica Human hair Nylon Wool Cat's fur Silk Aluminium Paper (Small positive charge) Cotton (No charge) 0 Steel (No charge) Acrylic Polystyrene Rubber balloon Brass, Silver Gold, Platinum Polyester Polyurethane Vinyl (PVC) Silicon Teflon Silicone rubber Ebonite − most negative 22 August 2011 5 examples Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 6 discrete nature and units • The charges of free particles are integer multiples of the elementary charge e, so that electric charge is quantized. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge. Robert Millikan's oil-drop experiment demonstrated this fact directly, and measured the elementary charge. • By convention, the charge of an electron is −e, while that of a proton is +e. Charge is measured in coulombs (C): 1e=−1.602×10−19 C, or, 1 C = 6.242×1018 e. 1 mole of electrons = 96475 C. • Coulomb's law quantifies the electrostatic force between two charges • The charge of an antiparticle equals that of the corresponding particle, but with opposite sign. Quarks have fractional charges of either −1⁄3 or +2⁄3, but free quarks have never been observed Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 7 classification of materials • How free to move are the charges? It depends on the material. • When charges can move easily, we call the material a conductor. • When they cannot move easily, we call it an insulator. • But… there is no perfect conductor or perfect insulator… • Examples of good conductors: most metals, solutions of salts (like tap water)… • Examples of good insulators: plastics, rubber, glass, wood, air, pure water… Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 8 the electroscope disk color coding: Positive Negative Neutral Physics 222 - Prof. Ruslan Prozorov - Iowa State University Gold leaves 22 August 2011 9 This is called separation of charge (or polarization) by induction negatively charged rod + Positive Negative Neutral - repulsion 22 August 2011 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 10 If we ground the electroscope while the rod is there, the charges in the electroscope that were “escaping” from the rod flow to the ground. “ground” is an infinite – capacity neutral reservoir. negatively charged rod - in practice, it is a large copper rod buried deep underground, often at the level of ground waters. + Positive Negative Neutral NO repulsion 22 August 2011 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 11 Now we cut the ground . . . negatively charged rod + Positive Negative Neutral still, NO repulsion 22 August 2011 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 12 and remove the negatively charged rod . . . now the positive charge is uniformly distributed over the device + so we charged the electroscope by induction without touching it by the charging rod! the amount of charge in the charging rod did NOT change! Positive Negative Neutral + + repulsion, again! 22 August 2011 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 13 Coulomb’s law Q1Q2 r Fk 2 r r k 1 8.99 109 Nm 2 C2 , 4 0 0 permittivity constant compare to Newton’s law for two masses, M1 and M2: M 1M 2 G 6.673 x 10 11 Nm 2 kg 2 Newton's constant F G , 2 r [Q] 1 C 1[A] 1[s] - total charge dQ C [ I ] 1 A - electric current - charge per second: I A dt s Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 14 vectors Q1Q2 r Fk 2 r r y r - + x F • vectors have magnitude and direction, but no fixed point of origin • a vector can be moved anywhere by arbitrary translation (but not rotation or scaling) • it is convenient to place a vector at the origin and assign coordinates of its end: these vectors are equivalent Physics 222 - Prof. Ruslan Prozorov - Iowa State University A Ax , Ay 22 August 2011 15 vector algebra reversed direction B B C AB A A C AB the same vector A B Ax Bx , Ay By A B Ax Bx , Ay By Cx Ax Bx Cx Ax Bx C y Ay By Physics 222 - Prof. Ruslan Prozorov - Iowa State University C y Ay By 22 August 2011 16 y r x2 x1 , y2 y1 y1 y2 x1 x2 think about x1,x2,y1 and y2 as special vectors along the principal axes x length of the vector (or magnitude if this is a physical quantity, such as force) is: r r r 2 x2 x1 y2 y1 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 2 2 22 August 2011 17 scalar (or dot) product A Ax , Ay B Bx , By C A B Ax Bx Ay By A B cos SCALAR, NOT VECTOR!! Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 18 the principle of superposition Q3Q2 F32 k 2 r32 Q3Q1 F31 k 2 r31 r32 r32 r31 r31 Ftotal Q1 r31 Q2 r32 kQ3 2 2 r31 r31 r32 r32 F32 Q1 Q3 Ftotal F31 F32 r31 r32 F31 parallel translation Q2 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 19 Example: Q1 1.0 C Q2 2.0 C Q3 12.0 C F12 Q1 r F13 Q2 r Q3 F1 F12 F13 r 0.10m F1 ? Q1Q2 1.0 106 C 2.0 106 C F12 k 2 9.0 109 Nm 2 / C 2 1.8 N 2 r 0.1m F13 k Q1Q3 2r 2 9.0 109 Nm 2 / C 1.0 106 C 12.0 106 C 2 2 0.1m 2 2.7 N F1 F12 F13 1.8 N 2.7 N 0.9 N Physics 222 - Prof. Ruslan Prozorov - Iowa State University 22 August 2011 20 Q Example: Q 1.0C a 0.10m F ? Ftot Ftot Q a Q Q F2 2 F1 F3 F3 Q2 F1 F2 k 2 a Q2 F3 k 2 2a Ftot F1 F2 F3 F1 Q2 Q2 2k 2 k a 2a 2 1 Q2 2 k 2 2 a 1 1.0 10 -6 C 9 2 2 2 8.99 10 Nm / C 2 0.10m 2 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 2 1.7 N 22 August 2011 21 Example: Compare the gravitational attraction and the electric repulsion of two electrons e 1.6 1019 C m 9.1 10 31 kg e2 FE k 2 r m2 FG G 2 r FE 9.0 109 Nm 2 C 2 1.6 10 19 C 4.2 10 42 ke2 2 FG Gm 6.7 10 11 Nm 2 kg 2 9.1 10 31 kg2 2 Big! Example: A student can resist a force of 100 lb (450 N) with his arms apart. You give him two charged balls with charges Q and Q to hold on each hand. How large a charge Q can he hold outstretched? Q2 F k 2 r Qmax Q -Q r ~ 1.5 m r2 Fmax 3.35 10-4 C k 1 electron 9.1 10-31kg 3.35 104 C 2 10-15kg 1.6 10-19C 1 electron Physics 222 - Prof. Ruslan Prozorov - Iowa State University Less than a cell in your 2011 body! 22 August 22 ...
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