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Announcements Physics Department Seminar: TITLE: "The fluid dynamics of climatic variations." SPEAKER: Professor Walter A. Robinson, Department of Atmospheric Sciences University of Illinois at Urbana-Champaign TIME: Thursday Jan. 13, 2005 at 4 PM Essays on Quizzes/Surveys: I do read and comment on them when appropriate.

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Reserve Books Several books are on reserve in the library: There will be required, supplemental readings from:: Biomedical Applications of Introductory Physics Optional, suggested, readings from:: Electricity and Magnetism, Purcell Div, Grad, Curl and all that For review: First-year Calculus, Hille and Salas Other optional books may be placed for your enjoyment.

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Matter and Charges All matter is made of positive and negative charges (or neutral) An object’s total charge is very close to zero When an object becomes charged, a tiny fraction of its charged particles (usually electrons) are lost or gained These particles (usually electrons) can flow through objects Some materials are better at allowing the flow of electrons than others Conductor A material that allows electrons or other charged particles to flow freely Insulator A material that resists the flow of electrons and other charged particles

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Elementary Charge Charges seem to come only in integer multiples of a fundamental charge unit called e We will treat e as a positive number (some sources treat it as negative) e = 1.602 10 -19 C know these Particleq Protone Neutron0 Electron-e Oxygen nuc.8e Calcium ion 2e Chlorine ion -e

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Some ways to charge objects By rubbing dissimilar objects By physical contact between a charge and a conductor By proximity between a charge and a conductor – charging by induction By chemical processes + - +

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Three pithballs are suspended from thin threads. Various Objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the balls is charged by touching them with one of these objects. It is found that pithballs 1 and 2 repel each other and that pithballs 2 and 3 repel each other. From this we can conclude that: B) All the balls carry charges of the same sign Charges of equal sign repel, so 1 and 2 have the same sign, as do 2 and 3, and so they all have the same sign. Quiz Three balls are suspended from thin threads. Various Objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the balls is charged by touching them with one of these objects. It is found that balls 1 and 2 repel each other and that balls 2 and 3 repel each other. From this we can conclude that: A)Balls 1 and 3 carry charges of opposite sign. B)All the balls carry charges of the same sign C)One ball carries no charge. D)Impossible to determine without more information.

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Coulomb’s Law Like charges repel, unlike charges attract Force is directly along a line joining the two charges k e = 8.988 10 9 N m 2 /C 2 q1q1 q2q2 r An inverse square law, just like gravity Can be attractive or repulsive – unlike gravity Constant is enormous compared to gravity Obeys the superposition principle just like gravity

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Coulomb’s Law: Applied A Helium nucleus (charge +2e) is separated from one of its electrons (charge –e) by about 3.00 10 -11 m. What is the force the nucleus exerts on the electron? Is it attractive or repulsive? r = 3.00 10 -11 m q 1 = 3.204 10 -19 C q 2 = -1.602 10 -19 C k e = 8.988 10 9 N m 2 /C 2 F e = - 0.513 N Attractive Force We just calculated the force on the electron from the nucleus. How does this compare with the force on the nucleus from the electron? A)The force on the nucleus is twice as big B)The force on the nucleus is half as big C)The forces are equal in magnitude

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Newton’s Laws and Kinematics Newton’s laws and all the kinematics you learned in 113 are still true! A body in motion tends to stay in motion, therefore changing velocity, i.e. acceleration, requires a force! If a does not depend on time, then

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Coulomb’s Law vs. Gravity A Helium nucleus (charge +2e) is separated from one of its electrons (charge –e) by about 3.00 10 -11 m, and we just calculated the electrostatic forces involved. k e = 8.988 10 9 N m 2 /C 2 Suppose we could adjust the distance between the nucleus (considered as a point particle) and one electron. Can we find a point at which the electric and gravitational forces are equal? A)Yes, move the particles apart. B)Yes, move the particles together. C)No, they will never be equal.

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Coulomb’s Law – more versions Force can be positive or negative. No absolute value signs unless you just want the magnitude! 0 = 8.854 10 -12 C 2 / (N●m 2 ) Permittivity of free space Force is a vector (remember from last semester)

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Conductors redistribute charge Conductor Conductors allow free flow of charge Like charges repel So the charges will redistribute themselves over the sphere Add charges, Q Q

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Spherical Shells Just like with gravity, a charge outside feels the charge from the sphere as if it were concentrated in the middle Q q Consider the forces from opposite charge elements and the vector decomposition

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Coulomb’s Law My body contains about 3 10 28 electrons, all repelling each other. How come I don’t explode? A)Electrons attract each other, not repel each other B)The gravitational force is so strong it holds me together, overcoming electric forces C)There are also positive charges that cancel out the negative charges D)Electrical forces are too weak to consider

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Electric Fields Electric Field is the ability to extert a force at a distance on a charge It is defined as force on a test charge divided by the charge Denoted by the letter E Units N/C + + + + + – – –Small test charge q

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E-Field: Why? When we have a charge distribution, and we want to know what effect they would have external charges, we can either Do many sums (or integrations) every time a charge comes in to find the force on that charge Or calculate the field from the charge distribution, and multiply the field by the external charge to obtain the force Simplification!

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Electric Field from a Point Charge Small test charge q Point charge Q Note: the field is a vector!

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Quiz T Two test charges are brought separately into the vicinity of a charge +Q. First, test charge +q is brought to point A a distance r from charge +Q. Next, the +q charge is removed and a test charge +2q is brought to point B a distance 2r from charge +Q. Compared with the electric field of the charge at A, the electric field of the charge at B is: +Q +q A +Q +2q B A)Greater B)Smaller C)The same.

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Electric Charge and Coulomb’s Law

Electric Charge and Coulomb’s Law

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