UT PHYS 2080 - Chapter 15
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Chapter 15 15 1 15 6 Quiz may be Tuesday or Wednesday of this week June 23 2014 15 1 Properties of Electric Charges There are two kinds of electrical charge positive and negative Like charges repel one another and unlike charges attract one another o Objects usually contain equal amounts of positive and negative charge they are neutral charge Electrical forces arise when those objects have net negative or positive Objects become charged by gaining or losing electrons because electrons are lighter than protons and are more easily accelerated by forces Electric charge is always conserved negative charge is transferred from one object to the other The SI unit of electric charge is the coulomb C 15 2 Insulators and Conductors Conductors electrics charges move freely in response to an electric force good conductors silver copper aluminum o When these materials are charged in some small region the charge readily distributes itself over the entire surface of the material Semiconductors somewhere in between silicon and germanium Insulators all other materials glass and rubber o When these materials are charged by rubbing only the rubbed areas becomes charged o Hold copper rod in hand rub with rod with fur or wool it will not attract a piece of paper Do the same but hold the rod with an insulator and the rod will remain charged and attract the paper in the first case the electric charge produced by rubbing readily moved from the copper through your body to the ground In the second case the insulator stopped the flow to the ground Charging by conduction the object being charged is always left with a charge having the same sign as the object doing the charging o Negatively charged rubber rod brought into contact with an insulated neutral conductive sphere o Before contact the negative rod repels the sphere s electrons creating a local positive charge on the neutral sphere o On contact electrons move from the rod flow onto the sphere neutralizing the o When the rod is removed negative charge remains on the sphere the sphere has local positive charges been left with a net negative charge Charging by induction the object is left with a charge opposite of the charging object and charging on object by induction requires no contact with the object inducing the charge o Grounded when an conducting wire or copper pipe is buried in the Earth can accept an infinite number of electrons o Negatively charged rubber rod brought near a neutral conducting sphere that is insulated o When negatively charged rod is brought close to sphere causes some electrons in sphere to move to the side of the sphere furthest from the rod which results in an excess positive charge nearest the negatively charged rod o Conducting grounded wire is added to sphere some electrons leave the sphere and enter the ground which leaves the sphere with excess positive charge o When rubber rod removed from vicinity the positive charge remains on the ungrounded sphere excess positive charge becomes uniformly distributed over the surface of ungrounded sphere because of repulsive forces of the like charged and high mobility of electrons in a metal o remove finger first then later the rod if remove rod before finger the negative charge will go back onto it Charging insulators by induction polarization doesn t change net charge o In the presence of a charged object these centers may separate slightly resulting in more positive charge on one side of the molecule than on the other polarization o The realignment of charge within individual molecules produces an induced charge on the surface of the insulator A balloon charged through rubbing will stick to an electrically neutral wall 15 3 Coulomb s Law The force exerted by one charged particle on another is given by o K 8 988 109 9 00 109 N m2 C2 Electric forces between unmoving charges is called electrostatic forces while moving charges create magnetic charges Charges o 1 e 6 25 1018 protons to create a total charge of 1 0 C Electrons to create a total charge of 1 0 C Forces are vectors so Coulomb s force law incorporates vectors and obey Newton s third law of equal and opposite always equal regardless of whether q1 and q2 have the same magnitude Comparing and contrasting electric and gravitational forces o Comparisons both act at a distance and not in contact both are inversely proportional to the distance squared with the force directed along a line connecting the two bodies mathematical form is the same o Two important differences electric forces can be either attractive or repulsive but gravitational forces are only attractive and the electric force between charged elementary particles is far stronger than the gravitational force between the same particles Superposition principle when a number of separate charges act on the charge of interest each exerts an electric force these electric forces can all be computed separately one at a time then added as vectors 15 4 The Electric Field said to exist in the region of space around a charged object SI unit of Newton per coulomb N C When a positive test charge is used the electric field always has the same direction as the Test charge is required to be very small so it doesn t cause any significant rearrangement electric force on the test charge of the charge creating the electric field Electric field of a point charge charges superposition principle 15 5 Electric Field Lines o Charges create electric fields and these fields in turn exert electric forces on other o Use vectors for multiple charges the total electric field is found using the 1 The electric field vector E is tangent to the electric field lines at each point 2 The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region E is large when the field lines are close together and small when the lines are far apart the lines are closer together as they get near the charge indicating that the strength of the field is increasing Rules for drawing electric field lines o 1 Closer lines mean a stronger field o 2 The field is tangent to the lines at every point o 3 Field lines start on positive charges and end on negative charges o 4 The number of lines entering or leaving a charge is proportional to the magnitude of the charge o 5 Field lines never cross 15 6 Conductors in Electrostatic Equilibrium Although electrically neutral copper has electrons charge that aren t bound to any atom and are free to

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# UT PHYS 2080 - Chapter 15

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