PHY 184AnnouncementsSlide 3ReviewElectrostatic ChargingCharging by ConductionInductionCharging by InductionCharging by inductionSlide 10Electric Force - Coulomb’s LawCoulomb’s Law (2)Slide 13Electric ForceElectric Force VectorSuperposition PrincipleExample - The Helium NucleusExample - Equilibrium PositionExample - Equilibrium Position (2)Example - Equilibrium Position (3)Example - Equilibrium Position (4)Example - Charged PendulumsExample - Charged Pendulums (2)Electric Force and Gravitational ForceExample - Forces between ElectronsExample - Four ChargesExample - Four Charges (2)1/10/2006 184 Lecture 3 1PHY 184PHY 184Spring 2007Lecture 3Title: The Coulomb Force1/10/2006 184 Lecture 3 2AnnouncementsAnnouncementsDon’t forget to register your clicker!Homework Set 1 is due Tuesday, January 16, at 8:00 amWe will soon post the complete SLC schedule.Strosacker Learning CenterRoom 1248 B. P. S.1/10/2006 184 Lecture 3 3Outline1 – Review2 – Electrostatic charging3 – Coulomb’s Law1/10/2006 184 Lecture 3 4ReviewReviewThere are two types of charge: negative and positive.Most objects are electrically neutral; they have equal numbers of negative and positive charges (net charge is 0).An object becomes charged by adding or removing electrons.An electron carries negative charge of magnitude e = 1.602×10-19 C.Law of Charges•Like charges repel and opposite charges attract.Law of charge conservation•The total charge of an isolated system is strictly conserved.Conductors are materials where some of the electrons can move freely.Insulators are materials where none of the charges can move freely.1/10/2006 184 Lecture 3 5Electrostatic ChargingElectrostatic ChargingThere are two ways to charge an object•Conduction•InductionCharging by conduction•We can charge an object by connecting a source of charge directly to the object and then disconnecting the source of charge•The object will remain charged–Conservation of charge1/10/2006 184 Lecture 3 6Charging by ConductionCharging by ConductionWe brought charge onto the electrode by contact.+ + + + + + + + +Electroscope1/10/2006 184 Lecture 3 7InductionInductionInductionThe presence of the positively charged rod leads to a redistribution of charge (a kind of polarization).It pulls electrons up to the electrode.+ + + + + + + + +- - - - -- - - -1/10/2006 184 Lecture 3 8Charging by InductionCharging by InductionWe can also charge an object without physically connecting to it•First we charge a rod positively•Then we ground the object to be charged•Connecting the object to the Earth provides an effectively infinite sink for charge•We bring the charged rod close to the object but do not touch it•We remove the ground connection and move the rod away•The object will be charged by induction1/10/2006 184 Lecture 3 9InductionThe presence of the positively charged rod leads to a redistribution of charge.Grounding pushes positive charge to Earth (or rather pulls electrons from Earth!) leaving the electroscope negative.+ + + + + + + + +Charging by inductionCharging by induction- - - - -- - - -ground1/10/2006 184 Lecture 3 10Coulomb’s Law1/10/2006 184 Lecture 3 11Electric Force - Coulomb’s LawElectric Force - Coulomb’s LawConsider two electric charges: q1 and q2The electric force F between these two charges separated by a distance r is given by Coulomb’s LawThe constant k is called Coulomb’s constant and is given by221rqkqF 229/CNm1099.8 k1/10/2006 184 Lecture 3 12Coulomb’s Law (2)Coulomb’s Law (2)The coulomb constant is also written as0 is the “electric permittivity of vacuum”•A fundamental constant of nature221200NmC 1085.8 where41k221041rqqF1/10/2006 184 Lecture 3 13Example:What is the force between two charges of 1 C separated by 1 meter?Answer: 8.99 x 109 N,i.e., huge!1/10/2006 184 Lecture 3 14Electric ForceElectric ForceThe electric force is given byThe electric force, unlike the gravitational force, can be positive or negative•If the charges have opposite signs, the force is negative•Attractive•If the charges have the same sign, the force is positive•Repulsive221rqqkF 1/10/2006 184 Lecture 3 15Electric Force VectorElectric Force VectorElectric force in vector formrrqqkFˆ2212xyq1q2r2r1rrrrrrrrrr1212ˆ rrqqkFˆ22111/10/2006 184 Lecture 3 16Superposition PrincipleSuperposition PrincipleThe net force acting on any charge is the vector sum of the forces due to the remaining charges in the distribution.znFzFzFzFynFyFyFyFxnFxFxFxFnnet,1,13,121,1,13,121,1,13,121,13,12,1,1 FFFF1/10/2006 184 Lecture 3 17Example - The Helium NucleusExample - The Helium NucleusPart 1: The nucleus of a helium atom has two protons and two neutrons. What is the magnitude of the electric force between the two protons in the helium nucleus?Answer: 58 NPart 2: What if the distance is doubled; how will the force change?Answer: 14.5 N Inverse square law: If the distance is doubled then the force is reduced by a factor of 4.1/10/2006 184 Lecture 3 18Consider two charges located on the x axisThe charges are described by•q1 = 0.15 C x1 = 0.0 m•q2 = 0.35 C x2 = 0.40 mWhere do we need to put a third charge for that charge to be at an equilibrium point?•At the equilibrium point, the forces from the two charges will cancel.x1x2Example - Equilibrium PositionExample - Equilibrium Position1/10/2006 184 Lecture 3 19Example - Equilibrium Position (2)Example - Equilibrium Position (2)The equilibrium point must be along the x-axis.Three regions along the x-axis where we might place our third chargex1x2x3 < x1x1 < x3 < x2x3 > x21/10/2006 184 Lecture 3 20Example - Equilibrium Position (3)Example - Equilibrium Position (3)x3<x1•Here the forces from q1 and q2 will always point in the same direction (to the left for a positive test charge)•No equilibriumx2<x3•Here the forces from q1 and q2 will always point in the same direction (to the right for a positive test charge)•No equilibriumx1x21/10/2006 184 Lecture 3 21Example - Equilibrium Position (4)Example - Equilibrium Position (4)x1x20)()(2323221331 xxqqkxxqqkx1 < x3 < x2Here the forces from q1 and q2 can balance.Answer: x3 = 0.16 mq3Check the signs!!1/10/2006 184
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