Lightning Review15.3 Coulomb’s Law - Observation15.3 Coulomb’s Law – Mathematical FormulationExample15.3 Coulomb’s Law – RemarksMini-QuizExample: Electrical ForceQuestion:The electron and proton of a hydrogen atom are separated (on the average) by a distance of about 5.3x10-11 m. Find tSuperposition PrincipleExample: Using the Superposition PrincipleConsider three point charges at the corners of a triangle, as shown below. Find the resultant force on q3.15.4 Electric Field - Discovery15.4 Electric Field – Quantitative Definition15.4 Electric Field – Quantitative Definition (2)15.4 Electric Field – Electric Field of a Charge “q”Problem-Solving StrategyExample:Example: Electric Field Due to Two Point ChargesQuestion: Charge q1=7.00 mC is at the origin, and charge q2=-10.00 mC is on the x axis, 0.300 m from the origin. Find the elQuestion: Charge q1=7.00 mC is at the origin, and charge q2=-10.00 mC is on the x axis, 0.300 m from the origin. Find the el15.5 Electric Field Lines15.5 Electric Field Lines (2)15.5 Electric Field Lines (3)15.5 Electric Field Lines (4)Application: Measurement of the atmospheric electric field15.6 Conductors in Electrostatic Equilibrium15.6 Conductors in Electrostatic EquilibriumElectric field is zero everywhere within the conductor.Any excess charge field on an isolated conductor resides entirely on its surface.The electric field just outside a charged conductor is perpendicular to the conductor’s surface.On an irregular shaped conductor, the charge tends to accumulate at locations where the radius of curvature of the surface isRemarksFaraday’s ice-pail experimentMini-quizMini-Quiz119/5/20039/5/2003General Physics (PHY 2140)Lecture IILecture II¾ Electrostatics9 Coulomb’s law9 Electric fieldChapter 15http://www.physics.wayne.edu/~apetrov/PHY2140/229/5/20039/5/2003Lightning ReviewLightning ReviewLast lecture:1. Properties of electric charge9 two types: positive and negative9 always conserved and quantized2. Insulators and conductors9 charges move freely in conductors; opposite is true for insulators9 conductors can be charged by conduction and induction; insulators can be polarizedReview Problem:OperatingOperating--room personnel must wear special conducting room personnel must wear special conducting shoes while working around oxygen. Why? What might shoes while working around oxygen. Why? What might happen if personnel wore ordinary rubber shoes happen if personnel wore ordinary rubber shoes (sneakers)?(sneakers)?339/5/20039/5/200315.3 Coulomb’s Law 15.3 Coulomb’s Law --ObservationObservationCharles Coulomb discovered in 1785 the fundamental law of Charles Coulomb discovered in 1785 the fundamental law of electrical force between two stationary charged particles.electrical force between two stationary charged particles.An electric force has the following properties:An electric force has the following properties:Inversely proportionalInversely proportionalto the to the square of the separationsquare of the separation, , rr, between the , between the particles, and is along a line joining them.particles, and is along a line joining them.Proportional to the product of the magnitudes of the charges Proportional to the product of the magnitudes of the charges |q|q11||and and |q|q22||on the two particles. on the two particles. AttractiveAttractiveif the charges are of if the charges are of opposite signopposite signand and repulsiverepulsiveif the charges if the charges have have the same signthe same sign..q1q2r449/5/20039/5/200315.3 Coulomb’s Law 15.3 Coulomb’s Law ––Mathematical Mathematical FormulationFormulationkkeeknown as the Coulomb constant.known as the Coulomb constant.Value of Value of kkeedepends on the choice of units.depends on the choice of units.SI unitsSI unitsForce: the Newton (N)Force: the Newton (N)Distance: the meter (m).Distance: the meter (m).Charge: the coulomb ( C).Charge: the coulomb ( C).Current: the ampere (A =1 C/s).Current: the ampere (A =1 C/s).EExperimentally measurement: xperimentally measurement: kkee= 8.9875= 8.9875××101099NmNm22/C/C22..Reasonable approximate value: Reasonable approximate value: kkee= 8.99= 8.99××101099NmNm22/C/C22..122eqqFkr=How do we know the units of ke?559/5/20039/5/2003Example: Fun with unitsExample: Fun with unitsRecall that units can be manipulated:[][][][][]122eqqFkr=122eqqFkr=[][][][][]2eCoulomb CoulombNewton kmeter=[]22eNmkC⋅=669/5/20039/5/2003ExampleExample1e = 1e = --1.60 1.60 ××1010--1919ccTakes 1/e=6.6 Takes 1/e=6.6 ××10101818protons to create a total charge of 1Cprotons to create a total charge of 1CNumber of free electrons in 1 cmNumber of free electrons in 1 cm33copper ~ 10copper ~ 102323Charge obtained in typical electrostatic experiments with Charge obtained in typical electrostatic experiments with rubber or glass 10rubber or glass 10--66C = 1 C = 1 µµccA very small fraction of the total available chargeA very small fraction of the total available chargeCharge and Mass of the Electron, Charge and Mass of the Electron, Proton and Neutron.Proton and Neutron.1.67 1.67 ××1010--272700NeutronNeutron1.67 1.67 ××1010--2727+1.60 +1.60 ××1010--1919ProtonProton9.11 9.11 ××1010--3131--1.60 1.60 ××1010--1919ElectronElectronMass (kg)Mass (kg)Charge ( C)Charge ( C)ParticleParticle779/5/20039/5/200315.3 Coulomb’s Law 15.3 Coulomb’s Law ––RemarksRemarksThe electrostatic force is often called Coulomb force.The electrostatic force is often called Coulomb force.It is a force (thus, a It is a force (thus, a vectorvector): ): a magnitude a magnitude a direction.a direction.Second example of action at a distance.Second example of action at a distance.++rq1q2F21F21+-rq1q2F21F21889/5/20039/5/2003MiniMini--QuizQuizName the first action at a distance force you have Name the first action at a distance force you have encountered in physics so far.encountered in physics so far.999/5/20039/5/2003Example: Electrical ForceExample: Electrical ForceQuestion:Question:The electron and proton of a hydrogen atom are separated (on theThe electron and proton of a hydrogen atom are separated (on theaverage) by a distance of about 5.3x10average) by a distance of about 5.3x10--1111m. Find the magnitude of the m. Find the magnitude of the electric force that each particle exerts on the other.electric force that each particle exerts on the other.10109/5/20039/5/2003Question:Question:The electron and proton of a