CHAPTER 15Electric charges have the following properties: (1) Unlike charges attract one another and like charges repel one another. (2)Electric charge is always conserved. (3) Charge comes in discrete packets that are integral multiples of the basic electric charge e= 1.6 ×10− 19C. (4) The force between two charged particles is proportional to the inverse square of the distance between them. Conductors are materials in which charge moves freely in response to an electric field. All other materials are called insulators. Coulomb’s Law states that electric force between two stationary charged particles separated by a distance r has the magnitude F=keq1q2r2 where q1 and q2 are magnitudes of the charges on the particles in coulombs. Electric force between two charges with same sign is repulsive, attractive when opposite signs. The Electric Field is defined as E ≡Fq0. The magnitude of the electric field due to a point charge q at a distance r from the point charge is E=keqr2. Electric Field Lines are useful for visualizing the electric field in any region of space. The electric field vector E is tangent to the electric field lines at every point. Further, the number of electric field lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field at that surface. Conductors in electrostatic equilibrium has the following properties: (1) the electric field is zero everywhere inside the conducting material. (2) Any excess charge on an isolated conductor must reside entirely on its surface. (3) The electric fieldjust outside a charged conductor is perpendicular to the conductor’s surface. (4) On an irregularly shaped conductor, charge accumulates where the radius of curvature of the surface is smallest, at sharp points. Electric Flux and Gauss’ Law states that the electric flux through any closed surface is equal to the net charge Q inside the surface divided by the permittivity of free space, ϵ0:EA=ΦE=Qinsideϵ0.CHAPTER 16Potential Difference and Electric Potential – the change in the electric potential energy of a system consisting of an object ofcharge q moving through a displacement Δ x in a constant electric field E is given by Δ PE=−WAB=−q ExΔ x where Ex is the component of the electric field in the x-direction and Δ x=xf−xi. The difference in electric potential between two points A and B is ∆ V =VB−VA=∆ PEq where ∆ PE is the change in electrical potential energy as a charge q moves between A and B. The unit of potentialdifference are joules per coulomb, or volts; 1 J/C = 1 V.The electric potential difference between two points A and B in a uniform electric field E isΔV =−ExΔ x where Δ x=xf−xi is the displacement between A and B and Ex is the x-component of the electric field in thatregion. Electric Potential and Potential Energy Due to Point Charges – The electric potential due to a point charge q at distance rfrom the point charge is V =keqr and the electric potential energy of a pair of point charges separated by r is PE=keq1q2r.These equations can be used in the solution of conservation of energy problems work-energy theorem.Potential and Charged Conductors - W =−q (VB− VA). No net work is required to move a chargebetween two points that are in the same electric potential. All points on the surface of a charged conductor in electrostaticequilibrium are in the same potential. The electric potential is a constant everywhere on the surface of a charged conductor in equilibrium. The electric potential is constant everywhere inside a conductor and equal to that same value at the surface. Equipotential Surfaces – electron volt is defined as the energy that an electron (or proton) gains when accelerated through a potential difference of 1 V. 1 eV = 1.60 x 10-19 CV = 1.60 x 10-19 J. Capacitance – two metal plates with charges that are equal in magnitude but opposite in sign. The capacitance C of any capacitor is the ratio of the magnitude of the charge Q on either plate to the magnitude of potential difference ΔV between them: C ≡QΔV. Capacitance has the unit coulomb per volt, or farads; 1 C/V = 1 F. Parallel-Plate Capacitor – the capacitance of two parallel metal plates of an area A separated by distance d isC=ϵ0Ad where ϵ0 is a constant called permittivity of free space. Combinations of Capacitors –The equivalent capacitance of a parallel combination of capacitors isCeq=C1+C2+C3…. If two or more capacitors are connected in series, the equivalent capacitanceof the series combination is 1Ceq=1C1+1C2+1C3…The Energy Stored in a Charged Capacitor – Three equivalent expressions for calculating the energy stored in a charged capacitor are Energy Stored =12Q ∆ V =12C(∆ V )2=Q22 C . CHAPTER 17Electric Current – The average electric current I in a conductor is defined as Iav=∆ Q∆ t where ∆ Q is the charge that passes through a cross section of the conductor in time ∆ t. SI unit of current is the ampere (A): 1 A = 1 C/s.Current is the time rate of flow of charge through a surface. By convention, the direction of current is the direction of flow of positive charge. A Microscopic View: Current and Drift Speed – the current in a conductor is related to the motion of the charge carriers byI=nq vdA where n is the number of mobile charge per unit volume, q is the charge on each carrier, vd is the drift speed of the charges and A is the cross-sectional area of the conductor. Resistance, Resistivity, and Ohm’s Law – the resistance R of a conductor is defined as the ratio of the potential difference across the conductor to the current in it: R=∆VI. The SI unit of resistance are volts per ampere, or ohms (Ω);1 Ω=1 V / A . Ohm’s law describes many conductors for which the applied voltage is directly proportional to the current it causes. The proportionality constant is the resistance: ΔV =IR. If a conductor has length l and cross-sectional area A, its resistance is R=ρlA where ρ is an intrinsic property of the conductor called the electrical resistivity. The SI unit of resistivity is the ohm-meter (Ω ∙ m). Temperature Variation of Resistance – over a limited temperature range, the resistivity of a conductor varies with temperature according to the expressionρ=ρ0[1+α(T −To)] where α is the temperature coefficient of resistivity and ρ0 is the resistivity at some reference temperatureTo (usually taken to be 20°C). The resistance of a conductor