1 sq centimeter = .0001 sq meters 1 N/C = 1 V/m Ch15 Electric Charges 1)Unlike charges attract and like repel 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 btw two charged particles is proportional to inverse square of distance btw them Charging by Conduction – charged rod touches sphere, transferring some charge Charging by induction – charged rod brought near sphere, briefly grounded allowing charge to flow off sphere, the +charge on the sphere is evenly distributed due to repulsion between the +charges,* charging by induction requires no contact with object inducing the charge* Polarization –changes can’t move around. The surface molecules get polarized Electric Force 1) directed along a line joining the two particles and is inversely proportional to the square of the separation distance r, between them 2)It is proportional to the product of the magnitudes of the charges, q1 and q2, of the two particles 3)It is attractive if the charges are of opposite sign and repulsive if the charges have same sign �F = ke|q1||q2|r2� Coulomb’s Law – mag of the electric force F between charges q1 and q2 separated by a distance r, where ke is Coulomb constant (units: N) �E→=F→q0=keQr2� Electric Field – produced by charge Q at the location of a small test charge q0 is defined as the electric force F→ exerted by Q on q0 divided by the test charge q0 (units: N/C) Electric Field Lines –1)The electric field vector E→ is tangent to the electric field lines at each point 2)The # 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 3)The lines start from positive and end at negative Electrostatic Equilibrium – no net motion of charge occurs within a conductor 1)Electric field is zero inside conducting material 2)Any excess charge on an isolated conductor resides on its surface 3)The electric field just outside a charged conductor is perpendicu-lar to the conductors surface 4)On an irregularly shaped conductor, the charge accumulates at sharp points, where the radius of curvature of the surface is smallest Ch16 |∆PE = −WAB= −qEx∆x| Change in electric potential energy – a system consisting of an object if charge q moving through a displacement ∆x in a constant electric field E, where Ex is the x-component of the electric field and ∆x = xf−xi (units: joule J), this is only valid for the case of a uniform electric field, for a particle that undergoes a displacement along a given axis �∆V = VB−VA=∆PEq� Potential difference between two points – electric potential diff ∆V between points A and B is the change in electric potential energy as a charge q moves from A to B divided by the charge q (units: joule per coulomb, or volt) |W = Fd = qEx(xf−xi)| and |∆PE = −W = −qEx∆x| Work and Potential Energy – uniform field between two plates -A positive charge loses electrical potential energy when it is moved in the direction of the electric field -A negative charge loses electrical potential energy when it moves in the direction opposite the electric field -If a charge is released in the electric field, it experiences a force and accelerates, gains kinetic energy, loses equal amount of PE �∆V = VB−VA=∆EPEq� Potential Difference (NOT PE) – between points A and B is defined as the change in potential energy (final value minus initial) of a charge q moved from A to B divided by the size of the charge *For a positive charge the higher the potential the higher the PE *For a negative charge the higher the potential the more negative (or lower) the PE Electric Potential Energy of two charges *If the charges have the same sing, PE is positive – pos work must be done to force the two charges together *If the charges have opposite signs, PE is negative – work must be done to hold back the unlike charges from accelerating together �V = keqr� Electric potential created by a point charge, to find the electric potential to be zero you will take the opposite value of V and determine q (this is the value needed to make the electric potential 0) Superposition principle – the total electric potential at some point P due to several point charges is the algebraic sum of the electric potentials due to the individual charges �PE = q2V1= keq1q2r� Potential energy of a pair of charges |W = −∆PE| →|∆PE = q(VB−VA)|→|W = −q(VB−VA)| No net work is required to move a charge between two points that are at the same electric potential �W = keq1q2r�this will give the amount of work in joules must be done by an external force to bring a charge of (x C) from infinity to the origin Electron Volt– the kinetic energy that an electron gains when accelerated through a potential difference of 1V Equipotential Surface– no work is required to move a charge at a constant speed on an equipotential surface, the electric field at every point of an equipotential surface is perpendicular to the surface �C ≡Q∆V� Capacitance of a pair of conductors– capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between conductors (units farad (F) = coulomb per volt (C/V)) �C =∈0Ad� Capacitance of a parallel-plate capacitor– where A is the area of one of the plates, d is the distance between the plates, and ∈0 is the permittivity of free space |∆V = Ed|→�E =∆Vd� Magnitude of uniform electric field btw the plates (units: N/C) �Ceq= C1+ C2+ ⋯� Parallel– capacitors in parallel both have the same potential difference ∆V across them and each is equal to the voltage of the battery �1Ceq=1C1+1C2+ ⋯� Series– combination of capacitors, the magnitude of the charge must be the same on all plates, Q is same for all capacitors in series, charge for an individual capacitor is Q = Ceq∆V, Ceq is only those in that series �∆V =QC� Voltage drop across the capacitor—Q is the charge in each compacitor and C is the individual farads �Energy =12Q∆V =𝟏𝟐𝐂(∆𝐕)𝟐=Q22C� Energy Stored in Capacitor (units: J) energy stored in multiple compacitors in series must equal the total energy stored (but opposite?) Chapter 17�Iav=∆Q∆t� Average Current—suppose ∆Q is the amount of charge that flows