Exam One Study Guide 10 20 14 9 54 AM Chapters 21 22 23 Electric Charge Like charges repel Opposite charges attract The mass of an electron is The electric charge of an electron e is A proton has a charge of e Coulomb s Law for point charges 9 1 10 31 kilograms 1 6 10 19 Coulombs Continuous Charges o o o Electric Fields and Forces Electric Field visualize the force field how forces are communicated between charges within a field o The charge q generates an electric field E around it When a test charge q0 is placed in that field it experiences force o F q0 E o E F q0 units are Newtons per Coulomb N C but be careful because adding a charge causes the field to change o E lim q0 approaches zero of F q0 so the q0 doesn t disrupt the field but for now electrostatics fixed positions we don t need the limit definition o Electric force in a uniform electric field Dipole moment d points from the negative to the positive charge Line of charge o o Infinite Line of Charge Ring of charge o Disk of charge o o Infinite disk of charge Two infinite parallel sheets that are opposite equal charges o Sphere NON conducting o Infinite conducting cylinder o o Note inside the cylinder electric field is zero Example o Example o Center z 0 E 0 z a point charge E k 1 4 Pi epsilon 2 Pi a lambda z 2 point charge times circumference Conduction 1 There can be NO E field inside a conductor o If there is an E field then the electrons will be moving Charges inside the conductor will produce an E induced which is exactly opposite the E external so the net electric field is zero inside the conductor 2 There can be NO unbalanced charge inside conductors o No charge inside the conductor all the charge goes to the surface o Any introduced induced charge resides on the surface The electric field that can exist on the surface of conductors o Example o Find E everywhere for a spherical conductor with charge q o o Potential Potential of a point charge Electric potential energy o o Infinite line charge Cylindrical Infinite charge E field lines intersect equipotential surfaces at right angles perpendicular gradient is always in the direction of greatest increase ie 90 degrees o o o Example find the potential V along the axis of a ring of charge Q evenly distributed of radius a o o Use E dV dz and find E to see if it compares with result above o Approximations o Gauss Law Electric flux o o o Gauss s Law Example o o Find the field of uniformly charged sphere of radius a and charge Q Outside Inside Capacitors 10 20 14 9 54 AM Properties o Positive and negative bodies are both conductors which implies that positive and negative potential are constant over respective conductor o Electric field E lines emerge from positive and disappear into negative conductor move from positive to the negative o Positive potential on conductor with charge q is greater than the negative potential on conductor with charge q assuming you define V final at any arbitrary point it will happen in the exact center equidistant from parallel and opposite plates Capacitance for cylinders o Energy stored in a capacitor o o Energy density in a capacitor Example one conducting sphere inside another spherical capacitor o o Dielectrics Note the charges on a dielectric are bound Conduction Current density j o o However if current is uniformly distributed o If current is not uniformly distributed Drift velocity o o Resistivity Power dissipated in a simple circuit just a resistor o o Electro motive force Internal resistance o o o Kirchloff s Laws o 1 Net current entering a junction equals net current leaving Charge conservation Junction a point where three or more conductors meet o 2 Signed sum of potential changes around a loop of circuit is zero Conventions Voltage source traversed From negative to positive Delta V emf From positive to negative Delta V emf Example o o o o Substitute some more then you get that I2 5 Amps and I3 1 Amps therefore the direction of I3 is the opposite that we guessed o From these we know that I4 4 Amps and I5 7 Amps o R equivalent V I 13 11 1 2 Ohms Resistor Capacitor Charging a capacitor Discharging a capacitor o o o o Magnetic Field 10 20 14 9 54 AM Magnetic field for a straight line o o Approximation for an infinite wire x L Ampere s Law o Rules for amperes law L must be a closed loop Only current enclosed by the loop counts in Ampere s law Current can be positive or negative depending on flow If current flows along thumb when magnetic field goes along curling fingers it is positive right hand rule o Example Ring of current o o o Example Infinite Cylinder of radius a carrying a uniform current I o o o o o o Infinite solenoid o Magnetic field outside is ZERO Magnetic Force Net work done by a magnet is ZERO A point charge confined to a magnetic field o Special cases o o Hall Effect o o o Note V a is voltage on the battery o o For a straight finite wire Example o o Faraday s Law o o Since there is no magnetic force in the case where the magnetic field is moving there is an effective electric field Magnetic Flux o o Example o o Resistive Force The amount of work required to keep the loop moving at a constant velocity v o o Example o o Note the electric field causes a current to run clockwise so a magnetic field is created to oppose the magnetic field on the solenoid I which is counter clockwise o o o Magnetic Properties 1 paramagnetic materials o Develop an induced weak dipole moment parallel to applied magnetic field o Weakly attractive o Occurs in systems with an unpaired electron Net magnetic moments due to pairs of electrons tend to cancel each other electrons in atoms behave like tiny current loops If an atom has an unpaired electron o The electron spinning implies that there is a dipole moment and the electron s orbital motion cause a net magnetic moment o The following diagram shows the weakly attractive force although the external magnetic field is trying to line up the electrons with the magnetic field there may be bonding between atoms because there is a net dipole moment and heat will cause motion o develop an induced weak dipole moment anti parallel to o 2 Diamagnetic applied magnetic field o weakly repulsive o Paired up electrons o 3 Ferromagnetic Therefore Diamagnetic is a weak repulsion o develop a net dipole moment due to atomic alignments even in the absence of applied magnetic field o strongly attractive o Ferromagnetic Fe Ni Co Characterized by spontaneous parallel arrangement of atomic moments even in the absence
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