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Chapter 16: Electric Charge and Electric Field Static electricity - Discuss charges that are at rest. Electric charge positive (+ attracting electrons to stabilize) negative ( - repelling, loosing electrons to stabilize) defined by Benjamin Franklin (1706 – 1790) Whenever a certain amount of charge is produced on one body in a process, an equal amount of the opposite type of charge is produced on another body. Unlike charges attract; like charges repel. Any charge is plus or minus – so many coulombs (C), in SI units. Law of conservation of electric charge: net amount of electric charge produced in any process is zero. The magnitude of the charge on protons and electrons is exactly the same, but their signs are opposite. An atom with extra or lacking electrons is an ion. Water molecules are polar – the charge is not distributed uniformly Metals are good conductors (contain a lot of free electrons) – other materials are insulators Charging: Charging by conduction – by contact (two objects end up with same charge) Charging by induction – bringing up close (one positive, other negative) Electroscope: device used for detecting charge. Coulomb’s Law QQ F k 12 2 r Coulomb’s law gives the force between two point charges q1 and q2, a distance r apart. k is a proportionality constant. k = 8.988 * 109Nm2C-2 = 9.0 * 109Nm2C-2 applicable for point charges if several charges are present, the net force on any one of them will be the vector sum of the forces due to each of the others. The Electric Field developed by Faraday (1791 – 1867) Electric field, E, at any point in space is defined by the magnitude of the test charge q F E : force per unit charge q E is defined as the limit of F/q as q is taken smaller and smaller, approaching zero. Q E k 2 (N/C or V/m) r Field Lines The number of lines starting on a positive charge, or ending on a negative charge, is proportional to the magnitude of the charge. The closer the lines are together, the stronger the electric field in that region Electric field lines start on positive charges and end on negative charges Chapter 17: Electric Potential and Electric Energy; Capacitance Electric Potential and Potential Difference Electric potential: the potential energy per unit charge. Only differences in potential energy are physically measurable (voltage) W Vab ba q Unit: J/C = V The ground of a conductor connected directly to the ground is often taken as zero potential Change in potential energy: PE qVba Relation Between Electric Potential and Electric Field W qVba W qEd Vba Ed The electric field in a given direction at any point in space is equal to the rate at which the electric potential changes over distance in that direction Equipotential Lines An equipotential surface must be perpendicular to the electric field at any point. A conductor must be entirely at the same potential in the static case, and the surface of a conductor is then an equipotential surface. Electron volt: 1eV = 1.6 * 10-19 J Electric potential due to point charges: V k Q r Chapter 18: Electric Currents The Electric Battery Electrodes are two plates of rods made of dissimilar metals (one can be carbon) Electrolyte: the solution such as a dilute acid into which the electrodes are immersed Electric cell: composed of 2 oppositely charges electrodes, and electrolyte Battery: several cells connected together Terminal: the part of each electrode remaining outside the solution Electric Current Circuit: a continuous conduction path between the terminals of a battery Electric current: a flow of charge through the wires, from one terminal to the other Q I t Ampere (A) = 1 C/s Conventional current flows from positive to negative Electron flow is form negative to positive Ohm’s Law: Resistance and Resistors IV Ohm’s Law: the definition of resistance V IR Ohm = V/A Resistors are used to control the amount of current Resistivity The resistance R of a metal wire is directly proportional to its length L and inversely proportional to the cross-sectional area A. L R A = resistivity, the constant of proportionality which depends on the material used. Unit is m. Effect of temperature: T 0 [1 (T T0 )] Electric Power P power P IV energy.transformed QV time t P I 2R V2 P R Microscopic View of Electric Current When an electric filed exists in the wire, the electrons feel a force and initially being to accelerate. But they soon reach a more of less steady average speed (due to collisions with atoms in the wire) know as their drift speed, vd. Q neA d I t N N N (1mole) n V m / m(1mole) Chapter 19: DC Circuits Resistors in Series and in Parallel Series: resistors are connected end to end I I1 I 2 I 3 V V1 V2 V3 IR1 IR2 IR3 Series circuit: V IReq Req R1 R2 R3 Parallel circuit: V V V V Req R1 R2 R3 1 1 1 1 Req R1 R2 R3 EMF and Terminal Voltage A device such as a battery or an electric generator that transforms once type of energy (chemical, mechanical, light, and so on) into electric energy is called a seat or source of electromotive force or of emf. A battery itself has some resistance, called its internal resistance. (r) Terminal voltage (Vab) Vab Ir Kirchhoff’s Rules Kirchhoff’s first or junction rule (conservation of charge): at any junction point, the sum of all currents entering the junction must equal the sum of all currents leaving the junction. Kirchhoff’s second or loop rule (conservation of energy): the sum of the changes in potential around any closed path of a circuit must be zero. Voltage drop: decrease in a voltage between the two ends of a resistor. Because of the decrease in a voltage, we use a negative sign when applying Kirchhoff’s loop rule DC Ammeters and Voltmeters Ammeter: used to measure current (inserted into the circuit) Voltmeter: measures potential difference or voltage (connected in parallel) Galvanometer: the reading is by a pointer on a scale – works on the principle of the force between a magnetic field and a current-carrying coil of wire The deflection of the needle of a galvanometer is proportional to the current flowing through it. The full-scale current sensitivity, Im of a galvanometer is the current needed to make the needle deflect full scale. An ammeter consists of a galvanometer in parallel with a resistor (shunt resistor) Voltmeter uses series resistor effects of meter resistance: the more sensitive the galvanometer the less effect it will have Chapter 20 Magnetism Magnets and Magnetic Fields Every magnet has a north pole and a south pole where the magnetic effect is strongest. Like poles repel; unlike poles attract Unlike electric charge, it is impossible to isolate a single magnetic pole Only iron and few others such as cobalt, nickel and gadolinium show strong magnetic effects (are ferromagnetic). A force one magnet exerts on the other can be described as the interaction between one magnet and the magnetic field of another. Magnetic field lines: o The direction of the magnetic field is tangent to a line at any point o The number of lines per unit area is proportional to the magnitude of the magnetic field o Lines point the way that a compass arrow points (always towards south) Magnetic field is a vector B with direction defined by compass arrow and magnitude by the torque exerted on a compass needle Electric Currents Produce Magnetism Hans Christian Oersted (1777 – 1851) found that an electric current produces a magnetic field. Right hand rule: the direction of the magnetic field is the direction of thumb & fingers. Force on an Electric Current in a Magnetic Field; Definition of B A magnet exerts a force on a current-carrying wire The direction of the force is always perpendicular to the direction of the current and also perpendicular to the direction of the magnetic field, B (use right-hand rule, again) F IlB sin (magnetic field B is in tesla, T = N/Am) Fmax IlB Force on an Electric Charge Moving in a Magnetic Field F qvB sin Fmax qvB - again use a right-hand rule Magnetic Field Due to a Straight Wire I B r - magnetic field due to current in straight wire 0 I B 2r 0 4 10 7 Tm / A Force between Two Parallel Wires F 0 I1 I 2 l 2 L Definition of the Ampere and the Coulomb One ampere is defined as that current flowing in each of two long parallel conductors 1m apart, which results in a force of exactly 2 10 7 Nm 1 of length of each conductor. Thus the coulomb is exactly one ampere-second: 1C = 1As Electromagnets and Solenoids (p.610) Solenoid: a long coil of wire consisting of many loops of wire The magnetic field is large (sum of the fields due to the current in each loop) Acts like a magnet (north and south poles) Ampere’s Law