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Chapter 8 Electricity and Magnetism Sections 8.1-8.5 Electric Charge & Force • Electric charge is a fundamental quantity – we don’t really know what it is – But we can describe it, use it, control it – Electricity runs motors, lights, heaters, A/C, stereos, TV’s, computers, etc. • Electric Forces – at the microscopic level they hold atoms and molecules together – Electric Forces hold matter together – Gravitational Forces hold the universe together • Magnetism is also closely associated with electricity Copyright © Houghton Mifflin Company. All rights reserved. Intro 8|2 Electric Charge and Current • Experimental evidence leads us to conclude that there are two types charges – Positive (+) – Negative (-) • All matter is composed of atoms, which in turn are composed of subatomic particles – Electrons (-) – Protons (+) – Neutron (neutral) Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8|3 Properties of Electrons, Protons, and Neutrons • Note that the Proton and Neutron each have about 1000x more mass than the Electron • If the atom has the same number of protons and electrons it is electrically neutral Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8|4 Coulomb = Unit of Electric Charge • Named after a French scientist – Charles Coulomb (1736-1806) • Note that the charge on a single electron (-) or proton (+) is 1.60 x 10-19 C (very small!) • When charge is in motion electric current • Current = time rate of flow of electric charge • Current = charge/time = I = q/t Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8|5 Current • I = q/t – I = electric current (amperes) – q = electric charge flowing past a point (coulombs) – t = time for the charge to pass point (seconds) • 1 ampere (A) = flow of 1 Coulomb per second • Rearrange equation above: – q = It or 1 coulomb = 1 ampere x 1 second • Therefore, 1 coulomb is the amount of charge that flows past a given point in 1 second when the current is 1 ampere Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8|6 Conductors/Insulators • Electrical conductor – materials in which an electric charge flows readily (most metals, due to the outer, loosely bound electrons) • Electrical insulator – materials that do not conduct electricity very well due to very tight electron bonding (wood, plastic, glass) • Semiconductor – not good as a conductor or insulator (graphite) Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8|7 Finding the Amount of Electric Charge - Example • A wire carries a current of 0.50 A for 2 minutes. a) how much (net) charge goes past a point in the wire in this time? b) how many electrons make up this amount of charge? • • • GIVEN: I = 0.50 A, t = 2 minutes (120 seconds) WANTED: q (charge) & n (number of electrons) (a) q = It = (0.50 A)(120 s) = 60 C (coulombs) Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8|8 Finding the Amount of Electric Charge - Example • A wire carries a current of 0.50 A for 2 minutes. a) how much (net) charge goes past a point in the wire in this time? b) how many electrons make up this amount of charge? • To solve for (b), we know that each electron has a charge of 1.6 x 10-19 C and we know the total charge from part (a) = 60 Coulombs • n = 60/(1.6 x 10-19 C / electron) = 3.8 x 1020 electrons Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8|9 Another Example • If 5.0 x 1019 electrons go by a given point in a wire in 2/3 minute, what is the current in the wire? • Given: n = 5.0 x 1019 electrons, t = 40 seconds, q = 1.6 x 10-19 C (for each electron) • I = q/t • = [(1.6 x 10-19 C)(5.0 x 1019)]/40 s = 8.0C/40s • = 0.20 A Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8 | 10 Electric Force – Law of Charges • An electric force exists between any two charged particles – either attractive or repulsive • Law of Charges – like charges repel, and unlike charges attract (this gives the direction of electric force) – Two positives repel each other – Two negatives repel each other – Positive and negative attract each other Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8 | 11 Coulomb’s Law • Force of attraction/repulsion between two charged bodies is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them • F = (kq1q2) / r2 – – – – – F = force of attraction or repulsion q1 = magnitude of the first charge q2 = magnitude of the second charge r = distance between charges k = constant = 9.0 x 109 N-m2/C2 Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8 | 12 Comparison of Coulomb’s Law & Newton’s Law of Universal Gravitation • Equations look similar – F = (kq1q2) / r2 & F = Gm1m2/ r2 • Both depend on r2 • Coulomb’s law can describe either an attractive or repulsive force – gravity is always positive • Electrical charges are much stronger than gravitational forces Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8 | 13 Negative/Positive • An object with an excess of electrons is said to be negatively charged • An object with a deficiently of electrons is said to be positively charged • Photocopier (xerography) – practical and widespread use of electrostatics Copyright © Houghton Mifflin Company. All rights reserved. Section 8.1 8 | 14 Repulsive and Attractive Electrical Forces Two negative charges repel Two positive charges repel Repulse Repulse Copyright © Houghton Mifflin Company. All rights reserved. One negative and one positive attract Attract Section 8.1 8 | 15 Electric Potential Energy • When work is done to separate positive and negative charges, we have electric potential energy Copyright © Houghton Mifflin Company. All rights reserved. Section 8.2 8 | 16 Voltage • Instead of measuring electric potential energy, we measure the potential difference, or voltage • Voltage – the amount of work it would take to move a charge between two points, divided by the value of the charge • Voltage = work / charge = V = W/q • Measured in volts (V) = 1 joule/Coulomb • When we have electric potential energy, this may be used to set up an electrical current Copyright © Houghton Mifflin Company. All rights reserved. Section 8.2 8 | 17 Ohm’s Law • Whenever there is an electrical current, there is resistance (R) within the conducting material – R is due to atomic/subatomic collisions • Georg Ohm (1787-1854) – formulated a simple relationship between voltage, current, and resistance • Ohm’s Law V = IR – V = voltage in volts, I = current in amperes, and R = resistance in ohms • 1 ohm = 1 volt/1 ampere (R=V/I) Copyright © Houghton Mifflin Company. All rights reserved. Section 8.2 8 | 18 Simple Electrical Circuit • Electrons flow from negative terminal to positive terminal (provided by the chemical energy of the battery) -negative to positive • Open switch – not a complete circuit and no flow of current (electrons) • Closed switch – a complete circuit and flow of current (electrons) exists • Closed Circuit Required – to have a sustained electrical current Copyright © Houghton Mifflin Company. All rights reserved. Section 8.2 8 | 19 Simple Electrical Circuit The light bulb offers resistance. The kinetic energy of the electric energy is converted to heat and radiant energy. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.2 8 | 20 Electrical Circuit & Waterwheel Analogy Insert figure 8.5, p.189, 11/e Section 8.2 Electrical Power • • • • • • • • • Recall: P = W/t (Power = work/time) – Ch. 4 V = W/q (Voltage = work/charge) – Ch. 8 Rearrange V=W/q W = qV Substitute W = qV into P = W/t equation Result P = qV/t Recall that I = q/t (Current = charge/time) \ P = IV (Electric power = current x voltage) also P = I2R (substitute in V = IR) P in watts, I in amperes, R in ohms, V in volts Copyright © Houghton Mifflin Company. All rights reserved. Section 8.2 8 | 22 Finding Current in Resistance -Example • Find the current and resistance of a 60-W, 120-V light bulb in operation. • Given: P = 60W, V = 120 V • Find: I (current in amperes), R (resistance in ohms) • Since P = IV I = P/V = 60 W/120 V = 0.50 A • Since V = IR R = V/I = 120 V/0.50A = 240 W • Since P = I2R R = P/I2 = 60 W/(0.50 A)2 = 240 W Copyright © Houghton Mifflin Company. All rights reserved. Section 8.2 8 | 23 Equation Review • Current: I = q/t – I = current (amperes), – q = electric charge (coulombs), – t = time (seconds) • • • • Coulomb’s Law: F = kq1q2/r2 Voltage: V = W/q [Work is in joules (J)] Ohm’s Law: V= IR Electrical Power: P = IV = I2R Copyright © Houghton Mifflin Company. All rights reserved. Section 8.2 8 | 24 Forms of Electric Current • Direct Current (dc) – the electron flow is always in one direction, from (-) to (+) – Used in batteries and automobiles • Alternating Current (ac) – constantly changing the voltage from positive to negative and back – Used in homes. – 60 Hz (cycles/sec) and Voltage of 110-120 V Copyright © Houghton Mifflin Company. All rights reserved. Section 8.3 8 | 25 Simple Electric Circuits in Series • Plugging appliances into a wall outlet places them in a circuit – either in series or in parallel • In a series circuit, the same current (I) passes through all the resistances. – The total resistance is simply the sum of the individual resistances. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.3 8 | 26 Series Circuit • Rs = R1+R2+R3+… • If one bulb were to burn out the circuit would be broken, and all the lights would go out Same current all the way Section 8.3 Simple Electric Circuits in Parallel • In a parallel circuit, the voltage (V) across each resistance is the same, but the current (I) through each may vary. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.3 8 | 28 Parallel Circuit I = I1+I2+I3+… for R in parallel: 1/Rp = 1/R1+1/R2+… for 2 R in parallel: Rp = (R1R2)/(R1+R2) Current Divides, Voltage is the same Copyright © Houghton Mifflin Company. All rights reserved. Section 8.3 8 | 29 Resistances in Parallel - Example • Three resistors have values of R1=6.0W, R2=6.0W, and R3=3.0W. What is their total resistance when connected in parallel, and how much current will be drawn from a 12-V battery if it is connected to the circuit? • 1/Rp = 1/R1+1/R2+1/R3 = 1/6 + 1/6 + 1/3 • 1/Rp = 1/6 + 1/6 + 2/6 = 4/6 W • Rp = (6 W)/4 = 1.5 W = Total Resistance • I = V/Rp = (12 V)/(1.5 W) = 8.0 A = current drawn Copyright © Houghton Mifflin Company. All rights reserved. Section 8.3 8 | 30 Household Circuits110-120 V • Wired in parallel independent branches any particular circuit element can operate when others in the same circuit do not. Section 8.3 Electrical Safety • Wires can become hot as more and more current is used on numerous appliances. • Fuses are placed in the circuit to prevent wires from becoming too hot and catching fire. • The fuse filament is designed to melt (and thereby break the electrical circuit) when the current gets too high. • Two types of fuses: Edison and S-type • Circuit Breakers are now used. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.3 8 | 32 Fuses Copyright © Houghton Mifflin Company. All rights reserved. Section 8.3 8 | 33 Electrical Safety with Dedicated Grounding • A dangerous shock can occur if an internal ‘hot’ wire comes in contact with the metal casing of a tool. • This danger can be minimized by grounding the case with a dedicated wire through the third wire on the plug. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.3 8 | 34 Magnetism • Closely associated with electricity is magnetism. • In fact electromagnetic waves consists of both vibrating electric and magnetic fields. These phenomena are basically inseparable. • A bar magnet has two regions of magnetic strength, called the poles. • One pole is designated “north,” one “south.” Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 35 Magnetic Poles • The N pole of a magnet is “north-seeking” – it points north. • The S pole of a magnet is “south-seeking” – it points south. • Magnets also have repulsive forces, specific to their poles, called … • Law of Poles – Like poles repel and unlike poles attract – N-S attract – S-S & N-N repel Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 36 Law of Poles All magnets have two poles – they are dipoles Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 37 Magnetic Field • Magnetic field - a set of imaginary lines that indicates the direction in which a small compass needle would point if it were placed near a magnet • These lines are indications of the magnetic force field. • Magnetic fields are vector quantities. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 38 Magnetic Field • The arrows indicate the direction in which the north pole of a compass would point. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 39 Source of Magnetism • The source of magnetism is moving and spinning electrons. • Hans Oersted, a Danish physicist, first discovered that a compass needle was deflected by a current-carrying wire. – Current open deflection of compass needle – Current closed no deflection of compass needle • A current-carrying wire produces a magnetic field: stronger current stronger field • Electromagnet – can be switched on & off Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 40 Magnetic Materials • Most materials have many electrons going in many directions, therefore their magnetic effect cancels each other out nonmagnetic • A few materials are ferromagnetic (iron, nickel, cobalt) – in which many atoms combine to create magnetic domains (local regions of magnetic alignment within a single piece of iron) • A piece of iron with randomly oriented magnetic domains is not magnetic. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 41 Magnetization • The magnetic domains are generally random, but when the iron is placed in a magnetic field the domains line up (usually temporarily). Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 42 Electromagnets • A simple electromagnet consists of an insulated coil of wire wrapped around a piece of iron. • Stronger current stronger magnet • Electromagnets are made of a type of iron that is quickly magnetized and unmagnetized – termed “soft.” Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 43 Curie Temperature & Permanent Magnets • Materials cease to be ferromagnetic at very high temperatures – the “Curie temperature” • Permanent magnets are made by permanently aligning the many magnetic domains within a piece of material. • One way to create a permanent magnet is to heat the ferromagnetic material above the Curie temperature and then cool the material under the influence of a strong magnetic field. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 44 Earth’s Magnetic Field • This planet’s magnetic field exists within the earth and extends many hundreds of miles into space. • The aurora borealis (northern lights) and aurora australis (southern lights) are associated with the earth’s magnetic field. • Although this field is weak compared to magnets used in the laboratory, it is thought that certain animals use it for navigation. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 45 Earth’s Magnetic Field • Similar to the pattern from a giant bar magnet being present within the earth (but one is not present!) Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 46 Earth’s Magnetic Field • The origin of the earth’s magnetic field is not completely understood. – Probably related to internal currents of electrically charge particles in the liquid outer core of the earth, in association with the earth’s rotation • The temperatures within the earth are much hotter than the Curie temperature, so materials cannot be ferromagnetic. • The positions of the magnetic poles are constantly changing, suggesting “currents.” Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 47 Magnetic Declination • Magnetic declination – the angle between geographic (true) north and magnetic north • The magnetic declination varies depending upon one’s location on Earth. – In the northern hemisphere the magnetic North Pole is about 1500 km from the geographic North Pole. • Therefore, a compass does not point to true north, but rather magnetic north. – An adjustment (magnetic declination) must be made to determine true north from a compass. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 48 Magnetic Declination Needs to be known for proper navigation Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 49 Useful Equations • Resistance in Series: Rs = R1+R2+R3+… • Resistance in Parallel: 1/Rp = 1/R1+1/R2+… • For 2 R in parallel: Rp = (R1R2)/(R1+R2) Copyright © Houghton Mifflin Company. All rights reserved. Section 8.4 8 | 50 Electromagnetism • • Electromagnetism – the interaction of electrical and magnetic effects Two basic principles: 1) Moving electric charges (current) give rise to magnetic fields (basis for an electromagnet). 2) A magnetic field will deflect a moving electric charge (basis for electric motors and generators). Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 51 Telephone – Electromagnet Application • Telephone transmission involves the conversion of sound waves into varying electric current • Sound waves at the transmitting end vibrate a diaphragm that puts pressure on carbon grains • The varying pressure on the carbon, results in varying amounts of resistance in the circuit • By Ohm’s law (V=IR), varying resistance results in varying current Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 52 Telephone – Electromagnet Application • The varying current gives an electromagnet at the receiving end varying magnetic strengths • The electromagnet is drawn toward/away a permanent magnet as a function of the electric current in the line • The electromagnet is attached to a diaphragm that vibrates, creating sound waves that closely resemble the original sound waves Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 53 Simple (one-way) Telephone Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 54 Magnetic Force on Moving Electric Charge • When a moving charge (a current) enters a magnetic field, the moving charge will be deflected by the magnetic field • The magnetic force (Fmag) is perpendicular to the plane formed by the velocity vector (v) of the moving charge and the magnetic field (B) Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 55 Magnetic Deflection • Electrons entering a magnetic field experience a force Fmag that deflects them “out of the page” Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 56 Magnetic Force on a Moving Charge • A beam of electrons is deflected downward due to the introduction of the magnetic field of a bar magnet Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 57 Magnetic Field and Force on a CurrentCarrying Wire • Since a magnetic field deflects a moving charge, a current-carrying wire loop will experience a force Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 58 A stationary wire with no current will not experience a force in a magnetic field Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 59 A current-carrying wire in a magnetic field experiences a force, out of the page as shown here Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 60 Motors • Electric motor – a device that converts electrical energy into mechanical work • When a loop of coil is carrying a current within a magnetic field, the coil experiences a torque and rotates Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 61 A dc Motor • The split-ring commutator reverses the loop current every half-cycle, enabling the loop to rotate continuously • The inertia of the spinning loop carries it through the positions where unstable conditions exist Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 62 Motion and Induced Current The Basic Principle of the Electric Generator • When a wire is moved perpendicular to a magnetic field, the magnetic force causes the electrons in the wire the move – therefore a current is set up in the wire Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 63 Generators • Generator – a device that converts mechanical energy into electrical energy • Generators operate on the principle of electromagnetic induction • Electromagnetic induction was discovered by the English scientist, Michael Faraday in 1831 – When a magnet is moved toward a loop or coil of wire, a current is induced in the wire – The same effect is obtained if the magnetic field is stationary and the loop is rotated within it Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 64 Electromagnetic Induction • A current is induced in the circuit as the magnet is moved toward and into the coil Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 65 An ac Generator • When the loop is rotated within the magnetic field a current is induced in the loop • The current varies in direction every halfcycle and is termed alternating current (ac) Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 66 Electrical Transformers • Transformers serve to step-up or step-down the voltage of electric transmissions • A transformers consists of two insulated coils of wire wrapped around an iron core – The iron core serves to concentrate the magnetic field when there is a current in the input coil • The magnetic field resulting from the primary coil goes through the secondary coil and induces a voltage and current Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 67 A Step-up Transformer • Since the secondary coil has more windings, the induced ac voltage is greater than the input voltage. • The factor of voltage step-up depends on the ratio of the windings on the two coils. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 68 Why Step-up the Voltage? • The main reason is to reduce the amount of current going through the lines – As the current is reduced, the amount of resistance is also reduced – If the amount of resistance is reduced, the amount of heat (called ‘joule heat’ or ‘I2R’ losses) • For example, if the voltage is stepped-up by a factor of 2, the resulting I2R losses would be reduced four-fold Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 69 Voltage Change for a Transformer Equation • The voltage change for a transformer is given by the following: • V2 = (N2/N1)V1 • V1 = primary voltage • V2 = secondary voltage • N1 = Number of windings in primary coil • N2 = Number of windings in secondary coil Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 70 Finding Voltage Output for a Transformer An Example • A transformer has 500 windings in its primary coil and 25 in its secondary coil. If the primary voltage is 4400 V, find the secondary voltage. • Use equation V2 = (N2/N1)V1 • Given: N1 = 500, N2 = 25, V1 = 4400 V • V2 = (25/500)(4400 V) = 220 V • This is typical of a step-down transformer on a utility pole near homes Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 71 Electrical Transmission System Voltage is dramatically stepped-up at the generating plant to minimize joule heat loss during long-distance transmission. The voltage must then be stepped-down for household use. Copyright © Houghton Mifflin Company. All rights reserved. Section 8.5 8 | 72