A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism SECTION V Electricity and Magnetism CIE A-Level [AS and A2] ________________________ Course Notes DIPONT Educational Resource - Science 1 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Syllabus Details______________________ DIPONT Educational Resource - Science 2 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism 17. Electric Fields [AS &A2]__________________ Content 17.1 Concept of an electric field 17.2 Uniform electric fields 17.3 Force between point charges 17.4 Electric field of a point charge 17.5 Electric potential [AS] [AS] [A2] [A2] [A2] Learning outcomes_____________________________________ Candidates should be able to: (a) show an understanding of the concept of an electric field as an example of a field of force and define electric field strength as force per unit positive charge acting on a stationary point charge Electric Field Force E=F/q Electric field = Force per unit test charge From Coulombs law E = q1 q2 Force q2 4 0r 2 q1 The electric field produced by a charge (q1) is defined in terms of a test charge (q2) This test charge will experience a force dependent only on the test charge The test charge must be so small as to not disturb the charge being considered The test charge is positive DIPONT Educational Resource - Science 3 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (b) represent an electric field by means of field lines Electric Fields Charged Sphere Parallel Plates + + + + + + + + + + + ------------ Point Charge + - + + Two Point Charges (c) recall and use E = V / d to calculate the field strength of the uniform field between charged parallel plates in terms of potential difference and separation Energy Difference in an Electric Field + + + + + + + + + + Lower electrical potential energy Higher electrical potential energy Force + q + q d - Change in electrical potential energy from A to B = force x distance Potential difference = electrical potential energy / charge Potential difference x charge = force x distance Electric field strength = force / charge = potential difference / distance E=V/d DIPONT Educational Resource - Science 4 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (d) calculate the forces on charges in uniform electric fields (e) describe the effect of a uniform electric field on the motion of charged particles (f) recall and use Coulomb’s law in the form F = Q1Q2/4πε0r 2 for the force between two point charges in free space or air Coulombs Law q1 force q2 force r F = kq1q 2 r OR 2 F = q1 q 2 2 4 0r 0 = permittivity of free space q = Charge r = Distance between charges k = coulombs constant q = Charge r = Distance between charges (g) recall and use E = Q/ 4πε0r 2 for the field strength of a point charge in free space or air Electric Field Force E=F/q Electric field = Force per unit test charge From Coulombs law E = q1 q2 Force q2 4 0r 2 q1 DIPONT Educational Resource - Science 5 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (h) define potential at a point in terms of the work done in bringing unit positive charge from infinity to the point zero potential at infinity potential increase F2 +Q F1 q q Force on q increases Electric Potential Energy of charge q = Qq 40r Electric potential energy: work done in moving a charge from infinity to a point Zero of potential energy is at infinity Potential energy taken as a negative value The work done in moving a charge between two points in an electril field is independent of the path taken Electric potential: Energy per unit test charge. (i) state that the field strength of the field at a point is equal to the negative of potential gradient at that point Electric potential Velec = Q 40r Gradient of this line = E r DIPONT Educational Resource - Science 6 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism F E= = q Q 40r 2 E = V r Electric Field = - potential gradient (j) use the equation V =Q/4πε0r for the potential in the field of a point charge Electric potential: Energy per unit test charge. Velec = V = Velec = work done test charge E q Q 40r V = electric potential (JC-1) Q = charge producing field This formula is given at the start of the test paper DIPONT Educational Resource - Science 7 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (k) recognise the analogy between certain qualitative and quantitative aspects of electric fields and gravitational fields. potential energy decreases as gravitational force does work zero potential energy at infinity F1 F2 M m m Force on m increases Gravitational potential energy of mass m= - GMm r Gravitational potential energy: work done in moving a mass from infinity to a point Zero of potential energy is at infinity Potential energy taken as a negative value The work done in moving a mass between two points in a gravitational field is independent of the path taken Gravitational potential: Energy per unit test mass. 18. Capacitance [A2]_________________________ Content 18.1 Capacitors and capacitance 18.2 Energy stored in a capacitor Learning outcomes_____________________________________ Candidates should be able to: (a) show an understanding of the function of capacitors in simple circuits Function of capacitors: Storing charge for rapid discharge (e.g. in a camera flash) DIPONT Educational Resource - Science 8 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (b) define capacitance and the farad (c) recall and solve problems using C= Q/V Capacitance: The charged stored (in coulombs) per volt of potential difference Farad (F): Unit of capacitance. 1 coulomb per volt. C= Q q/V (d) derive, using the formula C= Q/V , conservation of charge and the addition of p.d.s, formulae for capacitors in series and in parallel +q -q +q C1 V V2 V1 -q = +q -q C C2 V = V1 + V2 V1 = q / C1 and V2 = q / C2 (q = charge induced on one plate) q / C = q / C1 + q / C2 1 / C = 1 / C1 + 1 / C2 1/Ctotal = 1/C1 + 1/C2 DIPONT Educational Resource - Science 9 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism V V +q1 -q1 C1 = +q -q C +q2 -q2 C2 q = q1 + q2 q1 = C1V q2 = C2V CV = C1V + C2V C = C1 + C2 Ctotal = C1 + C2 These formula are given at the start of the test paper (e) solve problems using formulae for capacitors in series and in parallel DIPONT Educational Resource - Science 10 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (f) deduce, from the area under a potential-charge graph, the equation W=1/2 QV and hence W = ½ CV2. Potential Difference /V V0 q Charge /C Q = CV W= Ep = VQ Ep = V0q W = Ep = ½ QV W = Ep = ½ CV2 This formula is given at the start of the test paper DIPONT Educational Resource - Science 11 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism 19. Current of Electricity [AS]_________________ Content 19.1 Electric current 19.2 Potential difference 19.3 Resistance and resistivity 19.4 Sources of electromotive force Learning outcomes_____________________________________ Candidates should be able to: (a) show an understanding that electric current is the flow of charged particles Electrical Conduction Conventional Current Metal Wire Metal Ions Electrons Drift Velocity Current = Charge flowed time I = dQ dt 1 amp = 1 coulomb 1 second DIPONT Educational Resource - Science 12 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (b) define charge and the coulomb Charge: a fundamental property of some subatomic particles, which determines their electromagnetic interactions The Coulomb: The charge passing a point in a circuit when there is a current of one ampere for one second. (c) recall and solve problems using the equation Q = It Q = It (d) define potential difference and the volt (e) recall and solve problems using V = W/Q Potential difference: Energy difference between two points per unit charge for a charge in an electric field p.d. = Energy difference Charge Units of p.d. = JC-1 = Volt (V) V = W/Q (f) recall and solve problems using P = VI, P = I 2R Potential difference = energy difference / charged flowed Current = charged flowed / time taken Potential difference x current = (energy difference/charged flowed) x (charged flowed/time taken) Potential difference x current = energy difference / time taken = Power dissipated P = VI DIPONT Educational Resource - Science P = V2 R 13 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (g) define resistance and the ohm (h) recall and solve problems using V = IR Resistance: The ratio of the potential difference across an object to the current flowing through it. Ohm: The resistance when 1 Volt of potential difference gives a current of 1 Amp Resistance ) Potential Difference (V) Current (A) SEE PHET SIM R = V I (i) sketch and explain the I-V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp Ohmic and Non-ohmic behavior Filament Lamp Potential Difference Ohmic Behavior DIPONT Educational Resource - Science Current Diode Current Current Metal at constant temperature Potential Difference Potential Difference Non - ohmic Behavior 14 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Current (j) sketch the temperature characteristic of a thermistor (thermistors will be assumed to be of the negative temperature coefficient type) Hot Cold Potential Difference (k) state Ohm’s law Ohm’s Law: The current flowing through a piece of metal is proportional to the potential difference across it providing the temperature remains constant (l) recall and solve problems using R = L / A R= L A R = Resistance = Resistivity of material L = Length of conductor A = Area SEE PHET SIM DIPONT Educational Resource - Science 15 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (m) define e.m.f. in terms of the energy transferred by a source in driving unit charge round a complete circuit Electromotive force (e.m.f.): The total energy difference per unit charge around a circuit (n) distinguish between e.m.f. and p.d. in terms of energy considerations e.m.f. = (energy converted from other forms to electrical) / charge p.d. = (energy converted from electrical to other forms) / charge (o) show an understanding of the effects of the internal resistance of a source of e.m.f. on the terminal potential difference and output power. Internal Resistance Internal Resistance Perfect Battery e.m.f ri e.m.f Terminals of Battery R External Resistance = I x Rtotal = I(ri + R) = Iri + IR IR = e.m.f. - Iri Terminal p.d. ‘Lost’ volts SEE PHET SIM DIPONT Educational Resource - Science 16 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism 20. DC Circuits [AS]_________________________ Content 20.1 Practical circuits 20.2 Conservation of charge and energy 20.3 Balanced potentials Learning outcomes_____________________________________ Candidates should be able to: (a) recall and use appropriate circuit symbols as set out in the ASE publication Signs, Symbols and Systematics (b) draw and interpret circuit diagrams containing sources, switches, resistors, ammeters, voltmeters, and/or any other type of component referred to in the syllabus Cell Bell Variable resistor Fuse Resistor Transformer Lamp V Voltmeter A Ammeter Magnetizing Coils Relay Switch (c) recall Kirchhoff’s first law and appreciate the link to conservation of charge Kirchhoff’s First Law: The sum of the currents entering a junction is always equal to the sum of the currents leaving it DIPONT Educational Resource - Science 17 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (d) recall Kirchhoff’s second law and appreciate the link to conservation of energy Kirchhoff’s Second Law: The sum of the electromotive forces in a closed circuit is equal to the sum of the potential differences (e) derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in series R1 R2 V1 V2 For a series circuit… Emf = V1 + V2 IRtotal = IR1 + IR2 Rtotal = R1 + R2 (f) solve problems using the formula for the combined resistance of two or more resistors in series Series Circuit 24V Example at R1 I=2A V = IR V=2x3 V = 6V R1 = 3 R2 = 4 6V 8V R3 = 5 10V Rtotal = R1 + R2 + R3 This formula is given at the start of the test paper DIPONT Educational Resource - Science 18 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (g) derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in parallel V A R1 A1 V1 R2 A2 V2 I = I1 + I2 V / R = V1 / R1 + V2 / R2 V = V1 = V2 1 / R = 1 / R1 + 1 / R2 (h) solve problems using the formula for the combined resistance of two or more resistors in parallel Parallel Circuit 24V Itotal = 18.8 A 24V R1 = 3 I1 = 8 A 24V R2 = 4 I2 = 6 A 24V R3 = 5 I2 = 4.8 A 1/Rtotal = 1/R1 + 1/R2 + 1/R3 Itotal = I1 + I2 + I3 Itotal = V/R1 + V/R2 + V/R3 This formula is given at the start of the test paper DIPONT Educational Resource - Science 19 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (i) apply Kirchhoff’s laws to solve simple circuit problems (j) show an understanding of the use of a potential divider circuit as a source of variable p.d. Potential Divider Output voltage A Potentiometer: A variable potential divider. (k) explain the use of thermistors and light-dependent resistors in potential dividers to provide a potential difference that is dependent on temperature and illumination respectively Light Dependent Resistor (LDR) DIPONT Educational Resource - Science LDR When light shines on the LDR the resistance decreases 10 k When light shines on the LDR the p.d. across the fixed resistor increases 20 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Negative Temperature Coefficient (NTC) Resistors NTC Resistors 10 k When the temperature of the NTC increases the resistance decreases When the temperature of the NTC increases the p.d. across the fixed resistor increases (l) recall and solve problems using the principle of the potentiometer as a means of comparing potential differences. 21. Magnetic Fields [A2]______________________ Content 21.1 Concept of Magnetic Field Learning outcomes_____________________________________ Candidates should be able to: (a) show an understanding that a magnetic field is an example of a field of force produced either by current-carrying conductors or by permanent magnets (b) represent a magnetic field by field lines. Magnetic field lines Bar magnet DIPONT Educational Resource - Science 21 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Magnetic field around a current carrying wire 22. Electromagnetism [A2]____________________ Content 22.1 Force on a current carrying conductor 22.2 Force on a moving charge 22.3 Magnetic fields due to currents 22.4 Force between current-carrying conductors Learning outcomes_____________________________________ Candidates should be able to: (a) show an appreciation that a force might act on a current-carrying conductor placed in a magnetic field (b) recall, and solve problems using, the equation F = BIl sinθ, with directions as interpreted by Fleming’s left-hand rule The Left Hand Rule Direction of Force Direction of Magnetic Field Direction of Current DIPONT Educational Resource - Science 22 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism A current carrying wire in a magnetic field Magnetic Field Current Carrying Wire Direction of Force For a current carrying wire in a magnetic field… Magnetic Field, B Current, I Length of conductor in magnetic field, l Angle between field and current, F = BIl sin SEE PHET SIM (f) define magnetic flux density and the tesla Magnetic Flux Density: a measure of the strength of a magnetic field at a given point, expressed by the force per unit length on a conductor carrying unit current at that point. Tesla: The uniform magnetic flux density which, acting normally to a long straight wire carrying a current of 1 amp, causes a force per unit length of 1 Nm-1 on the conductor. DIPONT Educational Resource - Science 23 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (d) show an understanding of how the force on a current-carrying conductor can be used to measure the flux density of a magnetic field using a current balance A Magnetic field 00250.0g (e) predict the direction of the force on a charge moving in a magnetic field A moving charge in a magnetic field S Electron N Force (f) recall and solve problems using F = BQv sinθ For a moving charge in a magnetic field… Magnetic Field, B Charge, q Velocity of the charge, v Angle between field and velocity of charge, F = Bqv sin DIPONT Educational Resource - Science 24 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (g) sketch flux patterns due to a long straight wire, a flat circular coil and a long solenoid Solenoid Solenoid Magnetic Field Magnetic field around a current carrying wire DIPONT Educational Resource - Science 25 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Magnetic field lines A Flat Coil Circular current carrying coil SEE PHET SIM (h) show an understanding that the field due to a solenoid may be influenced by the presence of a ferrous core Magnetic field inside a Solenoid DIPONT Educational Resource - Science 26 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Current carrying conductors Current carrying conductors (i) explain the forces between current-carrying conductors and predict the direction of the forces Force Force Force Force (j) describe and compare the forces on mass, charge and current in gravitational, electric and magnetic fields, as appropriate. Substance Field Effect Uncharged mass Gravitational field Uncharged mass Uncharged mass Charged mass Electric field Magnetic field Gravitational field Positive charge Electric field Positive charge moving perpendicular to field Negative charge Magnetic field Negative charge moving perpendicular to field Current Current perpendicular to field Magnetic field Attracted in direction of field line No effect No effect Attracted in direction of field line Attracted in direction of field line Repelled perpendicular to field line Repelled in opposite direction to field line Repelled perpendicular to field line No significant effect Repelled perpendicular to field line DIPONT Educational Resource - Science Electric field Gravitational field Magnetic field 27 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism 23. Electromagnetic Induction [A2]_____________ Content 23.1 Laws of electromagnetic induction Learning outcomes_____________________________________ Candidates should be able to: (a) define magnetic flux and the weber (b) (b) recall and solve problems using Φ = BA Magnetic Flux ( ) a Are A B = BA cos Weber (Wb) = 1 Tm-2 Magnetic Flux: The product of the magnetic flux density and the area normal to the lines of flux Weber: A magnetic flux of 1 Tesla meter-squared = 1 Tm2 (c) define magnetic flux linkage Flux linkage = B N S Rotating coil Flux linkage = NBA cos N = number of turns on of coil DIPONT Educational Resource - Science 28 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (d) infer from appropriate experiments on electromagnetic induction: • that a changing magnetic flux can induce an e.m.f. in a circuit • that the direction of the induced e.m.f. opposes the change producing it • the factors affecting the magnitude of the induced e.m.f. (e) recall and solve problems using Faraday’s law of electromagnetic induction and Lenz’s law Electron moving in a metal conductor in a magnetic field Electron moving in magnetic field - X X X B X X X X X X X X X X X X - X X B X X X X X X X F = Bqv sin Induced Potential difference Velocity + X X X X X X X X X X X X - Electron at equilibrium V Wire length = l Magnetic field = B di f fe r en ce = Fm Po te n tia l Fe Velocity = v Electric force due to emf Magnetic force due to movement Fe = Eq = (V/l)q Fm = Bqv Bqv = (V/l)q V = Blv Induced emf = Blv (as no current is flowing V=emf) DIPONT Educational Resource - Science 29 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Wire length = l Magnetic field = B In time t …. Area A = lx velocity = v = Blv x v = x/t = Bl(x/t) = BA/t = BA = / t Area swept out by wire Faraday’s law: The magnitude of an induced emf is proportional to the rate of change of flux linkage. = N / t Lenz’s law: The direction of the induced emf is such that if an induced current were able to flow, it would oppose the change which caused it. Lenz’s law Force from induced current opposes original motion In d uc ed cu r re nt Magnetic field = B Velocity = v DIPONT Educational Resource - Science 30 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (g) explain simple applications of electromagnetic induction. Rotation AC Generator Induced emf Sinusoidal output Time 24. Alternating Currents [A2]_________________ Content 24.1 Characteristics of alternating currents 24.2 The transformer 24.3 Transmission of electrical energy 24.4 Rectification Learning outcomes_____________________________________ DIPONT Educational Resource - Science 31 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Candidates should be able to: (a) show an understanding of and use the terms period, frequency, peak value and root-mean-square value as applied to an alternating current or voltage (b) deduce that the mean power in a resistive load is half the maximum power for a sinusoidal alternating current p.d. + AC Supply current Time Power + Mean power Time - Period: The time for one complete cycle of the a.c. Root mean squared current (or voltage) is the value of the direct current (or voltage) that dissipates power in a resistor at the same rate. Peak Power Pmax = I02R Io = peak current Energy = power x time Energy supplied = area under the power-time graph Over one cycle the area under the graph = area under the midway level Mean power Pav= 1/2 I02R (Irms)2R = 1/2 I02R Irms = (1/√2) I0 R = Vo / Io = Vrms / Irms DIPONT Educational Resource - Science 32 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (c) represent a sinusoidally alternating current or voltage by an equation of the form x = x0sinωt p.d. V0 + current AC Supply I0 Time I = I0 sin wt - V = V0 sin wt t This formula is given at the start of the test paper (d) distinguish between r.m.s. and peak values and recall and solve problems using the relationship I rms = I0 /sqrt2 for the sinusoidal case Irms = (1/√2)Io Vrms = (1/√2)Vo (e) show an understanding of the principle of operation of a simple laminated ironcored transformer and recall and solve problems using Ns/Np = Vs/Vp = Ip/Is for an ideal transformer AC Generator Primary coil NP turns Secondary coil NS turns IP IS VP VS VP / VS = NP / NS = IS / IP DIPONT Educational Resource - Science 33 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (f) show an appreciation of the scientific and economic advantages of alternating current and of high voltages for the transmission of electrical energy Power losses in Electricity Transmission…. Resistance in the power lines causes heating Resistance in the coils of transformers causing them to heat up Eddy currents in the iron core. These can be reduced by making the core out of laminated sheets of metal connected with electrically insulating layers Flux losses caused by not all the magnetic flux produced by the primary coil linking with the secondary coil Electricity transmission lines have resistance, therefore, energy will be lost through heating in the wires Power dissipates in the wire as I2R. If a low current is used there will be less power dissipated. Transformers are used to step-up the voltage and so reduce the current used. High voltages also have risks (electrocution). The supply is passed through a step-down transformer before reaching the users. Full-wave rectification Potential Difference Output(V) Potential Difference Input (V) (h) distinguish graphically between half-wave and full-wave rectification DIPONT Educational Resource - Science Time Time 34 Half-wave rectification Time Potential Difference Output(V) Potential Difference Input (V) A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Time (h) explain the use of a single diode for the half-wave rectification of an alternating current Input AC Current Half-wave rectifier DIPONT Educational Resource - Science Output Rectified Current 35 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism (i) explain the use of four diodes (bridge rectifier) for the full-wave rectification of an alternating current Input AC Current Full-wave rectifier Output Rectified Current (j) analyse the effect of a single capacitor in smoothing, including the effect of the value of capacitance in relation to the load resistance. Potential Difference Output(V) Full-wave rectified input DIPONT Educational Resource - Science Output Time 36 A-Level Course Notes: PHYSICS SECTION V: Electricity and Magnetism Background Reading_________________ PHYSICS, Giancoli 6th edition, Chapter 16 - 21 Useful Websites______________________ http://phet.colorado.edu/en/simulations/category/new http://www.s-cool.co.uk/alevel/physics.html http://www.physicsclassroom.com/mmedia/index.cfm http://www.phys.hawaii.edu/~teb/java/ntnujava/index.html http://www.colorado.edu/physics/2000/index.pl Constants___________________________ [These are given on each test paper] DIPONT Educational Resource - Science 37