Introductory Physics PHYS 202
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Chapter 1 O 0 Research De ned as a process of steps used to collect and analyze information to increase our understanding of a topic or issue It consists of three steps Pose a question collect data to answer the question and present an answer to the question that in the absence of what we call a research question or a research problem research does not exist 0 independent variable what the researchers want to study 0 If for example the research question is quotWhat are the effects of sleep deprivation on motor performancequot the independent variable is sleep depnva on dependent variable the things the researchers will measure in order to study the effects of the independent variable 0 scienti c method 0 0000000 0 O O 0 Chapter 2 The scienti c method is a structured orderly process for conducting a research study Step 1 Understanding the Problem Area Step 2 Identifying the Research Question or Problem Step 3 Formulating the hypothesis Step 4 Planning Methodology for the study Step 5 Collecting the data Step 6 Analyzing the Data with Statistical Tools Step 7 Interpreting and Discussing the Results Internal validitv extent to which results can be attributed to the treatments External validity generalizability of results to population at large TVpes of Research Basic conducted purely for the discovery of new knowledge with little regard for whether there is an immediate application for that new knowledge Applied driven by the need to nd a solution to a speci c problem Quantitative enable description of existing conditions analysis of relationships among different variables and study of causeeffect relationships typically begins with identi cation of one or more research questions and related hypotheses that can be tested through collection and statistical analysis of numerical data Qualitative characterized by the collection of observations by the researchers through rst hand onsite note taking analysis of videotapes and audiotapes in depth interviews and researcherdesigned questionnaires Experimental carried out for the expressed purpose of con rming or refuting causeeffect relationships Experimental research questions aim at achieving understanding of the phenomenon being studied NonExperimental does not involve any manipulation of independent variables by the researchers an example would be descriptive amp correlational research 0 Characteristics of Good Research Writing 0 O grammatically correct and follows standard rules of punctuation and spelling instructive readily comprehensible and to the point 0 clear avoiding unnecessary jargon and long complex sentences and owing smoothly in a logically organized progression Importance of Develooino an Outline 0 it is important to have a clear written outline organizing your thoughts before you start writing 0 Your outline need not be formal a simple list of points that you want to convey in the order in which you wish to present them will typically suf ce 0 Elements involved in different editorial styles 0 Editorial style governs the speci c organization and formatting for elements such as the components of a paper and the headings for each section the reference list citation of references within the text gures and tables use of statistical symbols Chapter 3 0 Different Purposes That Literature Reviews Can Serve 0 General Purpose why your topic is of interest or importance what related research has been published on your topic and which important question remains unanswered o Other Purposes documenting that little to no research has been done in a new emerging area demonstrating that there is controversy or disagreement surrounding a particular practice or explaining why a study using new stateof theart instrumentation or methodology is needed to reevaluate an existing belief Strategies for Searching the Published Literature 0 There are a variety of online search engines available for identifying published papers related to a topic 0 Critique Quality of Papers oCritiquing a Research Paper One Section at a Time Questions about the Introduction 0 Do the rst several sentences capture the reader s attention o Is a compelling rationale for the study presented o Is it clear how the present study ts within the body of existing literature o Is the purpose of the study clearly and concisely stated Questions about the Methods section 0 Are the participants characteristics clearly identi ed o Is the apparatus or instruments described in suf cient detail that another researcher could repeat the study o Is the experimental protocol clearly spelled out o Are the statistical procedures explained Questions about the Results o Is the description of the results complete concise and well organized Are tables and graphs appropriately used to supplement the text without being redundant Chapter 4 Are tables and graphs clearly labeled and do they contain enough information to quotstand alonequot Are interpretive comments saved for the Discussion section Questions about the Discussion and Conclusions Are the results related back to the hypothesis Are the results explained within the context of the results of similar studies Are limitations of the study that con ne the applicability of the results mentioned Are any unexplained factors or loose ends addressed Are the conclusions appropriate given the results and delimitations of the study General Questions Is the reader left with the feeling of quotSo whatquot Is it clear that this study was worth conducting Was the study interesting Was the paper well written Did the study uncover new information Do the results of this study form the basis for new research questions 0 Importance of a Sound Research Question or Problem 0 the research question is the focal point or driving force for the study It is also sometimes referred to as the problem statement since it is in fact usually presented in the form of a statement rather than a question 0 Purpose and organization of each of the components of a typical research proposal 0 Proposals begin with an introduction that logically leads the reader down a path of understanding where the proposed research problem ts within the context of what is known based on the related research literature as well as why the projected results of the proposed study are of potential importance The introductory section ends with a clear statement of the research problem or the speci c aims and related research hypotheses The proposed methods section includes a description of the study participants the study protocol and the planned statistical analysis 0 Different purposes and associated target audiences for research proposals 0 Chapter 5 o Plagiarism Plagiarism is the dishonest act of presenting intellectual property including a piece of writing a drawing or an idea that originated with someone else as if it had originated with you In the United States most published writings are protected by copyright law 0 Research proposals are written in different lengths and formats depending on the target audience Audience may include thesisdissertation committee an Institutional Review Board or a potential funding source 0 Appropriate Range of Measures for Dealing with data outliers 0 An outlier is a measurement or observation that is way out of line with the rest of the data set Outliers can result from a transient malfunction of data collection O apparatus a quotbugquot in software or from collection of data on a subject who has characteristics that are markedly different in some way from the other subjects it would unquestionably be appropriate to discard the faulty data make sure everything is working properly and ask the subject to be retested 0 Ethical Considerations in the Protection of Human Subject 0 There are federal regulations that govern handling and storage of data protection of human subjects and protection of animal subjects and it is imperative that students develop a good understanding of the regulations relevant to their own research interests 0 Example would be informed consent Chapter 6 0 Criteria For a CauseEffect Relationship 0 A causeeffect relationship can only be documented through carefully designed studies that rst show a relationship between the cause and the effect but then go on to show through logical interpretation that one factor is the cause and the other the effect 0 Experimental research is carried out for the expressed purpose of con rming or refuting causeeffect relationships 0 if the study is designed with good internal validity any changes in the dependent variables can be attributed to the manipulation of the independent variable and a causeeffect relationship is shown 0 General Cateoories of Threats to Internal and External Validitv o Recognized categories of threats to internal validity include history maturation testing instrumentation statistical regression selection biases experimental mortality interaction of selection bias and experimental mortality and expectation o Recognized categories of threats to external validity include the interactive effects of testing the interaction of selection bias and experimental treatment the reactive effects of experimental setting and multiple treatment interference 0 Research designs are grouped into preexperimental designs which are weak in controllingthreats to validity true x 39 threats to valli je ma a li me Fm external validity is more of a priority HFafEE gm Mg pgtmr 0 Steps in The ExperimentahResearch Processff rimetai designs whic are strong in controlling quot rst are gsed in situations when lEerrniLlllate reaearalrl quea ena 4 Eerrnallate reaea rah fljrpatlheaea Plan and earnuet study 4 einalyae elala and evaluate reaulta Heaulta auggleat a A new reaeareh fellawu aluy intereat emrg ea 1F Chapter 7 0 Descriptive Research the research intends to capture thoughts attitudes behaviors physical attributes and other characteristics of groups so as to provide a characterization of the group at a certain point in time 0 Speci c Types of Descriptive Research Approaches o Correlational research Examining the relationship between or among variables 0 Survey Research Questionnaires Interviews 0 Other Descriptive Research Approaches Case Studies Developmental Observational Chapter 9 Both historical and philosophical research are important to the eld of kinesiology and health sciences Historical research involves developing a pertinent question then answering it through an exploration of primary and secondary evidence Philosophical research involved developing a thesis then searching for logical arguments through inductive or deductive reasoning that will support or refute the thesis Epidemiological research involves investigation populations for determinants of disease Cross sectional designs look at a cross section of the population at one point in time in order to determine current relationships among determinants There are three types of analytic designs Cohort designs start with a population and follow over time to see who does and does not develops a disease state Case Control designs examine a population retrospectively Randomized Controlled designs provide an intervention to a sample within the population and compare outcomes with control groups Single Subject design research provide a means for determining causation when the population under study are highly variable Single baseline and reversal designs involve adding an intervention one or several times and comparing dependent measures to those of the baseline Multiple baseline designs involve providing an intervention just one time but at different time intervals for each participant Metaanalysis is the process of examining a relatively large group of studies that have similar independent and dependent variables and determining a general effect size for all of the studies Exa m 1 Notes Chapter 21 Electric Current and Dielectric Electric Current 0 Electric current is the ow of electric charge 0 l AQAt Unit ampere 1 A 1 Cs Current ows from the positive to the negative charge ie the opposite to the ow of the electrons Battery 0 Uses chemical reactions to maintain a potential difference between its terminals 0 A battery that is not included in an electric circuit has an electric potential difference between its terminals that is called electromotive force emf Work done by battery moving charge around circuit W AQemf Enerov Storage in Capacitors 0 Energy is stored in the electric eld between the plates of the capacitor energy QV2 Parallel capacitors 0 U 12 EoE2Ad Ad D total volume of the capacitor 0 electric energy density per unit volume of the capacitor is then UAd l2 oE2 The energy stored in the capacitors of a circuit does not disappear when an electric device is turned off Resistance 0 Resistance in a conductor is due to the motion of the electrons in it 0 Ohm stated the relation of the voltage to the current 0 V IR D RVl measured in Ohms Example Question You double tlliie voltage The conclusion should be that Ohm39s law is not obeyed because it suggests a linear relation between potential and current When you across a certain conductor and you observe the current increases quot99 quot193 What double the voltage the current can you conclude should also double D this indicates Resistance and Resistivitv that Ohms law is not universal Two wires of the same diameter and length will have different resistance if they are made of different materials D this is called resistivity The de nition of the resistivity p is R pLA o L is the length of the wire and A is its cross section area Exa m 1 Notes 0 Example problem D The resistance of wire Two wares and aremade ofthe a GA 1 MB A is higher because its same metal and have equal length D an 213 cross section is 4 times but the resistance ofwire is four cl dA 1 dB smaller than that of wire timestlner esiist aliceolwire Hlow d GA 2 102 3 ThUS its radius ShOUld do their diameters compare e dA 14113 be 12 that Of Wire B o The resistance of a material goes up when the temperature increases because of thermal motion 0 Resistivity generally decreases when the temperature goes down The resistance of a superconductor drops suddenly to zero at the critical temperature Tc Energy and Power in Electric Circuits When a charge moves across potential difference its potential energy changes 0 AU AQV The power it takes to do this is l P AUAt AQ39VAt The current I AQAt so P W o The SI unit for power is a watt W o If the material obeys Ohm39s law P 2R V2R Kwh is a measure of the electric energy that one has used 0 1 kWh 1000 W3600 s 36x106J Resistors Resisters in Series 0 Resistors connected end to end are resistors in series 0 Such multiple resistors can be replaced by one with higher resistance without changing the current in the circuit l R c m A Req R1 R2 9 E V g H2 x g Rm V3 QM Tj B o The total potential in the circuit should be the sum of the potential differences over each of the resistors D Req ZRindividua Exa m 1 Notes 0 Example Problem Assume that the Voltage of the battery is 9V and that the 3 resistors are identical What is the potential difference acrc 39 a 7 7 T Since the three resistors are the same the voltage should drop 1 equally at all of them The potential 91 drop per reSIstor IS 3V 0 Example Problem 2 In the circuit l Pquot R a R 2n The potential difference over the rst 39i39 f 2 resistor should be twice as high as over the second one because Its reSIstance IS i twice as big Voltage is 12 V and the q 1 potential drop over the rst resistor Resistors in Parallel l o Resistors are in parallel if they are across the 1 same potential difference o Resistors in parallel can also be replaced by a single resistor but of a different value from the in series case 0 Total current is the sum of the currents over q each resistor o 1Req 1R1 1R2 1R3 ZlRi Note The equation above gives you the inverse of the resistance not the resistance itself 0 Example In the circuit below what is the current through R1 5 H J A v 3974 m I39l in 76 M A WV E I 3 V The voltage is the same 10 V across each resistor since they are in parallel We can use Ohm39s law AV R to nd the current through R1 WW The current is AVR 10 V Sohms 2A Complex CerUItS contaln rESISLUID Ill DCIICD allu ICDIDLUID Ill paIaIICI 1 i if i i l F771 l SE MR I I ll I l I 39 it ll LE1EEJ inl iii lcl We can rst deal with the two resistors in And the nally the total resistance R arae p IS 1Req 1R2 1R3 1Req R2 R3R2R3 Req R2R3R2 R3 R Req R1 R4 Exa m 1 Notes Kirchhoff39s rules Junction rule All current that enters a junction must also leave it Loop rule The algebraic sum of all potential charges around a closed loop must be zero Circuits containing Capacitors Capacitors in Parallel 0 When capacitors are in parallel the potential difference across each one is the same One can then replace them with an equivalent capac on o The equivalent capacitance in the case of parallel capacitors is the sum of the individual ones CeqC1C2C3 The SI unit is farad F Capacitors in Series 0 Capacitors arranged in series do not have the same potential difference but they all carry the same charge 0 1Ceq 1C1 1C2 1C3 o Capacitors in parallel combine as resistors in series and vice versa 0 Example Problem D What is the capacitance Ceq of the combination below M We rst have to solve for the two capacitors G l 39 are in series their total capacitance is C2 C a C 397 We are then left with two parallel capacitors quot9 CE C for which we have to add the capacitances o 0 o The answer then is 1 12 C 3C2 LU LIIC VUILUHC UI VL UMIUJJ the bCLUHU LddelLUl I If 2 Lil th The voltage across C1 is 10 V The other two capacitors are in series and the l voltage across the two of them is also as e g 10 V Their sum and C1 are in parallel TUE Z L luF so the voltage across each one is 5 V 0 RC ciI If a circuit contains only batteries and capacitors the charge appears almost simultaneously on the capacitors after the circuit is connected Exa m 1 Notes Chapter 22 Magnetism All magnets have two poles North and South 0 If we break a magnet its two pieces will also have two poles Magnetic Field Lines 0 Magnetic eld lines do not intersect 0 Magnetic eld lines are always closed loops 0 The southern magnetic pole of the Earth is close to the North rotational pole o The direction in which a compass points is the direction of the magnetic South 0 Geomagnetism The Earth magnetic eld is reversed with respect to to its North and South poles The geomagnetic eld is inclined by 1150 from its rotational axis The South magnetic pole lies in Eastern Canada Magnetic Force 0 Magnetic force on an electric charge is F qvBsine o e is the angle between the particle velocity and the direction of the magnetic eld 0 To determine the direction of the force in the case of a positive charge we use the righthand rule If the charge does not move the force is zero Right Handed Rule 1 RightHand Rule 1 determines the directions of magnetic force conventional current and the magnetic eld Given any two of theses the Using your righthand thirdb point your index nger in the direction of the charge39s velocity v can 9 recall conventional current Point your middle nger in the direction of the magnetic eld B Your thumb now points in the direction of the magnetic force Fmagnetic found 2 RightHand Rule 2 determines the direction of the magnetic eld around a currentcarrying wire and viceversa Exa m 1 Notes 0 Using your righthand Curl your ngers into a halfcircle around the wire they point in the direction of the magnetic eld B Point your thumb in the direction of the conventional current Using your righthand Curl your ngers into a halfcircle around the wire they point in the direction of the magnetic eld B Point your thumb in the direction of the conventional current Electric Charge Examples An electric eld a charge particle accelerates in the direction of the eld or opposite to it In a magnetic eld the force is in a direction that is perpendicular to both the magnetic eld and the particle velocity The electric eld does work on the charged particle the magnetic eld does not and the particle speed remains constant 0 If the particle motion is perpendicular to the magnetic eld it results in a circular motion around it F qvB mv2r gt r mVQB o If the particle motion is parallel to the magnetic eld it experiences no force and moves in a straight line o In case the particle moves at an angle to the magnetic eld it experiences helical motion 1 BELL 1F Particle 1 with a charge q1 of 36 pC and speed a V1 862 ms travels at right angle through an uniform magnetic eld It experiences a magnetic force of 425x103 N o For particle 1 sine 1 The magnetic eld B then equals Fqv 425x103 ch N36x106C862 ms r The magnetic eld B 137T tesla Particle 2 with charge 53pC moves at an angle of 55 deg with respect to B Find the strength of the magnetic eld B and the force that particle 2 experiences if it moves with 1300 ms 0 The force on the particle 2 is 53x106 C1300 ms137 Tsin 55 00773 N Circular Motion Exa m 1 Notes 0 Circular motion the centripetal acceleration of a particle with mass m moving with velocity v in a circle of radius r is a v2r The equation for the radius of the circle r is F qvB mv2r gtr mvlgBl Example problem If an electron moves perpendicular to B of 43mT on a circle of radius 28 mm what is its velocity r mvqB gt v rqBm v 00002816X103919 C000046 T911x103931 kg 226x106 ms T required for a particle of mass m and charge q to complete a circular orbit in magnetic eld B o T 2nmqB 0 Does not depend on the initial particle velocity v 0 particles with higher velocity before entering the magnetic eld area move on circles with larger radii Helical Motion 0 The fraction of the particle velocity that is parallel to B vcose remains constant while the part perpendicular to B vsine causes motion 0 The combination of both motions creates a helical path Force on Charoe A charge experiences a force in a magnetic eld independently of it moves in vacuum or on a wire 0 Charge D q IAt ILv force on a current carrying wire put at angle from the direction from the magnetic eld and carrying an electric ux o F qusineILBsine A charge moving in a magnetic eld experiences a force independently of the medium of its movement vacuum or a wire 0 Example problem A copper rod 15 cm long is suspended from two thin wires At right angle in the page is magnetic eld of 055 T Find the direction and the magnitude of the electric eld that can levitate the rod whose mass is 005 kq Solution We have to set the gravitational force downward In this case the magnetic force is F ILB perpendicular and the gravitational force is F mg For the magnetic force to go upwards we need the current to ow to the right Then making the forces equal ILB mg we have I mnlI F2 In nRIr IO Q1 mlc lln 1 mln RRT I 039 l Exa m 1 Notes 0 Torque l T NIAB sine o N is the number of turns on the general loop and A is the area of the loop 0 The units of the torque are Nm o Rectangle T IBA o the maximum torque on the loop will happen when its plane is perpendicular to the magnetic eld direction perpendicular to the page Example Problem with 2 Parallel Wires 5 I1 6 Magnetic e1d due to I 0 Two parae wires separated by of 22 V cm carry currents in the same direction The current in the rst wire GD 12 G is 15 A and in the second one is 45 A 8 EMagne c eMduemz Find the value of the magnetic eld between the wires 0 Solution The magnitude of the magnetic eld generated by wire 1 B pol2nd 27x10396 and the eld goes into the page 0 pa 4n x10397 T39mA Magnetic eld generated by wire 2 is 81x10396 T and comes out of the page Therefore The net magnetic eld is their difference 81 27x10396 T 54x10396 T that comes out of the page Ampere39s law 0 relates the current enclosed in a loop to the magnetic eld it creates The law is ZB polEndosed where B is the longitudinal magnetic eld uo is the permeability of free space and equals 4n x10397 T39mA Maonetic Field magnetic eld of a long straight wire carrying a current I generates a magnetic eld of magnitude B pol2m r is the distance from the wire 0 the forces between two wires carrying current is F JollIzLZl39ld o L is the length of the wires and d is the distance between them 0 The magnetic eld in the center of a current loop of N turns radius R and current I is Exa m 1 Notes o B poNlZR Solenoid Magnetic materials Homework 1 Conceptual Exercise 226 A solenoid is a loop of many turns that form a cylinder of length L The magnetic eld inside a solenoid is almost uniform and parallel to the solenoid axis For a solenoid of N loops in a length L carrying a current I the magnetic field is B poNLl and is independent of the radius of the solenoid It is often expressed in the number of loops per length nNL and becomes B JonL I B WltEgtl Lilli Ferromagnets are materials that organize their magnetic domains in the presence of external magnetic eld The domains arrange themselves almost parallel to the external eld Ferrormagnets retain their domains organized after the external eld is removed permanent magnets Paramagnets can organize their domains in the presence of external eld but do not retain this organization when the external eld is removed Diamagnetism is a magnetic effect in which some materials in which an external magnetic eld creates an oppositely directed magnetic eld These elds are usually small but in some cases it could be strong enough to generate levitation Suppose the three particles in the gure have the same mass and speed Rank the particles in order of decreasing magnitude of their charge Solution CltBltA A is the largest Steps 1 Fqusine l the force is perpendicular making 6 90 sine then equals 1 making the equation Fqu 2 Since the F is perpendicular because it moves along a circle it experiences a centripetal force which is equal to mv2r 3 You then set qu mv2r mV and B are stated to be the same for each charge making the relationship r 1q bigger radius has smaller q Problem 2228 An alpha particle the nucleus of a helium atom consists of two protons and two neutrons and has a mass of 664x10 27kg A horizontal beam of alpha particles is injected with a speed of 13x105ms into a region with a vertical magnetic eld of magnitude 0170T Exa m 1 Notes Part A How long does it take for an alpha particle to move halfway through a complete circle 1 V rqBm v 2nrT l combine rqBm2nrT l simplify to get T 2nmICIIB 2 Whole revolution T 2nmqB 2n664x10 27kg32x103919 0170T 7487x10397 3 Divide T by 2 to nd time for half of a revolution l 7487x103972 l 38x10397 seconds Part B If the speed of the alpha particle is doubled does the time found in part A increase decrease or stay the same 0 It will stay the same because time is not dependent on speed 0 V rqBm v 2nrT l combine rqBm2nrT l simplify to get T 2nmIQIB 3 Problem 2236 A highvoltage power line carries a current of 116A at a location where the Earth39s magnetic eld has a magnitude of 059 G and points to the north 72 below the horizontal Part A Find the magnitude of the magnetic force exerted on a 270m length of wire if the current in the wire ows horizontally toward the east 1 Given B596 59x10394 T 116A G18072108L270m 2 FBLsine 59x10394 T116A270msin108 18 N Part B Find the direction of the magnetic force exerted on a 270m length of wire if the current in the wire ows horizontally toward the east 0 Force points toward north 180 above the horizontal 0 9072 18 0 See picture Part C Find the magnitude of magnetic force exer on a 270m length of wire if the current in the wire flows horizontally toward the south 1 FBLsine 59x10394 T116A270msin108 18 N Exa m 1 Notes Part D Find the direction of the magnetic force exerted on a 270m length of wire if the current in the wire ows horizontally toward the south 0 force points toward the east 4 Problem 4 Find the magnetic eld 675cm from a long straight wire that carries a current of 788A Buoll2nr 47x103977882n0675 233 x10398T Physics Exam 1 Notes Chapter 19 Electric Charges Forces and Fields Electric Charde The unit of charge is coulomb C o All electrons have the same electric charge e 160 X 1019 C in SI units 0 The protons in an atomic nucleus also have the same amount of charge but it has the opposite sign 0 Similar charges repel one another while opposites attract Electron Proton Charge e e Mass 911 103931 kg 167 103927 kg Polarized moelt lel 16210490 0 materials can be polarized which means that their atoms rotate in response to external charge 0 note The material is still neutral but its inner structure has changed Insulators and Conductors Conductor is a material in which electrons are free to move 0 Most metals are conductive Insulator is a material whose electrons rarely move from atom to atom If you charge a conductor its charge excess will move to the surface of the conductor because equal charges repel each other If the charges are on the surface they are as far away from each other as possible 0 Ex A metal ba hangs from the ceiling by an insulating thread The ball is attracted to a positive charged rod held near the ball The charge of the ball must be The charge of the ball must be negative or neutral 0 This is because if the ball is attracted by a positive charge it has to be negatively charged If can also be neutral if it is polarized where its atoms are rotated by induction to create an attractive force Coulombs Law 0 iqiiirpi o F JCT measured in newtons N and the constant k 899 x 109 Nmzcz 0 force is attractive if the charges are opposite and it is repulsive if they are the same 0 Multiple Charges The forces add by superposition as shown in the gure below The total force I39lFl 1 illggiywi 3 t if F 3 I5139 in f 12 2 if 7 k r e 239 1 1 39 Physics Exam 1 Notes Coulomb39s law continued 0 Coulomb s Law is very similar to Newton39s third law force is proportional to the product of the masses of the 2 objects divided by the square of the distance between them normalized with the gravitational constant one big difference the gravitational force is always attractive while the electric force could also be repulsive The Electric Field 0 The electric eld is the force eld per charge at a given position in space E FqoEo k qr2 0 measured in WC and is in the direction of the force 0 Since the force is proportional to the distance from the charge squared so is the electric eld 0 A positive charge experiences a force in the direction of the eld 0 A negative charge experiences a force in the opposite direction 0 The magnitude of the force F qE POSEtiVE Charge the Negative charge the Electric e39d lJOlin ES electric eld points at it away from it x439 39rx f x 0 Electric Field Lines 0 Electric eld lines always point in the direction of the electric eld vector 0 Field lines start at positive charges or in nity 0 Field lines end at negative charges or in nity 0 There are denser where the eld is stronger 0 Electric eld lines cannot intersect Example problem Two positive point charges ql 16mC and q2 4mC are separated in vacuum by 30 m Find the spot on the line between the charges where the net electric eld is zero UL i i1 kll xw c k 40x10 6C I ii quot d2 awn d lt2 n m 18 kid2 2 4L llltlquot3d2 E Z k 2x3m d l d r d 20 m Physics Exam 1 Notes 0 Electric Field Lines for a Combination of Charges 0 Equal positive and negative charges at certain distance from each other 0 NoteD close to the charges eld lines are very similar to the eld lines for individual charges 0 Also Note D the eld is weaker where the eld lines are less dense but it is not zero between the lines Shielding and Charging bv Induction Shielding 0 electric charges on the surface of the sphere are at rest the electric eld inside is zero The conductor shields its interior from external elds but does not shield the exterior from elds that are inside it 0 Only works in one direction 0 Charging by induction 0 charge an object without touching it This is because electric forces can act at a distance 0 A charged rod induces and charges on the opposite sides of a conducting sphere If the rod is negatively charged the near side of the sphere is positively charged Electric Flux a measure of the electric eld perpendicular to a surface I A COS ibl Electric lluxlfl 1 Electric lluleE cos lzl SI unit N lzC Gauss39 law 0 States that the electric ux through a closed surface is proportional to the charge enclosed by the surface 1 r l 12 2 r r 2 a 39 I i 80 885 X 10 C Nm DE ZEms m If the Chi 5i the VOIUFFlTe is positive the electric eld leaves the enclosed volume and the electric ux is positive If the charge is negative the ux is negative because the eld enters the enclosed volume Homework Physics Exam 1 Notes 1 Problem 196 Part A Find the net charge of a system consisting of 623gtlt1O6 electrons and 787gtlt1O6 protons o Protons electrons 16 x 10 19 net charge 0 787X106 623X106 16 X 10 19 262X103913 C Part B Find the net charge of a system consisting of 220 electrons and 178 protons o Protons electrons 16 x 10 19 net charge 0 178 220 16 X 10 19 672X103918 C 2 Problem 1930 A point charge q 037nC is xed at the origin Where must an electron be placed in order for the electric force acting on it to be exactly opposite to its weight Let the yaxis be vertical and the Xaxis be horizontal o The electron will feel the repulsion of the negative charge so it must be placed vertically up above the given charge Thus x will be zero 0 To solve for y you use the equatio n H I and us mg for F H 12 o 911 x 1031 kg98 89539 quotquot 2 gtlt 10 19C37x103910r2 Solve for r l r 24x105 0 Coordinates for placement of the electron D O 24x105 3 Problem 1943 What is the magnitude of the electric eld produced by a charge of magnitude 710uC at a distance of a 100 m and b 200 m o E kqr2 O E 12 X10 titanium 0 B E 899x109 71x10396 22 16 x10 j15 g surface 4 Problem 1970 A thin wire of in nite extent has a charge per unit length of l Using the cylindrical Gaussian surface 395 shown in the gureFigure 1 show that the electric eld produced by this wire at a radial distance I has a magnitude given by El2neor 0 Solution The Gaussian surface is chosen to be a cylinder with radius r and length L and its axis is along the wire The eld is expected to have the same magnitude everywhere on the surface of the cylinder because the surface is a constant distance from the wire The ux through the curved surface of the cylinder is everywhere positive because the eld lines are leaving the volume The ux through the end caps is zero because none of the eld lines pierce those surfaces The total charge enclosed by the cylinder is the wire39s charge per unit length lambda times the cylinder length L Use these facts together with Gauss39s law to determine the magnitude of the eld at the surface of the cylinder Chapter 21 Homework Problem 2114 The tungsten lament of a light bulb has a resistance of 6x10 20 If the filament is 29cm long what is its diameter 0 Resistance of a wire R pLA R is resistance p is resistivity L is the length and A is the cross sectional area 0 the electrical resistivity of Tungsten is 528 nQm 528x10399 6x10 20 528x1039929mA A 2552x10397 m2 o A Hr2 2552x10397 d2r D 57 x 10 Conceptual Exercise 2124 Light A has four times the power rating of light B when operated at the same vo age Part A Is the resistance of light A greater than less than or equal to the resistance of light B o The resistance of light A is less than the resistance of light B Part B Explain part A o The resistance of light A will be less than the resistance of light B Power is equal to velocity squared over the resistance Therefore since A has 4 times the power of B this would mean that B has for times the resistance of A Ultimately making the resistance ratio of light A to B would be 25 A circuit consists of a battery connected to three resistors 650 300 and 1800 in parallel The total current through the resistors is 18A PartA Find the emf of the battery 0 1Req1R1 1R2 1R3 1651301180 0543 Req 184 0 Emf IR 184 18A 33V Part B Find the current through each individual resistor 0 650 I VR 3365 51 A 0 3OQllVR 3330 11A 0 1800 I I VR 33180 183 A Chapter 21 Homework Cl ll Terminals A and B in the gure are connected to a H 90Vbattery Figure 1 Consider C1 16pF C2 EE E 76JF and C3 22pF Find the energy stored in each C CH capacitor U a C1 is in parallel to the battery V1 Vbattery 9V U1 12CV2 1215x1039692 65 x 103 b C2 and C3 are in parallel to the battery and in series to each other C2 and C3 in series equals 2276296 565 uF C23 Ctotal 565 uF 16uF 2165 uF 2165x10398 F Capacitors in Series have the same charge D QZQ3Ql Charge on C2 and C3 D Q C23V 565x10399 F9 5085x10398 uC V2 Qz3C 2 5085X1039976X10399 669 V U2 1276X10399669V2 17x10397 V3 Qz3C3 5085X10391922 231 V U3 1222X103992312 59x103911 Exa m 1 N otes Chapter 20 Electric Potential and Electric Electric Potential Enerdv The electric potential at a given point is the electric potential energy of a small test charge divided by the charge itself joulecoulomb volt 0 V UCIo The change of the electric potential as a function of the position is 0 AV AUCIO WABq0 The electronvolt eV is an unit of energy it is the change of energy an electron experiences when moved through a potential difference of one volt o 1 eV 160x1019 Cx1 V 160x1019J o The electronvolt is the basic measure of energy in particle and nuclear physics 0 Electric Potential Energylj U Electric Potential or simply potential l V Relationship between the change of the electric potential and the electric eld 0 AV Wq EAs 5 direction qcharge Velectric potential Wwork q charge 0 Note 1 Wm 1 NC The electric eld depends on the rate of change of the electric potential with position Work and Potential Enerdv The work needed to assemble a collection of charges is the total potential energy of those charges 39 U leQzr Conservative and Nonconservative Forces Conservative force is one that stores the work it does in the form of energy that can be released at a later time 0 work done by a conservative force moving an object on a closed path is zero D not true for nonconservative forces 0 Example gravity Nonconservative Force 0 Nonconservative forces such as friction that depend on other factors such as velocity are dissipative and no potential energy can be de ned for them Work 0 Work in gravitational eld 0 WFdmghi hfUiUfAU Work in electric eld O W Fd qOEhihf Ui39Uf39AU The electric force is conservative Therefore there must be potential energy associated with it It takes work to move an electric charge in electric eld W qud Exa m 1 N otes The change of the potential energy is the negative of the work AU W qOEd Energy Conservation For a mass m moving from A to B due to a conservative force we have va22 UA I39TlVB2 Us For an electric force we have U qV so that D va22 qVA mv322 qVB The difference in the potential energy between the points A and B is I UA UB kqoqrA kqoqrB Superposition of electric potentials o The total electric potential due to two or more charges is the algebraic sum of the potentials due to all charges separately 0 Note that the electric potential is a scalar it does not have a direction It can have though positive or negative sign because of the different signs of the charges Example 7 Answer The difference 0 0 Four POIDt charges are between electric arranged at the corners and Potentl l IS that the of a 37 mare Firquotj the eld has a direction 0 q i 1 away from positive electric field Eanct the charges For this potential Vat the center r ason the Pfot ntial in 0 O 0 10 of the Square t e center 0 t e square cancels but the eld Electric potential and electric eld have the same relationship There are lines and in 3D surfaces that have the same constant potential The electric eld is perpendicular to these surfaces and stronger where the lines are closer together 0 2D example of equipotential lines for a single charge 10 v The stronger the potential the closer the t 39 equipotential lines are The electric eld 5 7 g is always perpendicular to them ED 20V 5 u quot15v 10V 1n it n 10 Example 2 At iiEghich point the potential is zero a b c d or in all t Answer All points are at the same distance from the charges The charges are 0 and Q Their contribution to the potential cancel at the midplane between the charges d Exa m 1 N otes Eduipotential Surfaces and Electric Field 0 An equipotential surface is a surface for which the potential is for all points of the surface constant o If two conductors have the same potential the one that is more curved will have a stronger electric eld around it o The same is true for different parts of the same conductor Same electric potential V HighChlrgli fjl ltl 39 high electric field I39ll Low charge density 1mm i k Equipntemtlal EU 139 Fa Example Prolem Which of these con gu l WhE El ias V O on all points of the x axis All None 2 C 1uiC 2 y 1 c i X X r x 39 O 39 o O f 1pC 1110 Answer D Ebure A has equal and oppobie charges that cancel each the X axis VO Figure B has none and C has charges where VO on the y axis 0 Example 2 Which two points have the same potential 0A g V kQ r for a pomt charge 39 39 quot 39 39 The equipotential surfaces are quotquotquot quotquotquot spheres with the charge at the origin The answer would be C I and E given they have the sa me rad i us quot ff 3quot all I gift Iquotquot nequotquot4 hquotquotquot39r uaquotquot Exa m 1 N otes Capacitors and Dielectrics o O Capacitors consists of two conductor plates separated by a nal distance this arrangement has the capacity to store both electric charge and ener The capaci gaynce relates the charge and the potential difference C QN Unit is farad F coulombvolt Parallel plate capacitor C EoAd so 885x103912 C2Nm2 l permittivity of free space so 25kn l where k is the dielectric constant Example A parallel plate capacitor consists of two plates of area 0028 m2at a distance of 56 mm Find the magnitude of the charges on the plates if V 20 V The capacitance C is de ned in two ways quotl c ov sAd We know the values of V A and d 0 Storage of Electric Energ Assume permittivity e 1 Q 5 VAd 20x0028l000056 Example 2 1000 C a C21 bl Ce c tooth have the same charge Capaciter C1 is connected across a battery of 5 V An identical capacitor is connected across a battery of 10 V Which one has more charge d it depends on other factors The correct answer is B C2 Q CAV Thus the capacitor that is connected to the battery of 10 V has twice the charge We can calculate h ng the amount of energy 1er one The voltage increa Je during charging correljncr 0 V 39b39i39f ewequot Chapter 20 Homework Problem 208 When an ion accelerates through a potential difference of 2120V its electric potential energy decreases by 136x10 15J What is the charge on the ion 0 AV AUq 0 2120V 136X10 15Jq E q 641X10 451 pt 23 M the gure in nitely far from one another How much work must be done to move the three charges in wmr WM 1 I iii m I O W UOOUi j U00 I zero 7 r y a ell 3961 X 10396 3392 27 X 106 0393 X 106 1393 ML r12 25 r13 16 r23 297 WHEN w Ui kq1q2r12 kq1q3r13 kq2q3r23 u 899 x 10961 x 106 27 x 106 25 899 x 10961 x 106 33 x 106 16 899 X 10927 X 10396 33 X 10396 297 Ui 5923 113 2697 268 0 W UwUi O 27 27 Part A What pate area is required if an air lled paraepate capacitor with a plate separation of 24mm is to have a capacitance of 27pF 0 C kEoAd k dielectric constant for air k 1 0 Given C 27pF 27x 103912 F k1 d24mm 0024m so 8854 X 10 12 A 27x 103912 18854 X 10 12A0024m C 00732 m2 Part B What is the maximum voltage that can be applied to this capacitor without causing dielectric breakdown V E x d For air dielectric strength 30 x 106 vm V 30 x 106 x 0024 7200V Problem 2068 What electric eld strength would store 160 of energy in every 300mm3 of space 0 Energy density energyvolume U 16 V300mm3 3 x 10399 50 8854 X 10 12 x2UVa E 0 3x10 9 216J 8854x1012 347 X 1010 Vm
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