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# General Physics (Calculus) PHY 213

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This 12 page Class Notes was uploaded by Wilson Gibson V on Monday October 19, 2015. The Class Notes belongs to PHY 213 at Portland Community College taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/224632/phy-213-portland-community-college in Physics 2 at Portland Community College.

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Date Created: 10/19/15

Phy213 General Physics III 412008 Chapter 21 Worksheet 1 Coulomb s Law amp Electric Fields 1 Consider a fixed point charge of 15 uCq1A 2quotd charge of 05 uC qz is placed at a distance of 05 m from ql q115uC q2 O5uC a What is the magnitude and direction of the electric force exerted on qz due to ql Ans s A 15x10395C 05X10395C A A FE kq1 2i899x109i00270N i d 05m b A 3rd charge of 10 uC q3 is placed 025 m directly to the right of qz What is the magnitude and direction of the electric force exerted on q3 A 5 q1 15HC q2 05uC 1340 I k q1q3 k q2q3 04 quot 04 quot90 E dia3 dgt3 d m d m s 15x10395C 05x10395C A A FE 899x109N f10gtlt10395c 00479N i 075m2 025m2 c If q3 is exactly halfway between ql and qz what is the magnitude and direction of the electric force exerted on q3 q1 15uC q q2 05uC Ans 04gto4gtO d 25 m d 25 m qlqg qzqgjo F k k l E dia3 dgt3 5 5 a 899x10910x10395c M DEX 102C i 0288Ni C 025m 025m d If q3 is moved 03 m downward but still equidistant to ql and qz what is the magnitude and direction of the electric force exerted on q3 Fql Ans eq 5E kq1cosalqzcosazi q1c0501q2c05023 A 10gtlt106c 15x10395C05gtlt10395C cos502 39 E 899x109 2 C 0391m 15gtlt10395C05gtlt10395Csin502 J a 0075N i 0045N3 Phy213 General Physics III 412008 Chapter 21 Worksheet 2 e Where would q3 need to be placed such that there is no electrical force acting on the charge Ans Assume all charge positions are referenced to the origin at q3 a k d jlq3 k d qu3 J k d jlq3 k qu3 3 o N l 00 Ni x 1gt3 x 2A3 y 1A3 y 2A3 2 in X k djlqs k dqu3 3 dxzsg 323 lg 058 x1a3 x2a3 x1a3 x1a3 ql when qu 075 ml then x 043 ml 52 Jq j 058 dy1gt3 q1 when 3711 075 m3 then 3712 043 m3 k jlqg y 1A3 iny k dqug y 2A3 dy 2A3 d y 1A3 2 Consider a simple model of an atomic nucleus In this case three protons are present in the nucleus of a lithium atom forming an equilateral triangle The distance r between each pair of protons is 15 x 103915 m a What is the magnitude of the electric force exerted between any two of the protons 1602gtlt103919c2 103N 15gtlt103915m2 s e2 9 2 Ans b What is the magnitude and direction of the total electric force exerted on a proton due to its neighboring protons You will need to assign an appropriate coordinate system Ans Using the bottom charge as a reference and applying the Law of Cosines to the forces 2 2 2 2 2 2 FE Jk k 2k c05150 178 N Applying the Law of Sines to obtain the direction of the resultant force sin o o 3 swam o501 103N 178 N FE 178 N g1g sin391050130 south of or 210 wr to l c Express the total electric force vector in component form Ans Using the bottom charge as a reference e2 39 a k d2 1 coseo l sin60 J 155 N l 892 N3 Phy213 General Physics III 412008 Chapter 21 Worksheet 3 d What is the net force acting on the subject proton in b amp c Explain Ans Since the protons are fixed static equilibrium there must be at least 1 additional force acting on each nucleon to oppose the net electric net force Em IEEIE 0 N i 0 N3 This is was the justification for proposing a strong nuclear force within the nucleus 3 Consider the Bohr Model of the atom where an electron moves around a proton in a circular orbit Assume that the proton and electron are separated by a distance r of 529x103911 m x h proton 04quot0 Q r 529x10391fm electron a What is the magnitude and direction of the electric force exerted on electron quotquot 1602gtlt103919c2 529x103911m2 Ans H k 899gtlt109N quot2 824x10398N b What is the centripetal force exerted on the electron such that it maintains this orbit Ans ne E a 824x10398N c What is the speed of the electron Ans 2 E r 824x10398N 529x103911m 2 m V 824x10398N 3 v1 31 219x105g r m 911gtlt10 kg d What is the kinetic and potential energy respectively for the electron in J and eV Ans 3 c mv2 K 218X103918J 136 eV u IEE rcos 180 824gtlt10398N529x103911m 436gtlt103918J 272 eV e What is the total energy of the electron in J and eV Ans Etut K u 218x103918J 436gtlt1039183 218gtlt103918J or E K u 136 eV 272 eV 136 eV tot f Calculate the orbital radius for an electron with a total energy KU of 340 eV Phy213 General Physics III 412008 Chapter 21 Worksheet 4 Ans E K U 340 eV 545gtlt103919J tot 2 2 2 Em m2V FE rcos 180 m V m Vrcos 180 l39 2 2 Etot mZV mv2 mV 545gtlt1039ng or mv2 109x10 18J since E FE you can solve for r 2 2 2 899gtlt109339quot212 1602x103919c2 mquot ke 2rk e2 C 212gtlt10391 m r r mv 109x103918J 4 What is the total electric charge of 10 moles of electrons Ans Q Ne 6022x1023 elegyms1602x103919 elegmn 96400 5 How many electrons are present in 15 uC Ans 15X10395C N g 936gtlt1012 electrons e 1602x103919m or 15x10395C 156gtlt103911 mol 96400 Phy 213 General Physics III 6142007 Chapter 30 Worksheet Faraday s Law of Electromagnetic Induction and Lenz s Law 1 For the following scenarios determine whether the magnetic flux changes or stays the same If the flux changes indicate whether it is increasing or decreasing and in which direction Explain your answer a The magnet is held stationary to the solenoid b The magnet is moving towar the solenoid Ans 13 increasing lt 39639 c The magnet is moving away from the solenoid Ans dch decreasing dt v 2 Find the direction of the induced current for the solenoid in the figure below when the magnet is a stationary to the solenoid b moving toward the solenoid Ans counterclockwise c moving away from the solenoid Ans clockwise w Phy 213 General Physics III 6142007 Chapter 30 Worksheet 2 3 A circular loop radius of 10 cm or 010 m is placed in a uniform magnetic field of magnitude B 20 T where the face of the loop is perpendicular to the direction of the lamI1novanuprcaunvrninlrocIIIIIon a Determine the magnetic flux through the loop Ans ch j dA BAcos 0628 Tm2 b The loop is then rotated 90 in 30 seconds What is the magnetic flux through the loop at the end of the 30 seconds Ans CDB J39l3dA BAcos 0 Tm2 c What is the induced emf in the loop during the rotation 2 dltIgtB 0628 T m 00209 Tn2or V dt 3 s 4 A person moves a 2m rod at a constant velocity of 3 ms in a magnetic field B 20 T The rod is perpendicular to the direction of the B field Ans 8 a What is the direction of induced current in the rod Ans in the 2 direction A ABA A A A y b Determine the induced emfin the rod WIEBEquL q q q c The resistance in the rod and connecting wires is 29 What is the current in the rod Ans I i R 29 d Determine the magnitude and direction of the magnetic force acting on the rod Ans VBL 12 V 6A Ans IEBiEx 24Ni e Determine the force the person exerts on the rod to keep it in motion Ans lEnetlEBlEhand0 3 and 433 24Ni Phy 213 General Physics III 6142007 Chapter 30 Worksheet 3 5 Consider a 1m conducting rod attached at each end by conducting rails The rails are connected at the top and the total loop has a resistance of 59 see figure below The rod falls to the ground at a constant velocity v The apparatus is inside a constant magnetic field B 30 T directed out of the page The mass of the rod is 05kg B 30 T out of page R AA39 VV i1mi l V constant a What is the magnetic force on the falling rod due to the magnetic field Ans IEB IEnet mg mg 49N b What is the induced current in the rod Ans FB iLBsin 49N 3 i Fi 163A LB 1m3T c What is the induced electromotive force 3 Ans e iR 163A5 2 815 V d What is the equation for the rate of change of magnetic flux for this problem Ans dch BdiA BdLh BL BLV 8 dt dt dt dt e How fast is the rod falling Ans 7 8 83915 Vi 272j BL 3 T m f When the rail falls for 1 sec verify that energy is conserved Ans ng P5 gt mgv si gt M milg 271 checks with e Phy 2 Chapter 30 Works enerator 6 13 General Physics 111 6142007 heet 4 A water powered generamr shown below m convert mechanical energy inm electrical energy A rolatin heel receives falling wamr forcing a wire loop N500 located within a constant magnetic field 3001 T as shown m rolate oounmrrclockwiae at a rate of 150 len segment normal m the B field side a are 020 m and the lenglh of line segment parallel to me field side b is 015 m a what is me area of the region of me coil within the magnetic field Ans ab A 015m20m A 0030 m2 b Determine lhe general 39 for lhe magnetic flux through lhe Ooll n mrms o BI dAB A cosmt c what is the angular velocity u of the rotating coil Ans a 1501 39quot39quotHJ 1571 60 s 1 rot d Calculam the induced electromotive foroe around the loop Ans dlt1gt d N B N7 B A t 2 dt dt cosm NBAmjsinatdt X D 2NBAC Sampt1 4NBA 3m f f D f g 15 v 3V9 The lnstanlaneous emf is 2t NBAwsinat whatdlrection does the induced current flow around lhe ooil Explain Ans The current will flow clockwise looking down on lhe armature in accordance wllh RHR 5quot Phy 213 General Physics III 6142007 Chapter 30 Worksheet 5 Self Inductance 7 A solenoid r001 m 003 m length and N100 is in series with a 10 Q resistor both of which are in parallel with a 10 Q resistor all of these are in series with a 5 V power supply a Determine the inductance L of the solenoid 1052 Ans L uDNZA 396X10395H 1052 b When the power supply is initially 5 v connected What is the current across the solenoid IIII W 39 Ans iosolenoid 0A c What is the initial current drawn from the power supply 0 Ans i X 050A R d After 1 minute what is the current through the solenoid Ans39 isolenoid imaX 1e 12139e3QSSSOJS A e What is the total current drawn from the power supply Ans it 100A f How much energy is stored in the inductor after 1 minute Ans U 12Li2 495x10397J Phy 213 General Physics III Chapter 26 Worksheet 7212010 1 Ohm s Law amp Electrical Circuits 1 mN W What is the magnitude and direction of the current How many coulombs of charge flow in 20 min for What is the magnitude and direction of the current How many coulombs of charge flow in 50 min for Electric Current flows through the following network I consta nt i How many electrons flow in 20 min for constant i Electric Current flows through the following network i constant I How many electrons flow in 50 min for constant i Starting at to Os a wire conducts a timechanging current it of the form it imaxe T where imax50 A and 105 5 The resistance in the wire is 5 Q How much charge in coulombs will flow along the wire in 25 min How many electrons flow along the wire in 25 min What is the equation for the voltage as a function of time across this wire Phy 213 General Physics III Chapter 26 Worksheet 7212010 2 4 U1 039 O39 A resistor has cylindrical geometry with a resistivity p 35 x 10395 Q39m at 20 C and temperature coefficient on 50x10395 C391 The length of the resistor is 50x10393 m and the radius is 13x10394m What is the cross sectional area of the wire Determine the resistance at 20 C What is the resistivity and resistance at 150 C Consider the electrons of a car battery traveling along a wire toward a starting motor Assume that a current of 300 A travels along copper wire diameter 03 cm and length 085 m and the of charge carriers is 849x1028 m393 Determine the cross sectional area of the wire What is the drift velocity of the electrons in this current How long will it take electrons to get from a car battery to the motor The bulb of a typical light bulb is conducts 03 A of current at 29 V At room temperature 20 C the resistance of the tungsten filament is 11 Q What is the resistance of the bulb filament at 29 V What is the temperature of the illuminated tungsten filament How thick is the tungsten filament if the length of filament is 20 cm Phy 213 General Physics III Chapter 26 Worksheet 7212010 3 7 O39 D An electrical cable consists of 125 strands each with a resistance of 265 M A constant potential difference is applied between the ends of the cable resulting in a total current of 075 A along the cable What is the current in each strand What is the applied potential difference What is the resistance of the cable A certain space heater operating at 120V dissipates heat energy at a rate of 500 W during operation What is the resistance of the heater during operation How much current flows through the heating element during operation At what rate do electrons flow through any given cross section of the heater element What is the rate of heat energy transfer per coulomb What is the rate of heat energy transfer per electron

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