W03D2 Work Potential Energy and Electric Potential Today s Reading Assignment Course Notes Sections 4 1 4 3 1 Announcements PS 3 due Week Three Tuesday at 9 pm in boxes outside 32 082 or 26 152 W03D3 Reading Assignment Course Notes Sections 4 7 4 10 Exam One Thursday Feb 27 7 30 9 30 pm Room Assignments See Stellar webpage announcements 2 Outline Electrical Work Electric Potential Energy Electric Potential Difference Calculating Electric Potential Difference 3 Electrical Work Electrical force on object 1 due to interaction between charged objects 1 and 2 q1q2 F12 ke 2 r 12 r12 Work done by electrical force moving object 1 from A to B W1 B A F12 d s12 PATH INTEGRAL 4 Concept Question Sign of W Suppose a fixed positively charged object charge qs 0 is at the origin and we move a negatively charged object charge q1 0 from A to B with rA rB where r is the distance from the origin 1 2 3 4 Work done by the electrostatic force is positive and we do a positive amount of work Work done by the electrostatic force is positive and we do a negative amount of work Work done by the electrostatic force is negative and we do a positive amount of work Work done by the electrostatic force is negative and we do a negative amount of work 5 Group Problem Work Done by Electrical Force A point like charged source object charge qs is held fixed A second point like charged object charge q1 is initially at a distance rA from the fixed source and moves to a final distance rB from the fixed source What is the work done by the electrical force on the moving object Hint What coordinate system is best suited for this problem 6 Sign of W Negative Work Suppose a fixed positively charged source charge qs 0 is at the origin and a positively charged object charge q1 0 moves from A to B with rA rB where r is the distance from the origin then W 0 1 1 1 1 rA rB 0 and qs q1 0 W ke qs q1 0 rB rA rB rA 7 Work and Change in Kinetic Energy W K 8 Group Problem Work Kinetic Energy In a Uniform Electric field Consider two thin oppositely uniform charged thin plates separated by a distance d The surface charge densities on the plates are uniform and equal in magnitude An electron with charge e and mass m is released from rest at the negative plate and moves to the positive plate What is the speed of the electron when it reaches the positive plate 9 Potential Energy Difference Suppose charged object 1 is fixed and located at the origin and charge object 2 moves from an initial position A a distance rA from the origin to a final position B a distance rB from the origin The potential energy difference due to the interaction is defined to be the negative of the work done object 2 in moving from A to B 1 1 U U B U A F12 d s W ke qs q1 A rB rA B 10 Potential Energy Zero Point Choose the zero point for the potential energy at infinity U 0 Then set rA and rB r The potential energy difference between and any point on a circle of radius r is ke qs q1 U r U U r r 11 Concept Question Motion of Charged Objects Two oppositely charged are released from rest in an electric field 1 2 3 4 Both charged objects will move from lower to higher potential energy Both charged objects will move from higher to lower potential energy The positively charged object will move from higher to lower potential energy the negatively charged object will move from lower to higher potential energy The positively charged object will move from lower to higher potential energy the negatively charged object will move from higher to lower potential energy 12 Configuration Energy What is the potential energy stored in a configuration of charged objects Start with all the charged objects at infinity Choose U 0 1 Bring in the first charged object U1 0 2 Bring in the second charged object U 2 U12 ke q1q2 r12 3 Bring in the third charged object U 3 U 23 U13 ke q2 q3 r23 ke q1q3 r13 4 Configuration energy U U12 U 23 U13 ke q1q2 r12 ke q2 q3 r23 ke q1q3 r13 13 Group Problem Build It How much energy does it take you to assemble the charges into the configuration at left assuming they all started out an infinite distance apart 14 Electric Potential Difference Change in potential energy per test object in moving the test object charge qt from A to B B U F V d s E d s qt q A t A B Units Joules Coulomb Volts 15 Demonstration Van de Graaf D29 Breakdown of dry air 33 kV cm Video of Tesla Coil http www youtube com watch v FY AS13fl30 16 How Big is a Volt AA Batteries 1 5 V High Voltage Transmission Lines 100 kV 700 kV Car Batteries 12 V Van der Graaf 300 kV US Outlet AC 120 V Tesla Coil 500 kV Distribution Power Lines 120 V 70 kV Lightning 10 1000 MV 17 E Field and Potential Effects If you put a charged particle charge q in a field F qE To move a charged particle charge q in a field and the particle does not change its kinetic energy then U q V 18 Concept Question Motion of Charged Objects Two oppositely charged are released from rest in an electric field 1 2 3 4 Both charged objects will move from lower to higher electric potential Both charged objects will move from higher to lower electric potential The positively charged object will move from higher to lower electric potential the negatively charged object will move from lower to higher electric potential The positively charged object will move from lower to higher electric potential the negatively charged object will move from higher to lower electric potential 19 Potential External Work Change in potential energy in moving the charged object charge q from A to B U q V Conservation of Energy Law Wext K U 20 Demonstration Kelvin Water Drop in 26 152 Wimshurst Machine in 32 152 21 Demonstration Kelvin Water 22 Potential Created by Pt Charge V VB V A B A E ds B dr r kQ 2 d s kQ 2 A A r r 1 1 kQ rB rA B Take V 0 at r kQ VPoint Charge r r r E kQ 2 r d s dr r r d 23 Concept Question Two Point Charges The work done in moving a positively charged object that starts from rest at infinity and ends at rest at the point P midway between two charges of magnitude Q and Q 1 2 3 4 is positive is negative is zero can not be determined not enough info is given 24 Potential Landscape Positive …
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