Physics 2102 Jonathan Dowling Physics 2102 Lecture 09 MON 02 FEB Electric Potential II Ch24 6 10 PHYS2102 FIRST MIDTERM EXAM 6 7PM THU 05 FEB 2009 Dowling s Sec 2 in Lockett Hall Room 6 YOU MUST BRING YOUR STUDENT ID The exam will cover chapters 21 through 24 as covered in homework sets 1 2 and 3 The formula sheet for the exam can be found here http www phys lsu edu classes spring2009 phys2102 formulasheet pdf THERE WILL BE A REVIEW SESSION 6 7PM WED 04 FEB 2009 in Williams 103 Conservative Forces Work and Potential Energy W F r dr Work Done W is Integral of Force F U W Potential Energy U is Negative of Work Done dU F r dr Hence Force is Negative Derivative of Potential Energy Coulomb s Law for Point Charge kq1q2 F12 2 r Force N Newton kq1q2 U12 r Potential Energy J Joule dU F12 12 dr q2 q1 P1 P2 U12 F12 dr kq2 E12 2 r Electric Field N C V m Electric Potential J C V Volt kq2 V12 r dV12 E12 dr q2 P2 P1 V 12 E 12 dr Electric Potential of a Point Charge P V E ds E ds f i R R kQ kQ kQ 2 dr r r R Note if Q were a negative charge V would be negative Electric Potential of Many Point Charges Electric potential is a SCALAR not a vector q4 Just calculate the potential due to each individual point charge and add together Make sure you get the SIGNS correct qi V k ri i r3 r4 q5 r5 Pr2 q2 r1 q1 q3 Electric Potential and Electric Potential Energy U Wapp q V Q a What is the potential energy of a dipole Q Q a Q First Bring charge Q no work involved no potential energy The charge Q has created an electric potential everywhere V r kQ r Second The work needed to bring the charge Q to a distance a from the charge Q is Wapp U Q V Q kQ a kQ2 a The dipole has a negative potential energy equal to kQ2 a we had to do negative work to build the dipole electric field did positive work Positive Work Q a Q Negative Work Q a Q Potential Energy of A System of Charges 4 point charges each Q and equal mass are connected by strings forming a square of side L Q Q If all four strings suddenly snap what is the kinetic energy of each charge when they are very far apart Q Q Use conservation of energy Final kinetic energy of all four charges initial potential energy stored energy required to assemble the system of charges Do this from scratch Potential Energy of A System of Charges Solution Q No energy needed to bring in first charge U1 0 L Energy needed to bring in 3rd charge kQ 2 kQ 2 U 3 QV Q V1 V2 L 2L Energy needed to bring in 4th charge 2kQ 2 kQ 2 U 4 QV Q V1 V2 V3 L 2L Q 2L Energy needed to bring in 2nd charge kQ 2 U 2 QV1 L Q Q potential energy is sum of Total all the individual terms shown on left hand side 2 kQ 4 2 L So final kinetic energy of each charge 2 kQ 4 2 4L Example qi V k ri i Positive and negative charges of equal magnitude Q Q Q are held in a circle of radius R 1 What is the electric potential at the center of each circle VB k 3Q 2Q r kQ r k 2Q 4Q r 2kQ r VC k 2Q 2Q r 0 VA A 2 Draw an arrow representing the approximate direction of the electric field at the center of each B circle 3 Which system has the highest electric potential energy UB Q Vb has largest un canceled charge C Electric Potential of a Dipole on axis What is V at a point at an axial distance r away from the midpoint of a dipole on side of positive charge V k Q k Q a a r r 2 2 a a r 2 r 2 kQ a a r r 2 2 Qa 2 a 4 0 r 2 4 p a Q Q r Far away when r a p V 4 0 r 2 Electric Potential on Perpendicular Bisector of Dipole You bring a charge of Qo 3C from infinity to a point P on the perpendicular bisector of a dipole as shown Is the work that you do a Positive b Negative c Zero U QoV Qo Q d Q d 0 a Q Q d P 3C Summary Electric potential work needed to bring 1C from infinity units V Volt Electric potential uniquely defined for every point in space independent of path Electric potential is a scalar add contributions from individual point charges We calculated the electric potential produced by a single charge V kq r and by continuous charge distributions V kdq r Electric potential energy work used to build the system charge by charge Use W qV for each charge
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