Physics 2102 Jonathan Dowling Physics 2102 Lecture 07 TUE 09 FEB Electric Potential II QuickTime and a decompressor are needed to see this picture PHYS2102 FIRST MIDTERM EXAM 6 7PM THU 11 FEB 2009 Dowling s Sec 4 in YOU MUST BRING YOUR STUDENT ID YOU MUST WRITE UNITS TO GET FULL CREDIT The 24 and can exam will cover chapters 21 through as covered in homework sets 1 2 3 The formula sheet for the exam be found here http www phys lsu edu classes spring2010 phys2102 for mulasheet pdf KNOW SI PREFIXES n cm k etc ervative Forces Work and Potential En W F r dr U W dU F r dr Work Done W is Integral of Force F Potential Energy U is Negative of Work Done Hence Force is Negative Derivative of Potential Energy Coulomb s Law for Point Charge v kq2 Electric kq1q2 F12 r kq1q2 U12 r q2 Force N Newton 2 Potenti al Energy J Jou le dU F12 12 dr q1 P1 P2 U12 F12 dr E12 r 2 kq2 V12 r Field N C V m Electric Potentia l J C V dV12 Volt E12 dr q2 P2 P1 V12 E12 dr Continuous Charge Distributions Divide the charge distribution into differential elements r Write down an expression for potential from a typical element treat as point charge Integrate Simple example circular rod of radius r total charge Q find V at center dq kdq r V dV k r k dq r Q Nm2 C Nm J Units 2 V C m C C Potential of Continuous Charge Distribution Line of Charge Uniformly charged rod Total charge Q Length L What is V at position P x P dx L a Q L dq dx L kdq k dx V r L a x 0 k ln L a x L 0 L a V k ln a Units Nm2 C2 C m Nm C J C V Electric Field Potential Simple Relationship Notice the following Point charge E kQ r2 V kQ r Dipole far away E kp r3 V kp r2 Focus only on a simple case electric field that points along x axis but whose magnitude varies dV with x E x E is given by a DERIVATIVE of V Of course r r V E ds f i A dx Note MINUS sign Units for E VOLTS METER V m E from V Example Q L L a Uniformly V k ln a charged rod Total charge Q k ln L a ln a Length L We Found V at P dV d Find E from V E da k da ln L a ln a x P dx L a Nm2 C m N V Units C 2 m m2 C m 1 1 k L a a a L a L k k L a a L a a Electric Field Electric Field Potential Question Hollow metal sphere of radius R has a charge q Which of the following is the electric potential V as a function of distance r from center of sphere q 1 r V a V r r R V c r R b r R 1 r r 1 r r Electric Field Potential Example q E V Outside the sphere Replace by point charge Inside the sphere E 0 Gauss Law E dV dr 0 IFF V constant 1 2 r 1 r dV E dr d Q k dr r Q k 2 r Equipotentials and Conductors Conducting surfaces are EQUIPOTENTIALs At surface of conductor E is normal perpendicular to surface Hence no work needed to move a charge from one point on a conductor surface to another Equipotentials are normal to E so they follow the shape of the conductor near the surface V E Conductors Change the Field Around Them An Uncharged Conductor Uniform Electric Field An Uncharged Conductor in the Initially Uniform Electric Field Sharp Conductors Charge density is higher at conductor surfaces that have small radius of curvature E for a conductor hence STRONGER electric fields at sharply curved surfaces Used for attracting or getting rid of charge lightning rods Van de Graaf metal brush transfers charge from rubber belt Mars pathfinder mission tungsten points used to get rid of accumulated charge on rover electric breakdown on Mars occurs at 100 V m NASA Ben Franklin Invents the Lightning R LIGHTNING SAFE CROUCH If caught out of doors during an approaching storm and your skin tingles or hair tries to stand on end immediately do the LIGHTNING SAFE CROUCH Squat low to the ground on the balls of your feet with your feet close together Place your hands on your knees with your head between them Be the smallest target possible and minimize your contact with the ground 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 field and electric potential E dV dx Electric potential energy work used to build the system charge by charge Use W U qV for each charge Conductors the charges move to make their surface equipotentials Charge density and electric field are higher on sharp points of conductors
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