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Physics 2102 Lecture: 09 MON 02 FEB

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!.

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Physics 2102 Lecture: 09 MON 02 FEB

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  1. Physics 2102 Jonathan Dowling Physics 2102 Lecture: 09 MON 02 FEB Electric Potential II Ch24.6-10

  2. 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

  3. Work Done (W) is Integral of Force (F) Potential Energy (U) is Negative of Work Done Hence Force is Negative Derivative of Potential Energy Conservative Forces, Work, and Potential Energy

  4. Electric Field [N/C]=[V/m] Force [N] = Newton Potential Energy [J]=Joule Electric Potential [J/C]=[V] =Volt Coulomb’s Law for Point Charge q2 q2 q1 P1 P2 P1 P2

  5. Electric Potential of a Point Charge Note: if Q were a negative charge, V would be negative

  6. q4 q3 r3 r4 P r2 r5 q2 q5 r1 q1 Electric Potential of Many Point Charges • Electric potential is a SCALAR not a vector. • Just calculate the potential due to each individual point charge, and add together! (Make sure you get the SIGNS correct!)

  7. –Q +Q a • First: Bring charge +Q: no work involved, no potential energy. • The charge +Q has created an electric potential everywhere, V(r) = kQ/r –Q +Q a • 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 Electric Potential and Electric Potential Energy What is the potential energy of a dipole? • 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).

  8. +Q +Q a –Q +Q a Positive Work Negative Work

  9. +Q +Q +Q +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 • If all four strings suddenly snap, what is the kinetic energy of each charge when they are very far apart? • 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!

  10. +Q +Q +Q +Q Potential Energy of A System of Charges: Solution L • No energy needed to bring in first charge: U1=0 • Energy needed to bring in 2nd charge: • Energy needed to bring in 3rd charge = Total potential energy is sum of all the individual terms shown on left hand side = • Energy needed to bring in 4th charge = So, final kinetic energy of each charge =

  11. –Q +Q UB =Q•Vb has largest un-canceled charge Example Positive and negative charges of equal magnitude Q are held in a circle of radius R. 1. What is the electric potential at the center of each circle? • VA = • VB = • VC = 2. Draw an arrow representing the approximate direction of the electric field at the center of each circle. 3. Which system has the highest electricpotential energy? A B C

  12. p a +Q –Q r 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)? Far away, when r >> a: V

  13. d U = QoV = Qo(–Q/d+Q/d) = 0  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: • Positive? • Negative? • Zero? a +Q -Q P –3C

  14. 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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