Electric Potential II Physics 2102 Jonathan Dowling Physics 2102 Lecture: 09 MON 02 FEB Ch

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: THERE WILL BE A REVIEW SESSION 6–7PM WED 04 FEB 2009 in Williams 103

Conservative Forces, Work, and Potential Energy 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 P1P1 P2P2 q1q1 q2q2 P1P1 P2P2 q2q2 Force [N] = Newton Potential Energy [J]=Joule Electric Potential [J/C]=[V] =Volt Electric Field [N/C]=[V/m]

Electric Potential of a Point Charge 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. Just calculate the potential due to each individual point charge, and add together! (Make sure you get the SIGNS correct!) q1q1 q5q5 q4q4 q3q3 q2q2 r1r1 r2r2 r3r3 r4r4 r5r5 P

Electric Potential and Electric Potential Energy +Q –Q a What is the potential energy of a dipole? +Q First: Bring charge +Q: no work involved, no potential energy. The charge +Q has created an electric potential everywhere, V(r) = kQ/r –Q a Second: The work needed to bring the charge –Q to a distance a from the charge +Q is W app = U = (-Q)V = (–Q)(+kQ/a) = -kQ 2 /a The dipole has a negative potential energy equal to -kQ 2 /a: we had to do negative work to build the dipole (electric field did positive work).

Positive Work Negative Work +Q a –Q a

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 +Q Do this from scratch!

Potential Energy of A System of Charges: Solution No energy needed to bring in first charge: U 1 =0 Energy needed to bring in 2nd charge: Energy needed to bring in 3rd charge = Energy needed to bring in 4th charge = +Q Total potential energy is sum of all the individual terms shown on left hand side = So, final kinetic energy of each charge = L

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? V A = V B = V C = 2. Draw an arrow representing the approximate direction of the electric field at the center of each circle. 3. Which system has the highest electric potential energy? –Q +Q A C B U B =QV b has largest un-canceled charge

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

Electric Potential on Perpendicular Bisector of Dipole You bring a charge of Q o = – 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? a -Q +Q –3C P U = Q o V = Q o (–Q/d+Q/d) = 0 d

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.