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Physics 102: Lecture 3 Electric Potential Energy & Electric Potential

Overview for Today’s Lecture Electric Potential Energy/ Work Uniform fields Point charges Electric Potential (like height) Show large and small battery 9 volt small, 6 volt large 07

Recall Work from P101 Work done by the force given by: W = F d cos(q) Positive: Force is in direction moved Negative: Force is opposite direction moved Zero: Force is perpendicular to direction moved Careful ask WHAT is doing work! Opposite sign for work done by you! Conservative Forces D Potential Energy = -W Use book or brick for prop. Ask students if I am doing positive or negative work, what about gravity. 09

Preflight 3.1 !!!!ACT!!!! Uniform E Set your iClicker Frequency to “BB” C Preflight 3.1 !!!!ACT!!!! F A B - Uniform E In what direction does the force on a negative charge at point A point? left right up 51% 48% 1% Electric field points in the direction a POSITIVE charge would feel force. 10

Preflight 3.2 motion - F C - F “I would say zero because the path is perpendicular to the field” - F - F - F A B Uniform E When a negative charge is moved from A to C the ELECTRIC force does positive work. zero work. negative work. 6% 89% 5% 11

Preflight 3.3 C “because the direction of the displacement is 180 degrees from direction of the force ” A B - F - F - F - F - F - Uniform E motion When a negative charge is moved from A to B the ELECTRIC force does positive work. zero work. negative work. 67% 4% 29% 13

Preflight 3.5 C A B - - - - - Uniform E When a negative charge is moved from A to B, the electric potential energy of the charge Increases is constant decreases 36% 14% 49% E.P.E. = -WE field Electric force did negative work so electric potential energy increased. 14

ACT: Electric Potential Energy AC: W=0 E + C CB: W<0 B A - - - - - When a negative charge is moved from A to B, the electric potential energy of the charge (A) increases (B) is constant (C) decreases Now switch to point charges! 1) The electric force is directed to bring the electron closer to the proton. 2) Since the electron ends up further from the proton the electric field did negative work. 3) So the electric potential energy increased 17

Work and D Potential Energy W = F d cos(q) Gravity Electric Brick raised yi yf Charge moved ∞  rf FE = kq1q2/rf2 (left) WE = -kq1q2/rf DUE= +kq1q2/rf FG = mg (down) WG = -mgh DUG= +mgh yf Fg=mg Fg=mg rf Fg=mg h Fg=mg Fg=mg Fg=mg Fg=mg yi Fg=mg 20

Work done by YOU to assemble 3 charges Example W1 = 0 W2 = k q1 q2 /r =3.6 mJ =(9109)(110-6)(210-6)/5 W3 = k q1 q3/r + k q2 q3/r (9109)(110-6)(310-6)/5 + (9109)(210-6)(310-6)/5 =16.2 mJ Wtotal = +19.8 mJ WE = -19.8 mJ DUE = +19.8 mJ (watch signs!) Do this live with balls on the table! 3 5 m 5 m 1 2 5 m 24

ACT: Work done by YOU to assemble 3 negative charges How much work would it take YOU to assemble 3 negative charges? Likes repel, so YOU will still do positive work! 3 W = +19.8 mJ W = 0 mJ W = -19.8 mJ 5 m 5 m 1 2 5 m 27

Preflight 3.11 1 + 5 m 5 m + - 2 5 m 3 The total work required by you to assemble this set of charges is: (1) positive (2) zero (3) negative Bring in (1): zero work Bring in (2): positive work Bring in (3): negative work x 2 55% 18% 27%

Electric Potential (like height)* Devil’s Tower Topographical map Moving to higher potential  moving uphill 30

Demo: electric potential – charge + charge Equipotential lines

Electric Potential (like height)* Units Joules/Coulomb Volts Batteries Outlets EKG Really Potential differences Equipotential lines at same height Field lines point down hill V = k q/r (distance r from charge q) V(∞) = 0 Comment on lab w/ equipotential lines 31

Preflight 3.7 Electric field Points from greater potential to lower potential The electric potential at point A is _______ at point B greater than equal to less than 51% 25% 24% 32

Preflight 3.9 The electric potential at point A is _______ at point B conductor The electric potential at point A is _______ at point B greater than equal to less than “The electric field within a conductor is zero, and therefore, the potential for points A and B are the same 33

Preflight Summary Path Vfinal - Vinitial Charge WE field D U = q DV + Negative A→ B Positive Negative Positive Negative A → C + - Zero C → B Negative + - 35

ACT: Electric Potential + C B A The electric potential at A is ___________ the electric potential at B. greater than equal to less than 1) Electric field lines point “down hill” 2) AC is equipotential path (perpendicular to E) 3) CB is down hill, so B is at a lower potential than (“down hill from”) A 38

Electric Potential due to Proton Example Electric Potential due to Proton What is the electric potential a distance r= 0.5310-10 m from a proton? (Let V()=0) V =U/q= k q/ r = (9109)(1.610-19) /0.5310-10 = 27.2 Volts rf = 0.510-10 m + 42

Electric Potential due to Proton What is the electric potential a distance r= 0.5310-10 m from a proton? (Let V()=0) V =U/q= k q/ r = (9109)(1.610-19) /0.5310-10= 27.2 Volts What is the electric potential energy of an electron a distance r= 0.5310-10 m from a proton? U = Vq = (27.2)(-1.610-19) = -4.3510-18J Hydrogen Balloon E≈ (4.3510-18)(610+23J )=106 J! rf = 0.510-10 m + - 42

Comparison: Electric Potential Energy vs. Electric Potential Electric Potential Energy (U) - the energy of a charge at some location. Electric Potential (V) - found for a location only – tells what the EPE would be if a charge were located there (usually talk about potential differences between two locations): U = Vq Neither has direction, just value. Sign matters!

Example Two Charges Calculate electric potential at point A due to charges Calculate V from +7mC charge Calculate V from –3.5mC charge Add (EASY!) V = kq/r V7=(9109)(710-6)/5 = 12.6103V V3=(9109)(-3.510-6)/5 = -6.3103V Vtotal = V7+V3 = +6.3103V A 4 m 6 m Q=+7.0mC Q=-3.5 mC W=DU=DVq =(+6.3103V)(2mC) =+12.6 mJ How much work do you have to do to bring a 2 mC charge from far away to point A? 46

ACT: Two Charges In the region II (between the two charges) the electric potential is 1) always positive 2) positive at some points, negative at others. 3) always negative I II III Q=+7.0mC Q=-3.5 mC Very close to positive charge potential is positive Very close to negative charge potential is negative 48

To Do Bring “Problem Solver” to discussion section Complete preflight 50