Physics 102 Lecture 3 Electric Potential Physics 102

Physics 102: Lecture 3 Electric Potential Physics 102: Lecture 3, Slide 1

Overview for Today’s Lecture • Electric Potential Energy/ Work – Uniform fields – Point charges • Electric Potential (like height) – Uniform fields – Point charges Physics 102: Lecture 3, Slide 2

Recall Work from P 101 • 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 Physics 102: Lecture 3, Slide 3

Physics 102: Lecture 3, Slide 4

Preflight 3. 1 C !!!!ACT!!!! A Uniform E In what direction does the force on a negative charge at point A point? 1) left 2) right 3) up Physics 102: Lecture 3, Slide 5 B

Preflight 3. 3 “because the direction of the displacement is 180 degrees from direction of the force ” C A B Uniform E When a negative charge is moved from A to B the ELECTRIC force does 1) positive work. 2) zero work. 3) negative work. Physics 102: Lecture 3, Slide 7

Physics 102: Lecture 3, Slide 8

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 1) Increases 2) is constant 3) decreases Physics 102: Lecture 3, Slide 9 E. P. E. = -WE field Electric force did negative work so electric potential energy increased.

ACT: Electric Potential Energy + E A AC: W=0 C B CB: W<0 When a negative charge is moved from A to B, the electric potential energy of the charge (A) increases (B) is constant (C) decreases Physics 102: Lecture 3, Slide 10

Work and D Potential Energy W = F d cos(q) Gravity • Brick raised yi yf • FG = mg (down) • WG = -mgh • DUG= +mgh yf Fg=mg h Fg=mg yi Fg=mg Physics 102: Lecture 3, Slide 11 Electric • Charge moved ∞ rf • FE = kq 1 q 2/r 2 (left) • WE = -kq 1 q 2/rf • DUE= +kq 1 q 2/rf rf

Physics 102: Lecture 3, Slide 12

Work done by YOU to assemble 3 charges • W 1 = 0 • W 2 = k q 1 q 2 /r =(9 109)(1 10 -6)(2 10 -6)/5 =3. 6 m. J • W 3 = k q 1 q 3/r + k q 2 q 3/r (9 109)(1 10 -6)(3 10 -6)/5 + (9 109)(2 10 -6)(3 10 -6)/5 =16. 2 • • • Wtotal = +19. 8 m. J WE = -19. 8 m. J DUE = +19. 8 m. J (watch signs!) Physics 102: Lecture 3, Slide 13 5 m 1 3 5 m 5 m 2 m. J

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! A. W = +19. 8 m. J B. W = 0 m. J C. W = -19. 8 m. J Physics 102: Lecture 3, Slide 14 5 m 1 3 5 m 5 m 2

Preflight 3. 11 1 5 m 2 + + 5 m 5 m - 3 The total work required by you to assemble this set of charges is: (1) positive (2) zero (3) negative Physics 102: Lecture 3, Slide 15

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Electric Potential (like height)* Mount Tabor Moving to higher potential moving uphill Physics 102: Lecture 3, Slide 17

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 Physics 102: Lecture 3, Slide 18

Preflight 3. 7 Electric field Points from greater potential to lower potential The electric potential at point A is _______ at point B 1) greater than 2) equal to 3) less than Physics 102: Lecture 3, Slide 19

Physics 102: Lecture 3, Slide 20

Preflight 3. 9 conductor The electric potential at point A is _______ at point B 1) greater than 2) equal to 3) less than Physics 102: Lecture 3, Slide 21

Preflight Summary Path A→ B A→C C→B Vfinal - Vinitial Negative Zero Negative Physics 102: Lecture 3, Slide 22 Charge D U = q DV Negative + Positive + + - WE field Positive Negative

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ACT: Electric Potential + C A B The electric potential at A is ______ the electric potential at B. 1) greater than 2) equal to 3) less than Physics 102: Lecture 3, Slide 25

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 + Physics 102: Lecture 3, Slide 26

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 -18 J -27. 2 e. V Hydrogen Balloon E≈ (4. 35 10 -18) (6 10+23 J )=106 J! rf = 0. 5 10 -10 m + Physics 102: Lecture 3, Slide 27 -

Physics 102: Lecture 3, Slide 28

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! Physics 102: Lecture 3, Slide 29

Two Charges • Calculate electric potential at point A due to charges – Calculate V from +7 m. C charge – Calculate V from – 3. 5 m. C charge – Add (EASY!) • V = kq/r V 7=(9 109)(7 10 -6)/5 = 12. 6 103 V V 3=(9 109)(-3. 5 10 -6)/5 = -6. 3 103 V Vtotal = V 7+V 3 = +6. 3 103 V Q=+7. 0 m. C 4 m A 6 m Q=-3. 5 m. C How much work do you have to do to bring W=DU=DVq 3 =(+6. 3 10 V)(2 m. C) a 2 m. C charge from far away to point A? =+12. 6 m. J Physics 102: Lecture 3, Slide 30

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 Q=+7. 0 m. C III Q=-3. 5 m. C Very close to positive charge potential is positive Very close to negative charge potential is negative Physics 102: Lecture 3, Slide 31

To Do • Bring “Problem Solver” to discussion section • Complete preflight. Physics 102: Lecture 3, Slide 32