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Understanding Electric Potential Energy in Physics Lecture

This lecture covers the electric potential energy, work, and forces in physics, emphasizing uniform fields and point charges. Learn about conservative forces, potential energy changes, and the interaction between electric fields and gravity.

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Understanding Electric Potential Energy in Physics Lecture

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  1. Physics 102: Lecture 3Electric Potential

  2. Recall from last lecture…. • E field has magnitude and direction: • E due to point charge Q: E=kQ/r2 • Force on charge q due to E: F=qE • E and F are vectors • Electric field lines • Density gives strength (# proportional to charge.) • Arrow gives direction (Start + end on -) • Conductors • E=0 inside a conductor

  3. Overview for Today’s Lecture • Electric Potential Energy/ Work • Uniform fields • Point charges • Electric Potential (like height) • Uniform fields • Point charges 07

  4. 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 (not friction) Change in Potential Energy = -Wconservative 09

  5. d q q Uniform E Fg=mg Fg=mg Fg=mg Fg=mg Fg=mg Fg=mg Fg=mg Fg=mg Work and D Potential Energy Gravity Uniform Electric Field • Brick raised yi yf • +charge q moved d to left • FE = qE (right) • WE = -qEd • DUE= +qEd • FG = mg (down) • WG = -mgh • DUG= +mgh yf h yi 20

  6. rf Work and D Potential Energy W = F d cos(q) Gravity Electric • Brick raised yi yf • + Charge moved ∞ rf • FE = kq1q2/r2 • WE = -kq1q2/rf • DUE= +kq1q2/rf • FG = mg (down) • WG = -mgh • DUG= +mgh yf h yi 20

  7. F Preflight 3.1 ACT C A B - Uniform E • In what direction does the force on a negative charge at point A point? • left • right • up 53% 43% 4% Force on charge is in same direction of field if POSITIVE and opposite direction if NEGATIVE. 10

  8. F F F F F - - - - - Preflight 3.2 motion C “I would say zero because the path is perpendicular to the field” A B Uniform E • When a negative charge is moved from A to C the ELECTRIC force does • positive work. • zero work. • negative work. 10% 85% 05% 11

  9. F F F F F - - - - - motion Preflight 3.3 ACT C A B “because the direction of the displacement is 180 degrees from direction of the force” - Uniform E • When a negative charge is moved from A to B the ELECTRIC force does • positive work. • zero work. • negative work. 66% 7% 21% 13

  10. Preflight 3.5 ACT 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 D(EPE) = -WE field Electric force did negative work so electric potential energy increased. Just like pushing mass uphill. 33% 14% 53% 14

  11. E ACT: Electric Potential Energy AC: W=0 + 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 1) The electric force is directed to bring the electron closer to be 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

  12. 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 3 5 m 5 m 2 1 5 m Note the units and watch signs: This is like moving mass uphill 24

  13. 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 2 1 5 m 27

  14. 1 Preflight 3.11 + 5 m 5 m Negative because i really hate physics. And i dont know what is being ask in this question. - + 2 3 5 m The total work required by you to assemble this set of charges is: (1) positive (2) zero (3) negative Bring in (3): zero work Bring in (2): negative work Bring in (1): zero work (see next page for explanation) 57% 16% 27%

  15. 1 + 5 m 5 m - + 2 3 5 m Preflight 3.11 Bring in (3): zero work because the other charges are far away so the electric field due to those charges is zero. Bring in (2): negative work. why? Let’s figure out the work done by the electric field, which is just the negative of the work done. The electric field felt by charge 2 is the field due to charge 3, which points toward charge 3. So, we are moving charge 2 in the same direction of the field. Therefore the work done by the field is positive, so the work done by you is negative Bring in (1): zero work. why? We must do negative work due to charge 3 and an equal amount of positive work due to charge 2, so the net work is zero. Another way to think about it is that the electric potential energy of charge 1 is zero, since it has equal but opposite contributions from charges 2 and3 Net result is the sum of 0,negative, and 0 and is therefore negative.

  16. 1 + 5 m 5 m - + 2 3 5 m Preflight 3.11 Yet another way to work the problem: Wyou = -WE = Electric Potential Energy (EPE) of the three charges. EPE = kq1q2/r + kq2q3/r +kq1q3/r where r is the separation between the charges (5 m). All three terms have the same magnitude, since all the charges have the same magnitude. The first term is positive but the next two are negative. Therefore, the EPE is negative, so that Wyou is negative. As a practice exercise, try calculating Wyou, assuming the magnitude of each charge is 5 C. Answer = -0.045 J.

  17. yf d q q h yi Uniform E Work and D Electric Potential Gravity Uniform Electric Field • Brick raised yi yf • +charge q moved d to left • DUE= +qEd = change in electric potential energy • DUE= +q(Ed) = charge(q) x change in electric potential (Ed) VE • Moving opposite to E increases VE • DUG= +mgh = change in gravitational potential energy • DUG = m(gh) = mass (m) x change in gravitational potential (gh) VG • Moving from low to high increases VG m m 20

  18. Electric Potential • Units Joules/Coulomb Volts (symbol V) • Batteries • Outlets • EKG • Really Potential differences • Equipotential lines at same “height” • Field lines point “downhill” from higher to lower potential • V = k q/r (distance r from charge q) V(∞) = 0 31

  19. 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 55% 26% 19% 32

  20. Preflight 3.9 89% 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

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

  22. E 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

  23. Electric Potential: Summary • E field lines point from higher to lower potential • For positive charges, going from higher to lower potential is “downhill” • For negative charges, going from lower to higher potential is “downhill” • For a battery, the + terminal is at a higher potential than the – terminal Positive charges tend to go “downhill”, from + to - Negative charges go in the opposite direction, from - to +

  24. 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 U would be if a charge were located there: U = Vq • Usually we talk only about changes in potential or potential energy when moving from one location to another • Neither U nor V has direction, just location. Sign matters!

  25. Example not covered during lecture Electric Potential due to a point charge What is the electric potential V a distance r from a point charge, assuming V=0 at  answer: V = k q/ r 42

  26. not covered during lecture 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

  27. not covered during lecture 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

  28. To Do • Read 17.5-6 • Extra problems from textbook Ch 17: • Concepts 1-8 • Problems 1, 9, 15, 19, 23, 25 • Bring “Problem Solver” to discussion section • Complete preflight before Monday 6:00am. 50

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