Electric Potential

1. Electric Potential • Electric Field and Potential Roadmap • Constant Electric Fields • Potential Energy and Electric Potential • PE and Electric Potential examples • Topographical Analogy • “Point” Electric Fields • Potential Energy and Electric Potential • PE and Electric Potential examples

2. Electric Field & Potential Road Map Similar to gravitational law Add multiple points as vectors. Coulombs’s Law Electric Field Background “field” without test charge Similar to gravitational ”g” Last week Constant Fields Coulomb’s law + lots integral calculus More used for practical problems! Constant-field PE We’re here Similar to gravitational mgh Constant-field Potential Like mgh divided by “m” Similar to gravitational gh Point-charge PE Back to point charges! 1/r , scalar quantities Point-charge Potential Just the potential PE/q

3. Work and PE/Potential • For constant electric field • Change in Potential Energy (negative of work done) • 4 cases sign convention • (+) Move with the field, PE goes down • (+) Move against the field, PE goes up • (-)Move with the field, PE goes up • (-)Move against the field, PE goes down • Define “universal” Potential, indep. of test charge • Potential always • Decreases going with field • Increases going against field • Units of are Joules/Coulomb or Volts

4. Potential vs. Potential Energy • Electric Potential • Universal • Independent of test charge • PE for (+) charge • Decreases going with field • Increases going against field • PE for (-) charge • Decreases going against field • Increases going with field

5. For Constant Field

6. Constant field problems • Example 17-2 • Electron volt • Energy of 1 electron across 1 volt • qV = (1.6*10-19 C) (1 J/C) = 1.6*10-19 Joule • 1 ev = 1.6*10-19 Joule • Problems • Chapter 17 – 1-8, 9,12 • Chapter 17 – 10 • Qualitative question 8

7. Slope/Elevation Analogy • Varying slope of incline (varying electric field) small slope (low electric field) large slope (high electric field) • “Height” (ΔV)is the difference of elevation (equipotential) • “Percent grade”steepness of slope (electric field) • The two are related Slope E Slope E ΔV height ΔV height width width

8. Hillside Slope/Elevation Analogy • Topographical Analogy • Elevation -> Potential • Slope -> Electric Field • Observations • Slope (E) is 3-D gradient of elevation (V) or contour lines • Change in Elevation (VA-VB) is independent of path to get there

9. Rocky Mountain Slope/Elevation Analogy Percent grade <-> electric field Elevation <-> electric potential • Other similarities • Percent grade and electric field vectors, elevation and electric potential scalars . • Constant elevation lines similar to equipotential lines, fall line similar to electric field lines. • Fall lines perpendicular to constant elevations lines, electric field lines perpendicular to equipotential lines • Closer the constant contour lines steeper the slope, closer the equipotential lines higher the electric field. • Can arrive at same elevation by different roads, can arrive at same potential by different paths

10. Skier’s Slope/Elevation Analogy - Slope http://www.skitaos.org/Taos, NM

11. Skier’s Slope/Elevation Analogy – Topo Lines http://topomaps.usgs.gov Taos, NM

12. EtownTopo Lines Android Google Play: “Backcountry Navigator” Map Layer: “USA Topo Maps – ArcGIS”

13. Constant field vs. Point Charge • Constant Field • Point Charge

14. Electric Potential for point charges • Coulomb’s Law and Electric Field (vectors!) • Potential Energy and Electric Potential (scalars!) • Can derive PE from calculus • Electric Potential is just PE without 2nd charge • Like E is represents “background” Potential energy • Units Joules/Coulomb or volts

15. Topo Analogy for point charges • Potential around positive and negative charges • Serway, 8th edition page 716

16. Point charge PE Examples • All scalar calculations. • Volcanic peaks and inverted sinkholes (analogy) • Example 17-5 • Work to bring 3 μC 0.5m from 20 μC • Work to separate -3 μC 0.5m from 20 μC • Problem 20 • Problem 23

17. Electric Potential vs. PE • Potential energy without the 2nd charge • Electric potential around (+) charge • Defined positive (volcanic peak) • (+) test charge (falls away) • (-) test charge (falls down in) • Electric potential around (-) charge • Defined negative (volcanic sinkhole) • (+) test charge (falls down in) • (-) test charge (falls away)

18. Topo Analogy for point charges • Potential around positive and negative charges • Serway, 8th edition page 716

19. Point charge Examples • All scalar calculations. • Volcanic peaks and inverted sinkholes (analogy) • Example 17-4 • Example 17-5 • Problem 16,18,19,21,22

20. Summary for point charges • Force and Electric Field • Add as vectors • Potential Energy and Electric Potential • Add as scalars

21. Chapter 17 – 3 confusing things • Electric Potential vs. Electric Field • Topo analogy – elevation vs. slope/grade • Scalar vs. vector (use +/- signs) • Electric Potential vs. Potential Energy • Potential is Potential energy without 2nd charge • Similar to relation between Field and Force • Constant field vs. Point Charge • Point charge • Constant field is point charge + integral calculus • Constant field means linearly varying potential (V= Ed)

22. Potential Energy and Electric Potential • Topographical analogy • Picture vs. Topographical map • Work, Potential Energy, and Electric Potential for constant fields • Constant field examples • Constant field summary • Work, Potential Energy, and Electric Potential for point charges • Point charge examples • Point charge summary