**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

**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

**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

**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

**For Constant Field**

**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

**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

**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

**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

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

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

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

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

**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

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

**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

**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)

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

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

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

**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)

**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