Electric Potential

Electric Potential • Constant electric fields • Work and PE moving in constant field • PE and Electric Potential in constant field • PE and Electric Potential examples • Topographic Analogy

Work moving ±q in constant field • Electric field in positive direction • Positive charge crossing in positive direction • Force vector positive • Motion vector positive • Work positive, ΔKE positive, ΔPE negative • Negative charge crossing in negative direction • Force vector negative • Motion vector negative • Work positive, ΔKE positive, ΔPE negative In both cases work positive, ΔKE positive, and ΔPE negative F F F

Work and ΔPE moving ±q in constant field Summary • For both charges: • F and Δx in same direction • Work positive • ΔKE positive • ΔPE negative • speeds up • For both charges: • (+) “falls” to negative electrode • (-) “falls” to positive electrode • For both ±q cases KE increases, PE decreases - as it should! Low PE High PE F Low PE High PE F

Electric Potential ΔV in constant field • Previously • Define Electric Potential • Move with field in positive direction • Electric field vector positive • Direction vector positive • Electric Potential decreases • Move against field in negative direction • Electric field vector positive • Direction vector negative • Electric Potential increases • Electric Potential always decreases in direction of Electric Field Low V High V High V Low V

ΔV and ΔPE moving ±q in constant field • Define Electric Potential • Move +q in positive direction • Field positive • Direction positive • Electric Potential decrease • Charge positive • PE decrease • Move -q in negative direction • Field positive • Direction negative • Electric Potential increase • Charge negative • PE decrease • Potential ΔV always decreases going with field, ± q flips sign for ΔPE High V Low V Low PE High PE High V Low V Low PE High PE

ΔV and ΔPE moving ±q in constant field • Electric Potential: Always decreases going with field. increases going against field. • Potential Energy: Rises or falls with sign of test charge (+) charge decreases going with field (high to low potential). (-) charge decreases going against field (low to high potential. • Units High V Low V Low PE High PE High V Low V Low PE High PE

Work crossing Electric Potential - Examples • Positive test charge • Negative test charge • Change in Potential • Change in Potential Energy

Velocity crossing Electric Potential • ΔPE for electron • Change in KE Change in Potential Energy

Example problems - 1 1. How much work does the electric field do in moving a -7.5 µC charge from ground to a point whose potential is +65 V higher? • How much work does the electric field do in moving a proton from a point with a potential of +113 V to a point where it is -45 V? Express your answer both in joules and electron volts.

Electron-volt (ev) • Definition 1 ev is energy electron picks up going across potential difference of 1 volt.

Example problems - 2 • An electron acquires 3.51 ✕ 10-16 J of kinetic energy when it is accelerated by an electric field from plate A to plate B. What is the potential difference between the plates, and which plate is at the higher potential? Toward + electrode

Example problems - 3 • How strong is the electric field between two parallel plates 6.0 mm apart if the potential difference between them is 110 V? • What is the speed of a proton whose kinetic energy is 2.8 keV?

Example problems - 4 • The work done by an external force to move a -7.50 µC charge from point a to point b is 25.0 ✕ 10-4 J. If the charge was started from rest and had 4.85 ✕ 10-4 J of kinetic energy when it reached point b, what is the magnitude of the potential difference between a and b? • Must increase PE by • Must move toward negative electrode

Electrostatic and Gravitational analogy • Comparison of height and gravitational PE, with electric potential and electrostatic PE • At least rocks don’t fall up! Change in Potential Change in Potential Energy

Slope/Elevation Analogy - 1 Electric field/Potential analogous to Slope/Elevation on Mountain Drive. Similarities • Closer equipotential lines mean higher electric field, closer elevation lines mean steeper slope. • Electric field has magnitude and direction, electric potential has only magnitude; slope has magnitude and direction, elevation has only magnitude. • Equipotential lines analogous to constant elevation lines, electric field lines analogousto (skiers) fall lines. • Electric field lines perpendicular to equipotential lines, fall lines perpendicular to constant elevation lines. • Can arrive at same potential by different electric filed paths, can travel to same elevation by different sloped roads. I-70 west of Denver, CO

Slope/Elevation Analogy - 2 • Slope vs. elevation in topography • horizontal any direction. (vector) • slope any direction. (vector) • elevation just up. (scalar) • Topographical • Electrostatic • scalar vectors

Slope/Elevation Analogy - 3 • Beartooth Pass, Wyoming

Topographic Analogy – Ski Map http://www.skitaos.org/Taos, NM

Topographic Analogy – USGS Topo Map http://topomaps.usgs.gov Taos, NM

Mt Gretna - Topographic Map If you know contour lines and spacing, you can calculate every slope!!

Electric Potential