Physics 102: Lecture 3 Electric Potential

Overview for Today’s Lecture Electric Potential Energy/ Work Uniform fields Point charges Electric Potential (like height) Show large and small battery 9 volt small, 6 volt large

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 D Potential Energy = -W Use book or brick for prop. Ask students if I am doing positive or negative work, what about gravity.

Preflight 3.1 !!!!ACT!!!! Uniform E B Uniform E In what direction does the force on a negative charge at point A point? left right up

Preflight 3.3 C “because the direction of the displacement is 180 degrees from direction of the force ” A B Uniform E When a negative charge is moved from A to B the ELECTRIC force does positive work. zero work. negative work.

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 Increases is constant decreases E.P.E. = -WE field Electric force did negative work so electric potential energy increased.

ACT: Electric Potential Energy AC: W=0 E + 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 Now switch to point charges!

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

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 (watch signs!) Do this live with balls on the table! 3 5 m 5 m 1 2 5 m

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 1 2 5 m

Preflight 3.11 1 + 5 m 5 m + - 2 5 m 3 The total work required by you to assemble this set of charges is: (1) positive (2) zero (3) negative

Electric Potential (like height)* Mount Tabor Moving to higher potential  moving uphill

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 Comment on lab w/ equipotential lines

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

Preflight 3.9 The electric potential at point A is _______ at point B conductor The electric potential at point A is _______ at point B greater than equal to less than

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

ACT: Electric Potential + C B A The electric potential at A is ___________ the electric potential at B. greater than equal to less than

Electric Potential due to Proton Example 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 +

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10-18J  -27.2 eV Hydrogen Balloon E≈ (4.3510-18)(610+23J )=106 J! rf = 0.510-10 m + -

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!

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?

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

To Do Bring “Problem Solver” to discussion section Complete preflight.