Physics 102: Lecture 3 Electric Potential Energy & 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 Phys 101 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 = -Wforce 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 55% 43% 2% Electric field points in the direction a POSITIVE charge would feel force.

Preflight 3.2 motion C “I would say zero because the path is perpendicular to the field” - F A B Uniform E When a negative charge is moved from A to C the ELECTRIC force does positive work. zero work. negative work. 8% 88% 4%

Preflight 3.3 C “because the direction of the displacement is 180 degrees from direction of the force ” A B - F Uniform E motion When a negative charge is moved from A to B the ELECTRIC force does positive work. zero work. negative work. 66% 5% 29% ΔUE = -WE field = +WYou Electric force did negative work You did positive work Electric potential energy increased

ACT: Work Uniform E Path does not matter! Only end points matter WA-B = work done by FE moving charge from A to B A B - F Uniform E The negative charge is moved from A to C to B. Is the work done by the electric force: A) Greater than WA-B B) Same as WA-B C) Less than WA-B Work out on slide: W_A-C-B = W_A-C + W_C_B = 0 + Fd_{C-B}cos(theta) = Fd_{A-B} = W_A-B Path does not matter! Only end points matter

Work and D Potential Energy W = F d cos(q) Gravity Electric Brick raised yi yf Charge moved xi xf FE = qE (left) WE = –qEd DUE= +qEd FG = mg (down) WG = –mgh DUG= +mgh yi  yf  h xi  xf  d - F FG=mg E

E.P.E. for point charges Example E.P.E. of two charges q1 and q2 separated a distance r: Example What is the electric potential energy of an electron a distance r = 0.5310-10 m from a proton (H atom)? UE = (+1.610-19)(-1.610-19)/0.5310-10 = -4.3510-18J rf = 0.510-10 m + -

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 A) W = +19.8 mJ B) W = 0 mJ C) 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 Bring in (1): zero work Bring in (2): positive work Bring in (3): negative work x 2 50% 18% 32%

Electric Potential (like height) Units Joules/Coulomb  Volts Examples: Batteries Outlets EKG Only potential differences matter Comment on lab w/ equipotential lines

Electric Potential (like height) Devil’s Tower Topographical map Moving to higher potential  moving uphill

Demo: electric potential Recall electric dipole + Equipotential lines + – – Electric field + (–) charge has high (low) potential Equipotential lines at same “height” Electric field lines point “downhill”

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 45% 32% 23%

Preflight 3.9 E=0 conductor The electric potential at point A is _______ at point B greater than equal to less than 7% 85% “The electric field within a conductor is zero, and therefore, the potential for points A and B are the same”

Potential for Point charges Electric potential a distance r from a charge q: Example What is the electric potential a distance r = 0.5310-10 m from a proton? (Let V()=0) V =UE/q= k q/ r = (9109)(1.610-19) /0.5310-10 = 27.2 Volts rf = 0.510-10 m +

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! NO VECTORS) A 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 4 m 6 m Q=+7.0mC Q=-3.5 mC How much work do you have to do to bring a 2 mC charge from far away to point A? W=DU=Vq = (+6.3103V)(2mC) = +12.6 mJ

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

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

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!

Relationship between F, E, UE, V Vector Number (“scalar”) F UE [N] [J] interacting charges Property of Ex: Ex: E V [N/C]=[V/m] [J/C]=[V] Property of point in space Sometimes is more useful to think in terms of F and E, other times U and V Ex: Ex: Why so many ways to describe electric force?

Electron microscope Uniform E Example ΔV=10kV Vi Vf Electron gun Vi Vf - Uniform E motion What is the final velocity of the e-? Solve by conservation of energy: K.E.i + P.E.i = K.E.f + P.E.f 0 + –eVi = ½mv2 + –eVf Could solve this using F=ma & kinematic equations (Phys 101) TRY AT HOME! (HARDER)

See everyone Monday!