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 = -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 3.2 motion C - 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.

Preflight 3.3 C 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.

ACT: Work C 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

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)? 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? 3 A) W = +19.8 mJ B) W = 0 mJ C) W = -19.8 mJ 5 m 5 m 1 2 5 m

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 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

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

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

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)