Physics 102: Lecture 3 Electric Potential Energy & Electric Potential. Physics 102: Lecture 2, Slide 1

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1 Physics 102: Lecture 3 Electric Potential Energy & Electric Potential Physics 102: Lecture 2, Slide 1

2 Overview for Today s Lecture Electric Potential Energy & Work Uniform fields Point charges Electric Potential (like height) Uniform fields Point charges Physics 102: Lecture 2, Slide 2

3 Recall Work from Phys 101 Work done by the force given by: W = F d cos(θ) 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 Δ Potential Energy = W Physics 102: Lecture 2, Slide 3

4 Preflight 3.1 C!!!!ACT!!!! A B Uniform E In what direction does the force on a negative charge at point A point? 1) left 2) right 3) up Physics 102: Lecture 2, Slide 4

5 Preflight 3.2 motion C F A B Uniform E When a negative charge is moved from A to C the ELECTRIC force does 1) positive work. 2) zero work. 3) negative work. Physics 102: Lecture 2, Slide 5

6 Preflight 3.3 C F A Uniform E B motion When a negative charge is moved from A to B the ELECTRIC force does 1) positive work. 2) zero work. 3) negative work. Physics 102: Lecture 2, Slide 6

7 ACT: Work W A-B = work done by F E moving charge from A to B F C A Uniform E B The negative charge is moved from A to C to B. Is the work done by the electric force: A) Greater than W A-B B) Same as W A-B C) Less than W A-B Physics 102: Lecture 2, Slide 7

8 Work and Δ Potential Energy Gravity W = F d cos(θ) Electric Brick raised y i y f F G = mg (down) W G = mgh ΔU G = +mgh Charge moved x i x f F E = qe (left) W E = qed ΔU E = +qed y f h y i F G =mg Physics 102: Lecture 2, Slide 8 F x i E d x f

9 E.P.E. for point charges E.P.E. of two charges q 1 and q 2 separated a distance r: 1 2 What is the electric potential energy of an electron a distance r = m from a proton (H atom)? r f = m + Physics 102: Lecture 2, Slide 9

W 1 = 0 Work done by YOU to assemble 3 charges W 2 = k q 1 q 2 /r =(9 109 )(1 10-6 )(2 10-6 )/5 =3.

10 W 1 = 0 Work done by YOU to assemble 3 charges W 2 = k q 1 q 2 /r =(9 109 )( )( )/5 =3.6 mj W 3 = k q 1 q 3 /r + k q 2 q 3 /r ( )( )( )/5 + ( )( )( )/5 =16.2 mj W total = mj W E = 19.8 mj ΔU E = mj (watch signs!) 5 m m 5 m 2 Physics 102: Lecture 2, Slide 10

11 ACT: Work done by YOU to assemble 3 negative charges How much work would it take YOU to assemble 3 negative charges? A) W = mj B) W = 0 mj C) W = mj 5 m m 5 m 2 Physics 102: Lecture 2, Slide 11

12 Electric Potential (like height) Units Joules/Coulomb Volts Examples: Batteries Outlets EKG Only potential differences matter Physics 102: Lecture 2, Slide 13

13 Electric Potential (like height) Devil s Tower Topographical map Moving to higher potential moving uphill Physics 102: Lecture 2, Slide 14

14 Demo: electric potential Recall electric dipole + Equipotential lines + Physics 102: Lecture 2, Slide 15 + ( ) charge has high (low) potential Equipotential lines at same height Electric field lines point downhill Electric field

15 Preflight 3.7 The electric potential at point A is at point B 1) greater than 2) equal to 3) less than Physics 102: Lecture 2, Slide 16

16 Preflight 3.9 conductor The electric potential at point A is at point B 1) greater than 2) equal to 3) less than Physics 102: Lecture 2, Slide 17

17 Potential for Point charges Electric potential a distance r from a charge q: What is the electric potential a distance r = m from a proton? (Let V( )=0) V =U E /q= k q/ r = ( )( ) / = 27.2 Volts r f = m + Physics 102: Lecture 2, Slide 18

18 Two Charges Calculate electric potential at point A due to charges Calculate V from +7μC charge Calculate V from 3.5μC charge Add (EASY! NO VECTORS) A V = kq/r V 7 = ( )( )/5 = V V 3 = ( )( )/5 = V 4 m V total = V 7 +V 3 = V Q=+7.0μC 6 m Q=-3.5 μc How much work do you have to do to bring a 2 μc charge from far away to point A? Physics 102: Lecture 2, Slide 19 W=ΔU=Vq = ( V)(2μC) = mj

19 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 Ι ΙΙ ΙΙΙ Q=+7.0μC Q=-3.5 μc Physics 102: Lecture 2, Slide 20

20 ACT: Electric Potential + Ε A C B The electric potential at A is the electric potential at B. 1) greater than 2) equal to 3) less than Physics 102: Lecture 2, Slide 21

21 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! Physics 102: Lecture 2, Slide 22

22 Relationship between F, E, U E, V Vector Number ( scalar ) F [N] U E [J] Ex: Ex: 1 2 E Ex: [N/C]=[V/m] / 2 V Ex: [J/C]=[V] / Why so many ways to describe electric force? Physics 102: Lecture 2, Slide 23

i + P.E. i = K.E. f + P.E. f 0 + ev i = ½mv 2 + ev f 2 Physics 102: Lecture 2, Slide 24 2 1.

23 Electron microscope ΔV=10kV V i Uniform E V f motion Electron gun 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 + ev i = ½mv 2 + ev f 2 Physics 102: Lecture 2, Slide / Could solve this using F=ma & kinematic equations (Phys 101) TRY AT HOME! (HARDER)

Physics 102: Lecture 3 Electric Potential Energy & Electric Potential. Physics 102: Lecture 2, Slide 1

Physics 102: Lecture 3 Electric Potential Energy & Electric Potential Physics 102: Lecture 2, Slide 1 Overview for Today s Lecture Electric Potential Energy & Work Uniform fields Point charges Electric