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 Gravity Work W = F d cos(q) Electric Brick raised y i y f F G = mg (down) W G = mgh W you = mgh Charge moved x i x f F E = qe (left) W E = qed W you = qed y f h y i F G =mg Physics 102: Lecture 2, Slide 3 W=0 F W=0 x i - E d x f

4 CheckPoint 1.1 C F A B Uniform E In what direction does the force on a negative charge at point A point? 65% 1) left 32% 2) right 3% 3) up Electric field points in the direction a POSITIVE charge would feel force. Physics 102: Lecture 2, Slide 4

5 CheckPoint 1.2 Force applied perpendicular to the direction of motion brings about no work F - motion C A B Uniform E When a negative charge is moved from A to C the ELECTRIC force does 20% 70% 10% 1) positive work. 2) zero work. 3) negative work. Physics 102: Lecture 2, Slide 5

6 CheckPoint 1.3 The work is negative because the electric force opposes the direction of motion F - C A Uniform E B motion When a negative charge is moved from A to B the ELECTRIC force does 48% 17% 35% 1) positive work. 2) zero work. 3) negative work. -W E field = +W You Electric force did negative work You did positive 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 Path does not matter! Only end points matter

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

9 CheckPoint 1.5 The movement of an electron from A to B requires energy from an outside source. The energy put in will be released when the electron moves from B to A. F - C A Uniform E B motion When a negative charge is moved from A to B the potential energy of the charge 45% 23% 32% 1) increases. 2) remains the same. 3) decreases. -W E field = +W You Electric force did negative work You did positive work Physics 102: Lecture 2, Slide 9

10 E.P.E. for point charges E.P.E. of two charges q 1 and q 2 separated a distance r: U E = k q 1q 2 r What is the electric potential energy of an electron a distance r = m from a proton (H atom)? U E = ( )( )( )/ r f = m + - = J Physics 102: Lecture 2, Slide 10

11 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 DU E = mj (watch signs!) 5 m m 5 m 2 Physics 102: Lecture 2, Slide 11

12 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! A) W = mj B) W = 0 mj C) W = mj 5 m m 5 m 2 Physics 102: Lecture 2, Slide 12

13 CheckPoint m m m - 3 The total work required by you to assemble this set of charges is: 57% 14% 28% (1) positive (2) zero (3) negative Bring in (1): zero work Bring in (2): positive work Bring in (3): negative work x 2 Physics 102: Lecture 2, Slide 13

14 Electric Potential V U E /q Electric potential energy per charge Units: Joules/Coulomb Volts Examples: Batteries EKG Only potential differences matter J/C more energy! Physics 102: Lecture 2, Slide 14

15 Electric Potential: like height Devil s Tower Topographical map Moving to higher potential moving uphill Physics 102: Lecture 2, Slide 15

Demo: electric potential Recall electric dipole + 150 Equipotential lines 100 + 50 Physics 102: Lecture 2, Slide 16 0 0 50 100

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

17 To go from B to A, a positive charge must climb up hill increases potential energy. Hence A is at higher potential than B. CheckPoint 1.7 The electric potential at point A is at point B 46% 1) greater than 32% 2) equal to 22% 3) less than Physics 102: Lecture 2, Slide 17

electric field points toward lower potential, but the electric field is zero

18 ACT E=0 Now points A and B lie inside a conductor conductor The electric potential at point A is at point B A) greater than B) equal to C) less than The electric field points toward lower potential, but the electric field is zero inside a conductor so the potential is equal everywhere! Physics 102: Lecture 2, Slide 18

19 Potential for Point charges Electric potential a distance r from a charge q: V U E /q V = k q r What is the electric potential a distance r = m from a proton? (V( )=0) V =U E /q= k q/ r = ( )( ) / = 27.2 Volts r f = m + Physics 102: Lecture 2, Slide 19

4 m 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 V 7 = (9 10 9 )(7 10-6 )/5 = 12.

20 4 m 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 V 7 = ( )( )/5 = V V 3 = ( )( )/5 = V V total = V 7 +V 3 = V Q=+7.0mC 6 m Q=-3.5 mc How much work do you have to do to bring a 2 mc charge from far away to point A? Physics 102: Lecture 2, Slide 20 W=DU=Vq = ( V)(2mC) = mj

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 21

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

23 Electron microscope ΔV=10kV - V i Uniform E V f motion What is the final velocity of the electron? Solve by conservation of energy: Electron gun v = K.E. i + P.E. i = K.E. f + P.E. f 0 + ev i = ½mv 2 + ev f 2e V m = ( ) = m/s Could solve this using F=ma & kinematic equations (Phys 101) TRY AT HOME! (HARDER) Physics 102: Lecture 2, Slide 23

24 Physics 102: Lecture 2, Slide 24 See you Monday!

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