Phys 102 Lecture 4 Electric potential energy & work

Size: px

Start display at page:

Download "Phys 102 Lecture 4 Electric potential energy & work"

Dwayne Gilmore
6 years ago
Views:

1 Phys 102 Lecture 4 Electric potential energy & work 1

2 Today we will... Learn about the electric potential energy Relate it to work Ex: charge in uniform electric field, point charges Apply these concepts Ex: electron microscope, assembly of point charges, dipole energy & hydration shells Phys. 102, Lecture 3, Slide 2

101 h x Gravitational potential energy (ex: falling object) Elastic potential energy

3 Potential energy Potential energy U stored energy, can convert to kinetic energy K Review Phys. 101 h x Gravitational potential energy (ex: falling object) Elastic potential energy (ex: spring) Total energy K + U is conserved Same ideas apply to electricity r + + Electric potential energy (ex: repelling charges) Phys. 102, Lecture 3, Slide 3

4 Work Review Phys. 101 Work transfer of energy when a force acts on a moving object Work done by force F W F r cos θ U F W you Displacement r It matters who does the work θ Angle between force and displacement Change in potential energy For conservative forces, work is related to potential energy F Units: J ( Joules ) Phys. 102, Lecture 3, Slide 4

5 Electric potential energy & work W W U F r cos θ F you Gravity Electricity Mass raised y i y f FG mg WG mgh Wyou mgh U mgh G down Charge moved x i x f (in uniform E field to left) FE qe left WE qed Wyou qed U qed E y f y i h r E F E x i + r d x f F G Phys. 102, Lecture 3, Slide 5

), you did positive work, force did negative work F + F + W you > 0 W F < 0 W you < 0

6 Positive and negative work If you moved object against external force (gravitational, electric, etc.), you did positive work, force did negative work F + F + W you > 0 W F < 0 W you < 0 W F > 0 If you moved object along external force (gravitational, electric, etc.), you did negative work, force did positive work Phys. 102, Lecture 3, Slide 6

7 Checkpoint 1.2 C ra C E A B When a negative charge is moved from A to C the ELECTRIC force does A. positive work B. zero work C. negative work Phys. 102, Lecture 3, Slide 7

8 ACT: Checkpoint 1.3 C A ra B B E When a negative charge is moved from A to B the ELECTRIC force does A. positive work B. zero work C. negative work Phys. 102, Lecture 3, Slide 8

9 ACT: Work in a uniform E field C Let W A-B be the answer to the previous problem E A B The negative charge is now moved from A to C to B. The work done by the electric force is A. Greater than W A-B B. Same as W A-B C. Less than W A-B Phys. 102, Lecture 3, Slide 9

10 Path independence of work A B E For conservative forces (ex: gravitational, electric), work is independent of path. Work depends only on end points. WA B U ( UB U A) Potential energy of charge at position B Potential energy of charge at position A Phys. 102, Lecture 3, Slide 10

Calculation: Electron microscope (revisited) A

accelerates electrons in an electron microscope.

11 Calculation: Electron microscope (revisited) A uniform E field generated by parallel plates accelerates electrons in an electron microscope. If an electron starts from rest at the top plate what is its final velocity? Q d = 1 cm +Q E = 10 6 N/C Electron microscope Phys. 102, Lecture 3, Slide 11

12 E.P.E of two point charges Electric potential energy of two charges q 1 and q 2 separated by a distance r qq 1 2 UE k r Note: NOT r x C = q 1 q 2 + = 1.6 x C r = 0.53 x m Ex: What is the electric potential energy of the proton and the electron in H? Phys. 102, Lecture 3, Slide 12

13 ACT: E.P.E. of 2 charges In case A, two charges of equal magnitude but opposite sign are separated by a distance d. In case B, they are separated by 2d. Case A Which configuration has a higher electric potential energy? +q + q d Case B +q + q 2d A. Case A has a higher E.P.E. B. Case B has a higher E.P.E. C. Both have the same E.P.E. Phys. 102, Lecture 3, Slide 13

14 Sign of potential energy What does it mean to have a negative electric potential energy? Ex: H atom + Proton U E < 0 relative to energy of an electron very far away (r ), away from E field of proton, i.e. a free electron Electron U E Free electron Energy must be added in order to free electron bound to proton 0 U E 2 q k r r Electron bound to proton in H atom Phys. 102, Lecture 3, Slide 14

15 Calculation: two charges Two +5 C, 1 kg charges are separated by a distance of 2 m. At t = 0 the charge on the right is released from rest (the left charge is fixed). What is the speed of the right charge after a long time (t )? +5C r = 2 m +5C From EX 1, SPRING 10 Fixed Free to move Phys. 102, Lecture 3, Slide 15

16 Work done to assemble charges How much work do you do assembling configuration of charges? q 1 q 2 + r Imagine bringing charges from infinitely far away to a separation r qq 1 2 Wyou U E k 0 r Potential energy of charges in final configuration Potential energy of charges infinitely far Phys. 102, Lecture 3, Slide 16

17 Calculation: assembling charges How much work do you do to assemble the charges q 1 = +2 μc, q 2 = +7 μc, and q 3 = 3.5 μc into a triangle? q 1 5 m 4 m q 2 3 m 3 m q 3 Phys. 102, Lecture 3, Slide 17

18 + ACT: Checkpoint 2.1 d d Charges of equal magnitude are assembled into an equilateral triangle + d The total work required by you to assemble this set of charges is: A. positive B. zero C. negative Phys. 102, Lecture 3, Slide 18

19 Calculation: dipole in E-field An electric dipole with moment p = 6.2 x C m is placed in a uniform external electric field E = 10 6 N/C at an angle θ = 60. Calculate the total electric potential energy of the dipole. θ = 60 p qd E Phys. 102, Lecture 3, Slide 19

20 +q q ACT: dipole energy Which configuration of dipole in a uniform electric field has the lowest electric potential energy? A. B. C. +q q q +q Phys. 102, Lecture 3, Slide 20

21 Hydration shell radius Recall that H 2 O dipole aligns to electric field of ions. However, at room temperature, H 2 O also has rotational kinetic energy that tends to randomize dipole orientation K K dip. Udip. 0 Dipoles are randomized (bulk water) dip. Udip. 0 Dipoles tend to be aligned (hydration shell) We can estimate distance to interface between bulk and ordered water for a monovalent ion (Ex: Na + ) H 2 0 near a charge Phys. 102, Lecture 3, Slide 21

22 Summary of today s lecture Electric potential energy & work W W U F r cos θ F you Path independence Conservation of energy Electric potential energy for point charges U E k qq r 1 2 Phys. 102, Lecture 3, Slide 22

Phys 102 Lecture 3 The Electric field

Phys 102 Lecture 3 The Electric field 1 Today we will... Learn about the electric field Apply the superposition principle Ex: Dipole, line of charges, plane of charges Represent the E field using electric