The Electric Potential Energy

Transcription

1 Lecture 6 Chapter 25 The Electric Potential Energy Course website:

2 Today we are going to discuss: Chapter 25: Section 25.1 Electric Potential Energy Section 25.2 The potential energy o a point charge

3 New Idea So ar, we used vector quantities: 1. Electric Force (F) Depressed! 2. Electric Field (E) But, as you know, it is not easy to deal with vectors Idea!!!! Let s introduce scalar quantities instead o a FORCE and FIELD

4 Let s deine a conservative orce and give an idea o PE Consider dierent paths between two points in a ield F ds U =5J Recall or Physics I, a work done by a orce i U 0 I a work done by a orce is path independent, then this orce is called conservative (since it leads to conservation o mechanical energy) PE idea: That is what we have in our example. So, you can attach this number to the inal point and give this number 5 a ancy name the potential energy (PE) (U =5J) with respect to the initial point, where we can assume PE to be zero (the reerence point). For every conservative orce a potential energy can be introduced. Since the gravitational and electrical orces are conservative orces, corresponding potential energies can be introduced.

5 i Gravitation U initial U 0 + mgy i F=mg U inal U 0 + mgy U 0 =0 (Reerence Level) This all can be described using a gravitational orce (vector quantity), which describes an interaction between the Earth and a cat. F grav mg U grav mgy Since the gravitational orce is a conservative orce, a gravitational potential energy (scalar quantity) can be introduced. The case o two point masses G Physics I G F el qe Electrostatics i F=qE Uniorm Electric ield Let s derive these electric PE: The case o two point charges k Goal 1 U qes Goal 2 U r k r

6 Potential energy is an energy o interaction, so there must be at least two interacting electric objects.

7 Potential energy o q in a uniorm electric ield (in a capacitor)

8 q 0 si Potential energy o q in a uniorm electric ield The work done on q is: ds E s W F ds Consider a charge q inside a capacitor. It moves rom an initial point to a inal point. There is a constant orce F qe E s i q E ds q i Recall rom Physics I i Eds qe U W i ds K U U U i qes s i U U i qes qes U i U 0 qe s s i To get the most general expression, let s introduce U 0, which is a potential energy at the reerence point s=0 U U i 0 Electric potential energy o charge q and a charged capacitor It is convenient to choose the potential energy at the reerence point U 0 0 qes U 0 U qes i U qes qes

9 ConcepTest Two positive charges are equal. Which has more electric potential energy? Potential energy A) Charge A B) Charge B C) They have the same potential energy D) Both have zero potential energy U qes s

10 ConcepTest Two negative charges are equal. Which has more electric potential energy? Potential energy A) Charge A B) Charge B C) They have the same potential energy D) Both have zero potential energy U q Es s

11 ConcepTest A positive charge moves as shown. Its kinetic energy Potential energy A) Increases. B) Remains constant. C) Decreases. U qes s increases U 0 K 0 decreases U K

12 Potential energy o two point charges

13 The potential energy o two point charges This is explicitly the energy o the system, not the energy o just q or Q. Note that the potential energy o two charged particles approaches zero as r.

14 ConcepTest Potential energy A positive and a negative charge are released rom rest in vacuum. They move toward each other. As they do: A) A positive potential energy becomes more positive. B) A positive potential energy becomes less positive. C) A negative potential energy becomes more negative. D) A negative potential energy becomes less negative. E) A positive potential energy becomes a negative potential energy.

15 Example Approaching a charged sphere Example 25.2

16 Thank you

17 s Potential energy o a positive charge, +q near( plate) near( plate) Ok, now we know the PE expression o a charge inside o a capacitor. Let s play with that expression to see where PE is larger or smaller, etc. s U qes U plate U plate lower PE higher PE I +q moves in the direction o E, then I we use Conservation o energy We will get U W K 0 K K plate U 0 K plate 0 s

18 Potential energy o a positive charge, -q s Since, the charge is negative, let s rewrite U in this orm near( plate) near( plate) s U q Es U plate U plate higher PE (less negative) lower PE (more negative) I -q moves in the direction opposite o E, then I we use conservation o energy We will get U W K 0 K K plate K plate U 0 0 s From these two examples, you see that PE can be used to analyze motion instead o orce.