The electric potential energy of charge q in a uniform electric field is

Transcription

1 The electric potential energy of charge q in a uniform electric field is where s is measured from the negative plate and U 0 is the potential energy at the negative plate (s = 0). It will often be convenient to choose U 0 = 0, but the choice has no physical consequences because it doesn t affect ΔU elec, the change in the electric potential energy. Only the change is significant.

2 Analogy to Gravitational PE Gravitation PE depends on mass Electric potential energy depends on charge General Physics 2 Electric Potential 2

3

4 Consider two point charges, q 1 and q 2, separated by a distance r. The electric potential energy is This is explicitly the energy of the system, not the energy of just q 1 or q 2. Note that the potential energy of two charged particles approaches zero as r.

5

6 Which set has a positive potential energy?

7 Which set has a negative potential energy?

8

9

10 The potential energy of an electric dipole p in a uniform electric field E is The potential energy is minimum at ø = 0 where the dipole is aligned with the electric field. Remember p = qs

11 Electrical Potential Energy For a charge in a uniform electric field For point charges

12 Think-Pair-Share What is the potential energy of this system, taking U = 0 at a great distance? +4Q General Physics 2 Electric Potential 12

13 Workbook Problems on Electric Potential Energy P #1 P.29-3 #5, 6 P29-4 #7, 8 General Physics 2 Electric Potential 13

14 We define the electric potential V (or, for brevity, just the potential) as Charge q is used as a probe to determine the electric potential, but the value of V is independent of q. The electric potential, like the electric field, is a property of the source charges. The unit of electric potential is the joule per coulomb, which is called the volt V:

15 Let q be the source charge, and let a second charge q', a distance r away, probe the electric potential of q. The potential energy of the two point charges is By definition, the electric potential of charge q is The potential extends through all of space, showing the influence of charge q, but it weakens with distance as 1/r. This expression for V assumes that we have chosen V = 0 to be at r =.

16

17 Equipotential Lines connect points in space at same potential equipotential surface is perpendicular to electric field lines General Physics 2 Electric Potential 17

18 Electric Field & Equipotential Lines Draw field lines and equipotential lines for the following charge distributions - General Physics 2 Electric Potential 18

19 Electric Field & Equipotential Lines Draw field lines and equipotential lines for the following charge distributions + General Physics 2 Electric Potential 19

20 QUESTIONS:

21

22 Plug & Chug What is the electric potential 15.0 cm from a 4.00 x 10-6 C point charge? General Physics 2 Electric Potential 22

23 In prac(ce, you are more likely to work with a charged sphere, of radius R and total charge Q, than with a point charge. Outside a uniformly charged sphere, the electric poten(al is iden(cal to that of a point charge Q at the center. That is, Or, in a more useful form, the poten(al outside a sphere that is charged to poten(al V 0 is

24 Plug & Chug What is the electric potential 15.0 cm from a charged sphere with a charge of 4.00 x 10-6 C and a radius of 1.0 cm? What is the electric potential 20.0 cm from a 1.0 cm diameter charged sphere that has been charged to 1000V? General Physics 2 Electric Potential 24

25 The electric poten(al V at a point in space is the sum of the poten(als due to each charge: where r i is the distance from charge q i to the point in space where the poten(al is being calculated. In other words, the electric poten5al, like the electric field, obeys the principle of superposi5on.

26 QUESTION:

27

28 The electric potential inside a parallel-plate capacitor is where s is the distance from the negative electrode. The electric potential, like the electric field, exists at all points inside the capacitor. The electric potential is created by the source charges on the capacitor plates and exists whether or not charge q is inside the capacitor.

29 Electric Potential Think of analogy with gravitational PE, where object with positive PE will fall if released. Here, p+ has high PE when near + plate and will fall toward negative plate when released Think of + charge when wondering if something is high or low potential + charges move from high to low potential

30 Electric Potential Unlike mass, charge can be + or -. Thus, PE depends on the sign of the charge. low PE - - High PE For example, an e- will have high PE when near the - plate and will fall toward the + plate when released - charges move from low to high potential

31 QUESTIONS:

32

33

34

35

36

37 Electrostatic Potential & PE When dealing with discrete point charges: U = kq 1 q 2 r F = kq 1 q 2 r 2 r ˆ V = kq r U and V are scalars E = kq r 2 r ˆ F and E are vectors General Physics 2 Electric Potential 37

38 Workbook P29-6 #11, 13 P29-7 #15 P29-9 #17, 18 P29-10 #20 P29-11 #22 General Physics 2 Electric Potential 38