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§16.5 Motion of a Point Charge in a Uniform E-Field

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1 §16.5 Motion of a Point Charge in a Uniform E-Field
Q) What is E-field around a metal plate w/ +Q? Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 14. + + Q) A metal plate w/ –Q? + +

2 Parallel metal plates  uniform E
Fig Charge +q & mass m

3 “Cathode Ray Tube” (TV)
“Electron gun”

4 Use kinematic equations w/ constant a from Ch. 4:
Charge +q & mass m. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 14. Use kinematic equations w/ constant a from Ch. 4:

5 Example: What electric field is needed to keep an electron suspended in the air against gravity?
Direction? Strength? Would a proton require the same field? Example (PP 16.48): An electron is placed in a uniform electric field of strength 232 N/C. If the electron is at rest at the origin of a coordinate system at t = 0 and the electric field is in the positive direction, what are the x- and y-coords of the electron at t = 2.3 ns? The velocity?

6 §16.6 Conductors in Electrostatic Equilibrium
• Conductors are easily polarized: free electrons move around freely inside the material. • Any charges placed on a conductor will arrange themselves in a stable, unmoving distribution: electrostatic equilibrium. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 15. • For a conductor in electrostatic equilibrium: 1) The E-field inside it is zero (no field lines) 2) Any net charge must reside on the surface 3) Just outside the surface, E is perpendicular to the surface 4) Any excess charge will accumulate where the surface is highly curved (i.e. a sharp point): E is strongest there.

7 Put 16 nC on the following surface: Q) Where will charges go
Put 16 nC on the following surface: Q) Where will charges go? Q) What will the E-field look like? Lightning rod

8 Chapter 18: Electric Potential
Electric Potential Energy Electric Potential (Voltage) How are the E-field and Electric Potential related? Motion of Point Charges in an E-field Capacitors Dielectrics For Wed recitation: do Online Problems (WA) do Practice Problems: Ch 17 #45, 87 Ch 18 tbd Lab: 2.03 (vsound) this week Read instructions Do Pre-Lab & turn in Quiz #1 (Ch 13, 17, 18) Wed Sep 18 during recitation (indiv, group) More help: SPS drop in MW 8:30-9:30am TR 11am-noon 178 Overman Hall Canvas goodies

9 §17.1 Electric Potential Energy
Electric potential energy (PEe) is: energy stored in the electric field, work (W=F.d) done to put charges in place. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 17, Question 13. +Q +Q h m +q -q

10 Example: Two point charges, Q = +6. 0 mC and q = +5
Example: Two point charges, Q = +6.0 mC and q = +5.0 mC are separated by 15.0 m. What is their potential energy? If Q is fixed and q is free to move, what will q do? How does q’s motion affect the potential energy? Explain in terms of conservation of energy.

11 Q) What if there are four charges?
Q) What is the potential energy of three point charges arranged as a right triangle? This slide is animated to walk through the process of bringing in the charges (for the configuration on the left) one at a time and accounting for the change in potential energy at each step. The second arrangement is brought in as a single entity. The purpose of the ending question is to make the students look hard at the two arrangements and conclude that they are different and because they are different their potential energies will differ. Q) What if there are four charges? (scalar sum)

12 §17.2 Electric Potential Electric potential is the electric potential energy per unit charge: scalar 1 V = 1 J/C. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 17, Questions 2, 4, 12, and 17. For a point charge Q: When a charge q moves through a potential difference of V, its potential energy change is PEe = qV.

13 (a) Compare the potential at points d and g.
Example: A charge Q = +1 nC is placed somewhere in space far from other charges. Take ra = rb = rc = rd = 1.0 m and re = rf = rg = 2.0 m. Q b a c e d g f (a) Compare the potential at points d and g. (b) Compare the potential at points a and b.

14 Example: A charge Q = +1 nC is placed somewhere in space far from other charges. Take ra = rb = rc = rd = 1.0 m and re = rf = rg = 2.0 m. Q b a c e d g f (c) Place a charge of nC at point e. What will the change in potential (V) be if this charge is moved to point a? (d) What is the change in potential energy (PE) of the nC charge ?

15 §17.3 The Relationship between E and V
Equipotentials: surfaces of equal potential. Q b a c e d g f +9 V Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 17, Questions 1, 3, 14, 16, 18, and 19.

16 E points in direction of maximum potential decrease.
E is perpendicular to the equipotential surfaces. Q b a c e d g f +9 V +4.5 V E Q) What is V at 3m? At 0.5 m?

17 Q: What do the equipotentials look like around a – charge?
Fig Q: What do the equipotentials look like around a – charge?

18 Equipotentials and field lines for a dipole:

19 Uniform E-field: Equipotential surfaces V1 V2 V3 V4 E
Where d is the distance over which V occurs.

20 Example: Two parallel plates are separated by 2. 0 mm
Example: Two parallel plates are separated by 2.0 mm. One is at a potential of V while the other is at 0.0 V. What is the E-field between them? Q) Why is E negative?

21 Hollow Conducting Sphere (radius = R):
(Similar for other hollow shapes)

22 Van de Graaff generator

23 §17.4 Moving Charges When only electric forces act on a charge, its total mechanical energy, E, will be conserved: Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 17, Questions 5 and 15.

24 Example (PP 17. 40): Point P is at a potential of 500
Example (PP 17.40): Point P is at a potential of kV and point S is at a potential of kV. The space between these points is evacuated. When a charge of +2e moves from P to S, by how much does its kinetic energy change? (b) If the particle has a mass of 2.0x10-9 kg and starts from rest at P, what is its speed at S?

25 Example (text problem 17.41): An electron is accelerated from rest through a potential difference. If the electron reaches a speed of 7.26106 m/s, what is the potential difference?

26 Chapter 17: Electric Potential
Electric Potential Energy Electric Potential How are the E-field and Electric Potential related? Motion of Point Charges in an E-field Capacitors Dielectrics For Mon recitation: do Online Problems do Practice Problems: Ch 17 (pp.634-7) 42, 70, 83, 87, 91 Lab: 2.04 (E-field) this week Read instructions Do Pre-Lab & turn in 2.05 (Current) next week Exam #1 (Ch 12, 16, 17) Wed Sep 12, 7:30-8:45pm, 095 Overman Hall Free Tutoring & Study See BlackBoard/C.I. Practice Exam on BB

27 Parallel plate capacitor
§17.5 Capacitors A capacitor stores electric potential energy by storing separated (+) and (–) charges. Work must be done to separate the charges. + Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 17, Questions 6, 8, and 9. Parallel plate capacitor Why?

28 Fig

29

30 where the proportionality constant C = capacitance
+ V For a parallel plate capacitor: Or Q = CV where the proportionality constant C = capacitance [ Farad = C/V ]

31 What is the capacitance for a parallel plate capacitor?
Note: C is a property of the device, it depends on A & d, “capacity” to hold charge.

32 Example (PP 17. 56): A parallel plate capacitor has a capacitance of 1
Example (PP 17.56): A parallel plate capacitor has a capacitance of 1.20 nF. There is a charge of magnitude C on each plate. What is the potential difference between the plates? If the plate separation is 0.3 mm, what is the area? If the plate separation is doubled while the charge is kept constant, what will happen to the potential difference, and to the potential energy stored in the capacitor?

33 §17.6 Dielectrics – I. Air-filled capacitor: Increase Q  increase E
+ I. Air-filled capacitor: Increase Q  increase E Atoms in air b/w plates gets polarized: Eventually electrons pulled off (ionized), Charge arcs across gap = “breakdown” Need a better insulator! dielectric strength (kV/mm) Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 17, Question 7.

34 Charge separation at ends Reduces E inside dielectric
+ II. Add a dielectric w/ dielectric constant k Atoms polarize Charge separation at ends Reduces E inside dielectric Can add more Q to plates Higher C = Q/DV Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 17, Question 7.

35

36 (b) How much charge can it hold before breakdown?
Example (PP 17.71): A capacitor can be made from two sheets of aluminum foil separated by a sheet of waxed paper. If the sheets of aluminum are 0.3 m by 0.4 m and the waxed paper, of slightly larger dimensions, is of thickness mm and has  = 2.5, (a) what is the capacitance of this capacitor? (b) How much charge can it hold before breakdown? (c) How much energy is stored at this point? McGuiver?!

37 §17.7 Energy Stored in a Capacitor
Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 17, Questions 10 and 20. A capacitor will store energy equivalent to the amount of work that it takes to separate the charges.

38 } The energy stored in the electric field between the plates is:
(Sub in Q = CV) Summary: • C is set by the device (A, d, k) • V is set by the strength of the battery (“pump”) • Q and U depend on C and V.

39 Example (PP 17.79): A parallel plate capacitor is composed of two square plates, 10.0 cm on a side, separated by an air gap of 0.75 mm. (a) What is the charge on this capacitor when the potential difference is 150 volts? (b) What energy is stored in this capacitor?

40 Summary Electric Potential Energy Electric Potential
The Relationship Between E and V Motion of Point Charges (conservation of energy) Parallel Plate Capacitors (capacitance, dielectrics, energy storage)

41 §16.6 Conductors in Electrostatic Equilibrium
• Conductors are easily polarized: free electrons move around freely inside the material. • Any charges placed on a conductor will arrange themselves in a stable, unmoving distribution: electrostatic equilibrium. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 15. • For a conductor in electrostatic equilibrium: 1) The E-field inside it is zero (no field lines) 2) Any net charge must reside on the surface 3) Just outside the surface, E is perpendicular to the surface 4) Any excess charge will accumulate where the surface is highly curved (i.e. a sharp point): E is strongest there.

42 Put 16 nC on the following surface: Q) Where will charges go
Put 16 nC on the following surface: Q) Where will charges go? Q) What will the E-field look like? Lightning rod


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