Electric Potential Energycontent.njctl.org/courses/science/ap-physics-2/electric... · Web view2015/08/11 · Define the characteristics of a parallel plate capacitor, describing

Chapter Questions

1. If there are two negative charges near each other, is the Electric Potential Energy positive or negative? What does this imply?

2. If there is a negative charge near a positive charge, is the Electric Potential Energy of this arrangement negative or positive? What does this imply?

3. How is the Electric Potential derived from the Electric Potential Energy?

4. What is the unit for Electric Potential? Express this unit in terms of Joules and Coulombs. Explain what this means.

5. What is an Equipotential line? How does it relate to an Electric Field line?

6. How much work is required to move an electric charge between two points which have equal potential?

7. Can two Equipotential lines cross or touch in free space?

8. Describe the Electric Field between two parallel plates of opposite charge. What is the value of the Electric Field outside the parallel plates?

9. What is the function of a capacitor, explained in terms of charge and energy?

10. Define the characteristics of a parallel plate capacitor, describing what each metal plate contains in charge and how the Electric Potential, V, is established.

11. An electric field at any point in the region between two parallel plates of a capacitor is directly proportionally to what?

12. A battery supplies voltage and current for a capacitor. As charge builds up on the capacitor, how is the potential difference affected?

13. The value of Q (charge) is calculated to be 50 mC. How much charge is on the plate with higher potential? How much charge is on the plate with lower potential?

14. A capacitor is charged with a power supply of voltage V. The power supply is disconnected after the capacitor becomes fully charged, isolating the capacitor. The plates are then pulled closer together. How does the capacitance and the voltage change?

15. Putting a dielectric in between the plates of a capacitor will have what effect on the capacitance? Explain without the use of quantitative variables/equations.

Electric Potential and Capacitors v 1.1 ©2009 Goodman & Zavorotniy

Chapter Problems

I. Electric Potential Energy

Classwork1. What is the potential energy of an electron and a proton in a hydrogen atom if the distance between

them is 5.3 x 10-11 m?

2. What is the potential energy of two charges of +4.2 μC and +6.1 μC which are separated by a distance of 50.0 cm?

3. What is the potential energy of two charges of -3.6 μC and +5.2 μC which are separated by a distance of 75.0 cm?

4. There are three charges, 4.0 µC, 3.5 µC and -6.4 µC, each at the vertex of an equilateral triangle of side length 0.020m. What is the potential energy of the system?

Homework5. What is the potential energy of two charges of -5.2 μC and -8.2 μC which are separated by a distance of

50 cm?

6. What is the potential energy of two charges of 4.2 μC and -6.1 μC which are separated by a distance of 75.0 cm?

7. What is the potential energy of two electrons that are separated by a distance of 3.5 x 10 -11 m?

8. What is the potential energy of three charges of 2.0 µC, -4.5 µC and -3.4 µC that are in a straight line, with the -4.5 µC charge in the middle, and each charge is 5.0 cm away from its adjacent charge?

II. Electric Potential (Voltage)

Classwork9. Draw equipotential lines due to a positive point charge.

10. What is the Electric Potential 50.0 cm from a –7.4 μC point charge?

11. What is the Electric Potential 25 cm from a +5.0 μC point charge?

12. Two point charges of +3.5 μC and +8.3 μC are separated by a distance of 4.0 m. What is the Electric Potential midway between the charges?


13. A proton passes through a potential difference of 350 V. Find its kinetic energy and velocity (e = 1.60 x 10-19 C, mp = 1.67 x 10-27 kg).

14. How much work is done in moving a +2.6 µC charged particle from a point with a potential of 100.0 V to a point with a potential of 20.0 V?

15. An Electric Field does 40.0 mJ of work to move a +6.8 μC charge from one point to another. What is the potential difference between these two points?

Homework16. Draw Equipotential lines due to a negative point charge.

17. What is the Electric Potential 65.0 cm from a –8.2 μC point charge?

18. What is the Electric Potential 30.0 cm from a +6.8 μC point charge?

19. Two point charges of +2.5 μC and -6.8 μC are separated by a distance of 4.0 m. What is the electric potential midway between the charges?

20. An electron falls through a potential difference of 200.0 V. Find its kinetic energy and velocity (e = 1.60 x 10-19 C, me = 9.11 x 10-31 kg).

21. An Electric Field does 25 mJ of work to move a +7.4 μC charge from one point to another. What is the potential difference between these two points?

22. How much work is required by an Electric Field to move a -4.3 μC from a point with a potential 50.0 V to a point with a potential –30.0 V?

23. An Electric Field does 150 μJ of work to move a –8.4 μC charge from one point to another? What is the potential difference between these two points?

III. Uniform Electric Field

Classwork24. Draw Equipotential lines in a uniform Electric Field, with the positive line of charge on the top, and the

negative line of charge on the bottom.

25. An Electric Field of 440 N/C is desired between two plates which are 4.6 mm apart; what voltage should be applied?

26. What is the magnitude of the electric force on an electron in a uniform Electric Field of 2,500 N/C?


27. A 240 V power supply creates an Electric Field of 4.5 x 106 N/C between two parallel plates. What is the separation between the plates?

28. A proton is accelerated by a uniform 360 N/C Electric Field. Find the kinetic energy and the velocity of the proton after it has traveled 50.0 cm.

29. A uniform 450 N/C Electric Field moves a +3.4 μC charge 10.0 cm; how much work is done by the Electric Field?

30. How much work is done by a uniform 760 N/C Electric Field on a proton in accelerating it through a distance of 60.0 cm?

31. What is the magnitude and direction of the electric force on an electron in a uniform Electric Field of 4200 N/C that points due west? What is the acceleration of the electron?

Homework32. Draw Equipotential lines in a uniform Electric Field, with the negative line of charge on the top, and the

positive line of charge on the bottom.

33. How strong is the Electric Field between two metal plates 5.0 mm apart if the potential difference between them is 240 V?

34. How much voltage should be applied to two parallel plates, which are 12 mm apart, in order to produce a 1500 N/C Electric Field between them?

35. Two plates are connected to a 120 V battery which have a small air gap. How small can the gap be if the Electric Field cannot exceed the air’s breakdown value of 5.0 x 106 N/C, causing a spark?

36. An electron is released from rest in a uniform Electric Field and accelerates to the west at a rate of 2.4 x 108 m/s2. What is the magnitude and direction of the Electric Field?

37. An electron falls a distance of 25 cm in a uniform 500.0 N/C Electric Field; how much work is done on the electron?

38. A potential difference of 120 V is applied between two parallel plates. What is the Electric Field strength between the plates if they are 2.5 mm apart?

39. An initially stationary electron is accelerated by a uniform 640 N/C Electric Field. Find the kinetic energy and velocity of the electron after it has traveled 15 cm.


IV. Capacitors and Capacitance

Classwork 40. A capacitor has a value of 4F. A capacitor’s plate separation is halved. What is the new capacitance

value?

41. In a parallel plate capacitor, the plates are 4.2 mm apart with an electric potential of 8000 V. What is the electric field between the plates?

42. What is the capacitance of a capacitor with a plate area of 2.8 x 10 -3 m2 and a distance d of 2.5 x 10-3 m? What is its capacitance after a dielectric material of acrylic of k = 2.7 is inserted?

43. A parallel plate capacitor has a capacitance of 70.5 pF. If the plates are 9.0 mm apart, what is the area of the plates?

44. A parallel plate capacitor has a charge of 46 μC with a potential difference of 9000 V. What is its capacitance?

45. The capacitance of a given parallel plate capacitor is 3.9 nF. It is applied 2000V. What is the charge on the capacitor?

46. How much energy is stored in a fully charged 4.5 mF parallel plate capacitor with 2.0 V across its plates?

47. The charge on a capacitor is 2.4 x 10-9 C. The potential across it has a value of 4.2 V. What is the electrical potential energy stored on the capacitor?

48. The charge on a capacitor is determined to be 3.0 μC. What must the potential difference be in order to have an electrical potential energy of 0.076 J?

Homework

49. A capacitor has a value of 2.2 F. Another capacitor has the same capacitance but its area is larger by a factor of 4. What is its new capacitance?

50. In a parallel plate capacitor, it is found the potential difference between the two plates are 25,000 V and the distance between them to be 7 mm. Find the electric field between the plates.

51. What is the capacitance of a capacitor with a plate area of 3.6 x 10 -3 m2 and a distance d of 2.5 x 10-3 m? What is its capacitance after a dielectric of silicon with value k = 11 is inserted? 1.3 x 10 -11 F; 1.4 x 10-10 F


52. A parallel plate capacitor has a capacitance of 2.0 μF. If the plates are 4.0 x 10-6 cm apart, what is the area of the plates?

53. A parallel plate capacitor has a charge of 32 μC with a potential difference of 800 V. What is its capacitance?

54. The capacitance of a given parallel plate capacitor is 3.0 nF. It is applied 2400V. What is the charge on the capacitor? 7.2 x 10-6 C

55. How much energy is stored in a fully charged 6.0 mF parallel plate capacitor with 3.0 V across its plates?

56. The charge on a capacitor is found to be 1.2 x 10-8 C, and its potential to be 8V. What is the electrical potential energy stored on the capacitor?

57. The charge on a capacitor is determined to be 9.0 mC. What must the potential difference be in order to have an electrical potential energy of 0.11 J?

General Problems

Classwork

D

A C

B E

+100V +50V 0V -50V -100V

1. In a region of space, the electric potential is described by the set of equipotential lines shown above. A –35.0 μC charge will be moved from one location to another in this region.

a. On the diagram, indicate the Electric Field direction at the points: A, B, C, D and E.b. Between which two points is there the greatest potential difference?c. Between which two locations will the work done by the Electric Field on the charge be the

greatest? d. How much work is done by the Electric Field on the charge if it moves from point B to point C?e. How much work is done by the Electric Field on the charge if it moves from point E to point D?f. Compare the magnitude of the work done on the charge when it moves from point A to point B;

when it moves from point A to point E; and from point E to point B.


+Q1 -Q2

-4 -3 -2 -1 0 1 2 3 4 5 6 7 x(m)

2. A positive charge, Q1 = +4.60 μC, is located at point x1 = -4.00 m and a charge, Q2 = -3.80 μC, is located at a point x2 = 6.00 m.

a. Find the magnitude and direction of the electric force between the charges.b. Find the magnitude and direction of the Electric Field at the origin due to charge Q1.c. Find the magnitude and direction of the Electric Field at the origin due to charge Q2.d. Find the magnitude and direction of the net Electric Field at the origin.e. Find the electric potential at the origin due to charge Q1.f. Find the electric potential at the origin due to charge Q2.g. Find the net electric potential at the origin.h. How much work must be done to bring a 1.00 μC test charge from infinity to the origin?

3. A parallel plate capacitor of value 6.4 μF is given. It is connected to a power source of a 6 V battery.a. What is the charge on each plate? b. Calculate how much energy is stored on the capacitor once fully charged. c. What would be the value of this charge if the area of the plates were doubled? What would be the value of the charge if the separation between the plates was halved? d. Suppose the capacitor has been fully charged and disconnected from its original power source. What would a reading with a voltmeter across the two plates read (assuming there is no discharge)? What would the voltmeter read if plate separation quadrupled?

4. There are two of the same, parallel plate capacitors. Each have been connected to a power source of 12 V, leading them to store a charge Q respectively. Each is now disconnected: one (C1) remains as it is without discharge, and C2 is filled with a dielectric.

a. Explain what happens to the original electric field between the parallel plates once a dielectric is inserted qualitatively. What property is responsible for this phenomenon, rearranging charges between the plates? b. Calculate the dielectric inserted capacitance C2 if original capacitance was 10 μF and the dielectric has a value of 8. c. Determine which capacitor stores greater charge, if any (just stating which capacitor will gain sufficient credit for this question).d. Determine the relationship between the voltages of the two capacitors by choosing one of the following.

i) V1 = V2

ii) V1 < V2

iii) V1 > V2


Homework

D A

C E B

-40V +40V -20V 0V +20V

5. In a region of space, the electric potential is described by the set of equipotential lines shown above. A –35 μC charge will be moved from one location to another in this region.

a. On the diagram, indicate the Electric Field direction at the points: A, B, C, D and E.b. Between which two points is there the greatest potential difference?c. Between which two locations will the work done by the Electric Field on the charge be the

greatest? d. How much work is done by the Electric Field on the charge if it moves from point A to point D?e. How much work is done by the Electric Field on the charge if it moves from point C to point A?f. The charge is moved from point A to point B in the first trial. In the second trial, the charge is

moved from point A to point E, and then it is moved to point B. Compare the magnitude of the work done on the charge between the two trials.

-Q1 +Q2

-3 -2 -1 0 1 2 3 4 5 6 x(m)

6. A negative charge, Q1 = -5.4 μC, is located at a point x1 = -2.0 m and positive charge, Q2= 7.6 μC, is located at a point x2 = 4.0 m.

a. Find the magnitude and direction of the electric force between the charges.b. Find the magnitude and direction of the Electric Field at the origin due to charge Q1.c. Find the magnitude and direction of the Electric Field at the origin due to charge Q2.d. Find the magnitude and direction of the net Electric Field at the origin.e. Find the electric potential at the origin due to charge Q1.f. Find the electric potential at the origin due to charge Q2.g. Find the net electric potential at the origin.


h. How much work must be done to bring a 10.0 nC test charge from infinity to the origin?

7. An alpha particle (q = +3.20 x 10-19 C and m = 6.64 x 10-27 kg) is accelerated from rest by a potential difference of 5000.0 V in a uniform Electric Field. The potential difference is applied over a distance of 10.0 cm.

a. What is the maximum kinetic energy of the alpha particle?b. What is the maximum speed of the alpha particle?c. What is the Electric Field strength?d. What is the acceleration of the alpha particle?e. How long will it take for the alpha particle to travel the 10.0 cm?

8. A parallel plate capacitor can store up to 460 nC, connected to a 10 V battery, and has a plate separation of 45 mm.

a. What is the area of the plates? b. What is the electric field between the plates? c. Calculate the stored energy on the capacitor.

A dielectric material with permittivity value of 3.0 is inserted. d. Re-calculate the new electric field. e. Does the electric field increase or decrease with the dielectric? Why? f. Calculate the new capacitance and energy able to be stored on the capacitor.

9. Two metal sheets are aligned parallel to each other, each with opposite electric charges of equal magnitude. These plates are separated by 60 mm. The electric field between the plates is uniform, and is given to be 740 N/m.

a. Calculate the potential difference between the sheets.b. In what direction does the electric field exist? c. Which of the two sheets has the higher potential?d. Suppose this is given to be used as a capacitor, and a dielectric material of glass (K = 5.2) is inserted between the plates. If the original capacitance is given to be C, what is the new capacitance given in terms of C?e. With the newly inserted dielectric, what is the new potential difference?

Answers

Chapter Questions

1. The Electric Potential Energy is positive. That means that it takes positive work by an external agent to overcome the repulsive force between the two like charges as they are brought together.

2. The Electric Potential Energy is negative. That means that it takes negative work by an external agent to keep the charges from accelerating towards each other due to the attractive force between them.


3. The equation for Electric Potential Energy is divided by a small positive test charge, q, leaving the Electric Potential dependent only on the source charge.

4. The unit is the Volt. 1 Volt = 1 Joule/Coulomb. 1 Volt means that a Coulomb of charge passing through a battery would increase its energy by 1 Joule.

5. An Equipotential line describes a region in space where the Electric Potential is the same. An Equipotential line is perpendicular to the tangent of the Electric Field line at all points.

6. Zero work is required since Work is equal to the charge magnitude times the change in Electric Potential which is equal to zero. This can be quantitatively explained by W = qV.

7. No. Otherwise, the point of intersection would have two different values of V – which is impossible.8. The Electric Field is uniform – which means it is constant in magnitude and in the same direction at all

points within the plates. Outside the plates the Electric Field is zero.9. A capacitor can store charge and Electric Potential Energy.10. A capacitor with parallel plates will have one plate holding a charge +Q, and the other plate is charged

to –Q. This difference in charge (one plate is positive and the other is negative) is what accounts for electric potential.

11. The charge, Q.12. The Electric Potential difference, V, increases at the same rate as the charge.13. The plate with the higher potential has a charge of +50 mC and the plate with the lower potential has a

charge of -50 mC.14. Pulling the plates closer together will increase the capacitance. Meanwhile, because the capacitor has

been fully charged and then isolated, no charge can leave (Conservation of Charge). By Q = CV, a constant charge and increased capacitance will result in a decreased Electric Potential, V.

15. A dielectric is an insulating material which increases capacitance by affecting the electric field. It consists of atoms that are polarized by the charges on both plates in the capacitor. The slightly positive end of the atom will be attracted by the negative plate, and the slightly negative end will be attracted by the positive plate, thus setting up an electric field that opposes the electric field created by the plates. There is now more charge in the capacitor due to the separated charges of the dielectric due to polarization. Since C = Q/V, for a given voltage and greater charge, the capacitance increases with the insertion of the dielectric.


Chapter Problems

1. -4.3 x 10-18 J2. 4.6 x 10-1 J3. -2.2 x 10-1 J4. -1.5 x 101 J5. 7.7 x 10-1 J6. -3.1 x 10-1 J7. 6.6 x 10-18 J8. 5.2 x 10-1 J

9.

10. -1.3 x 105 V11. 1.8 x 105 V12. 5.3 x 104 V13. KE = 6.0 x 10-17 J; v = 2.4 x 105 m/s14. -2.1 x 10-4 J15. 5.9 x 103 V

16. 17. -1.1 x 105 V18. 2.0 x 105 V19. -1.9 x 104 V20. KE = 3.2 x 10-17 J; v = 8.4 x 106 m/s21. 3.4 x 103 V22. -3.4 x 10-4 J


23. 18 V24.

25. 2.0 V26. 4 x 10-16 N27. 5.3 x 10-5 m28. KE = 2.9 x 10-17 J; v = 1.9 x 105 m/s29. 1.4 x 10-4 J30. 7.3 x 10-17 J31. FE = 6.7 x 10-16 N to East; a = 7.4 x 1014 m/s2

32.

33. 4.8 x 104 V/m34. 18 V35. 2.4 x 10-5 V36. 1.4 x 10-3 N/C towards the East37. -2.0 x 10-17 J38. 4.8 x 104 V/m39. KE = 1.5 x 10-17 J; v = 5.8 x 106 m/s40. 8F41. 1.9 x 106 V/m42. 9.9 pF; 27 pF43. 0.07 m2

44. 5.1 nF45. 7.8 μC46. 9 mJ47. 5.0 x 10-9 J48. 2.5 x 104 V49. 8.8F50. 3.6 x 106 V/m51. 13 pF; 140 pF52. 0.9 m2


The horizontal linesare the Equipotentials.

The horizontal linesare the Equipotentials.

53. 4.0 x 10-8 F54. 7.2 μC55. 2.7 x 10-2 J56. 4.8 x 10-8 J57. 12 V

General Problems

1.

a.b. Between A and Ec. Between A and Ed. WB→C = 1.75x10-3 Je. WE→D = -1.75x10-3 Jf. WA→B < WE→B < WA→E

2. a. 1.57 x 10-2 N, F12 to the left, F21 to the rightb. 2.59 x 103 N/C to the rightc. 9.50 x 102 N/C to the rightd. 3.54 x 103 N/C to the righte. 1.04 x 104 Vf. -5.70 x 103 Vg. 4.70 x 103 Vh. 4.70 x 10-3 J

3. a. 38.4 μF b. 1.152 x 10-4 Cc. 76.8 μF


d. 6 V; using a voltmeter to see if the voltage across the capacitor is the value it is charged up to with the power source, then the capacitor is working. So if Q remains the same (due to being disconnected without loss of charge) and V remains the same as well, then capacitance C (how much charge can be stored) will remain the same even plate areas/distance is changed.

4. a. Electric field is decreased/reduced; polarization within particles of the dielectric rearrange so negative charges point to positive plate and positive charges point to negative plate b. 80 μF c. Neither, as Q1 = Q2 d. iii) V1 > V2

5.

A.B. Between A and EC. Between A and ED. WA→D = -2.1 x 10-3 JE. WC→A = 1.4 x 10-3 JF. WA→B < WE→B < WA→E

6.a. 1.03x10-2 N, F12 to the left, F21 to the rightb. 1.22 x 104 N/C to the leftc. 4.28 x 103 N/C to the leftd. 1.64 x 104 N/C to the lefte. -2.43 x 104 Vf. 1.71 x 104 Vg. -7.20 x 103 Vh. -7.20 x 10-5 J

7. a. 1.60 x 10-15 Jb. 6.94 x 105 m/s


c. 5.00 x 104 N/Cd. 2.41 x 1012 m/s2

e. 2.88 x 10-7 s

8. a. 233.9 m2 b. 222.2 N/mc. 2.3 x 10-6 J d. 74.1 N/m e. Decreased; polarization of particle in dielectric oppose existing electric field f. 1.38 x 10-7 F; 6.9 x 10-6 J

9. a. 44.4 V b. Positively charged plate to negatively charged plate/higher potential to lower potential c. Positively charged plate d. 5.2C Farads e. 230.9 V


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Electric Potential Energycontent.njctl.org/courses/science/ap-physics-2/electric... · Web view2015/08/11 · Define the characteristics of a parallel plate capacitor, describing