# Electric Potential Practice Problems

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1 Electric Potential Practice Problems AP Physics Name Multiple Choice 1. A negative charge is placed on a conducting sphere. Which statement is true about the charge distribution (A) Concentrated at the center of the sphere (B) Charge density increases from the center to the surface (C) Uniformly distributed on the sphere's outer surface. (D) Uniformly distributed inside the sphere (E) More information is required 2. An electric charge Q is placed at the origin. What is the ratio between the absolute potential at point A and point B? (A) 4/1 (B) 2/1 (C) 1 (D) 1/2 (E) ¼ 3. Which of the following statements about conductors under electrostatic conditions is true? (A) Positive work is required to move a positive charge over the surface of a conductor. (B) Charge that is placed on the surface of a conductor always spreads evenly over the surface. (C) The electric potential inside a conductor is always zero. (D) The electric field at the surface of a conductor is tangent to the surface. (E) The surface of a conductor is always an equipotential surface. 4. Which of the following represents the magnitude, of the potential V as function of r, the distance from the center of a conducting sphere charged with a positive charge Q, when r > R? (A) 0 (B) kq/r (C) kq/r (D) kq/r 2 (E) kq/r 2

2 5. Points A and B are each the same distance r from two unequal charges, +Q and +2Q. The work required to move a charge q from point A to point B is: (A) dependent on the path taken from A to B (B) directly proportional to the distance between A and B (C) positive (D) zero (E) negative 6. An electric field is created by a positive charge. The distribution of the electric field lines and equipotential lines is presented on the diagram. Which statement about electric potential is true? (A) V A > V B > V C > V D > V E (B) V A < V B < V C < V D < V E (C) V A = V D > V B > V C = V E (D) V A > V B = V C > V D = V E (E) V A > V B > V C = V D = V E 7. An electric field is created by a positive charge. The distribution of the electric field lines and equipotential lines is presented on the diagram. A test charge +q is moved from point to point in the electric field. Which statement about work done by the electric field on charge +q is true? (A) W A B >W A C (B) W A D >W A E (C) W D C <W A E (D) W A D =W C E =0 (E) W A B =W A E

3 8. Two parallel conducting plates are charged with an equal and opposite charges. Which statement is true about the magnitude of the electric potential? (A) Greater at point A (B) Greater at point B (C) Greater at point C (D) Greater at point D (E) The same at points B, C, D and zero at point A 9. A point charge q is released from rest at point A and accelerates in a uniform electric field E. What is the ratio between the work done by the field on the charge: W A B /W B C? (A) 1/2 (B) 1/4 (C) 1 (D) 2/1 (E) 4/1 10. A point charge q is released from rest at point A and accelerates in a uniform electric field E. What is the ratio between velocities of the charge V B /V C? (A) 1 2 (B) 2 3 (C) 1 (D) 2 1 (E) 3 2

4 11. A point charge Q 1 = +4.0 µc is placed at point -2 m. A second charge Q 2 is placed at point +3 m. The net electric potential at the origin is zero. What is charge Q 2? Magnitude (A) 9.0 µc (B) 6.0 µc (C) 3.0 µc (D) 6.0 µc (E) 9.0 µc Sign Positive Positive Positive Negative Negative 12. A conducting sphere is charged with a positive charge +Q. Which of the following is correct relationship for the electric potential at the points A, B, and C? (A) V A < V B < V C (B) V A > V B < V C (C) V A < V B > V C (D) V A = V B < V C (E) V A = V B > V C 13. An electric field is presented by a series of equipotential lines. At which location is the electric field strength the greatest? (A) A (B) B (C) C (D) D (E) C

5 14. A uniform conducting sphere of radius R is charged with a positive charge +Q. Which of the following is correct relationship between the potential and distance from the center of the sphere? (A) (B) (C) (D) (E)

6 15. A uniform conducting sphere of radius R is charged with a positive charge +Q. Which of the following is correct relationship between the electric field and distance from the center of the sphere? (A) (B) (C) (D) (E)

7 16. Two positive charges A and B are placed at the corners of equilateral triangle with a side r. What is the net electric potential at point C? (A) 2kQ r (B) 3kQ r (C) kq r (D) 5kQ r (E) 2kQ r 17. Two charges +Q and Q are placed at the corners of equilateral triangle with a side r. What is the net electric potential at point C? (A) 0 (B) 3kQ r (C) kq r (D) 5kQ r (E) 2kQ r 18. Four positive Q charges are arranged in the corner of a square as shown on the diagram. What is the net electric potential at the center of the square? (A) 0 (B) 8kQ 2r (C) 4kQ 2r (D) 16kQ 2r (E) 2kQ 2r

8 19. Two conducting spheres of different radii are charged with the same charge -Q. What will happen to the charge if the spheres are connected with a conducting wire? (A) Negative charge flows from the large sphere to the smaller sphere until the electric field at the surface of each sphere is the same (B) Negative charge flows from the smaller sphere to the larger sphere until the electric field at the surface of each sphere is the same (C) Negative charge flows from the large sphere to the smaller sphere until the electric potential at the surface of each sphere is the same (D) Negative charge flows from the smaller sphere to the larger sphere the electric potential at the surface of each sphere is the same (E) There is no charge flow between the spheres 20. A charged particle is projected with its initial velocity perpendicular to a uniform electric field. The resulting path of the particle is: (A) spiral (B) parabolic arc (C) circular arc (D) straight line parallel to the field (E) straight line perpendicular to the field 21. A positive charge of +3 µc is moved from point A to point B in a uniform electric field. How much work is done by the electric field on the charge? (A) 100 µj (B) 120 µj (C) 140 µj (D) 160 µj (E) 180 µj

9 22. Two positive charges with a magnitude of Q are located at points (+1,0) and (-1,0). At which of the following points is the electric potential the greatest in magnitude? (A) (+2,0) (B) (0,-1) (C) (0,0) (D) (+3,0) (E) (0,+1) 23. An electron with energy of 200 ev enters a uniform electric field parallel to the plates. The electron is deflected by the electric field. What is the kinetic energy of the electron just before it strikes the upper plate? (A) 50 ev (B) 100 ev (C) 200 ev (D) 300 ev (E) 400 ev 24. A parallel-plate capacitor has a capacitance C 0. What is the capacitance of the capacitor if the area is doubled and separation between the plates is doubled? (A) 4 C 0 (B) 2 C 0 (C) C 0 (D) 1/2 C 0 (E) 1/4 C A parallel-plate capacitor is charged by a battery and then disconnected. What will happen to the charge on the capacitor and voltage across it if the separation between the plates is decreased and the area is increased? (A) Both increase (B) Both decrease (C) Both remain the same (D) The charge remains the same and voltage increases (E) The charge remains the same and voltage decreases 26. A parallel-plate capacitor is charged by connection to a battery and remains connected. What will happen to the charge on the capacitor and voltage across it if the separation between the plates is decreased and the area is increased? (B) Both increase (B) Both decrease (C) Both remain the same (D) The voltage remains the same and charge increases (E) The voltage remains the same and charge decreases

10 27. A parallel-plate capacitor is connected to a battery with a constant voltage. What happens to capacitance, charge, and voltage if a dielectric material is placed between the plates? Capacitance Charge Voltage (A) Increases Increases Decreases (B) Decreases Increases Remains the same (C) Remains the same Decreases Increases (D) Increases Increases Remains the same (E) Decreases Remains the same Increases 28. A parallel-plate capacitor is connected to a battery and becomes fully charged. The capacitor is then disconnected, and the separation between the plates is increased in such a way that no charge leaks off. What happens to the energy stored in the capacitor? (A) Remains the same (B) Increased (C) Decreased (D) Zero (E) More information is required 29. A parallel-plate capacitor is connected to a battery with a constant voltage. The capacitor becomes fully charged and stays connected. What happens to the energy stored in the capacitor if the separation is decreased? (A) Remains the same (B) Increased (C) Decreased (D) Zero (E) More information is required 30. A parallel-plate capacitor is connected to a battery. The capacitor is fully charged before the battery is disconnected. A uniform dielectric with a constant K is inserted between the plates. What is the ratio between the energy stored in the capacitor with the inserted dielectric U k to the energy without dielectric U 0? (A) 1/K (B) 1/K 2 (C) K/1 (D) K 2 /1 (E) Two parallel conducting plates are connected to a battery with a constant voltage. The magnitude of the electric field between the plates is 1200 N/C. If the voltage is halved and the distance between the plates is tripled from the original distance. The magnitude of the new electric field is: (A) 800 N/C (B) 600 N/C (C) 400 N/C (D) 500 N/C (E) 200 N/C

11 Multi-correct Multiple Choice 32. Which of the following statements is true about the charged conducting sphere? (A) The electric field is maximum at the center of the sphere (B) The electric potential is minimum at the center of the sphere (C) The electric field is zero inside the sphere (D) The electric potential everywhere inside the sphere and at the surface is the same 33. Which of the following is true about the electro-static filed? (A) The electric file lines are parallel to the equipotential lines (B) The electric file lines are perpendicular to the equipotential lines (C) The electric field lines point in the direction where potential is less (D) The electric field lines point in the direction where potential is greater 34. A parallel plate capacitor is fully charged and disconnected form a battery. When the space between the plates is filled with a dielectric the charge, voltage and energy stored in the capacitor are: (A) Charge stays the same and energy increases (B) Charge stays the same and energy decreases (C) Charge stays the same and voltage increases (D) Charge stays the same and voltage decreases 35. A parallel plate capacitor is fully charged and stays connected to a battery. When the space between the plates is filled with a dielectric the charge, voltage and energy stored in the capacitor are: (A) Voltage stays the same and energy increases (B) Voltage stays the same and energy decreases (C) Voltage stays the same and charge increases (D) Voltage stays the same and charge decreases

12 Answers to Multiple Choice: 1. C 2. B 3. E 4. C 5. D 6. C 7. D 8. B 9. C 10. A 11. D 12. E 13. B 14. D 15. A 16. E 17. A 18. B 19. D 20. B 21. B 22. C 23. D 24. C 25. E 26. D 27. D 28. B 29. B 30. A 31. E 32. C,D 33. B,C 34. B,D 35. A,C Chapter Problems x J x 10-1 J x 10-1 J x 10 1 J x 10-1 J x 10-1 J x J x 10-1 J x 10 3 V x 10 5 V x 10 5 V x 10 4 V 20. KE = 3.2 x J; v = 8.4 x 10 6 m/s x 10 3 V x 10-4 J V 24. The horizontal lines are the Equipotentials x 10 5 V x 10 5 V x 10 4 V 13. KE = 5.6 x J; v = 2.6 x 10 5 m/s x 10-4 J V x N x 10-5 m

13 28. KE = 2.9 x J; v = 1.9 x 10 5 m/s x 10-4 J x J 31. F E = 6.7 x N to East; a = 7.4 x m/s x 10 4 V/m V x 10-5 V x 10-3 N/C towards the East x J x 10 4 V/m 39. KE = 1.5 x J; v = 5.8 x 10 6 m/s The horizontal lines are the equipotentials. General Problems 1. a x 10 5 V b. 0.4 J c N d. 6 X 10 6 V/m e m/s 2. a. -2 x 10-5 C b N; Away c J d x 10 5 V e. 1 x 10-3 J 3. a N b. c. 13,000 N/C d J e. -9,000 V f. -9 x 10-6 J

14 4. a. 0 b. 4 (2) kq/d c. 4 (2) kqq O /d d. (2) 4kq/d 2 e. 0 f a. Down b. 10,000 V/m c. 4.8 x C; must be negative d. 5 m/s 2 6. a. Up b. 2,400 V/m c. Parabolic, Downward d. 4.2 x m/s 2 e. It will leave the plates

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