1. Four equal and positive charges +q are arranged as shown on figure 1.

Transcription

1 AP Physics C Coulomb s Law Free Response Problems 1. Four equal and positive charges +q are arranged as shown on figure 1. a. Calculate the net electric field at the center of square. b. Calculate the net electric force on the positive charge Q placed at the center of square. Two positive charges are replaced with equal negative charges, as shown in figure 2. c. Calculate the net electric field at the center of square. d. Calculate the net electric force on the positive charge Q placed at the center of the square.

2 2. Two positive charges of equal magnitude Q are placed at the corners of equilateral triangle with a side length r, as shown above. a. What is the magnitude and direction of the electric field at point C due to charge Q located at point A? b. What is the magnitude and direction of the electric field at point C due to charge Q located at point B? c. What is the magnitude and direction of the net electric field at point C due to two charges? d. What is the net electric force on a test charge q placed at point C? 3. Two charges, one is positive and the other is negative, of equal magnitude Q are placed at the corners of equilateral triangle with a side length r, as shown above. a. What is the magnitude and direction of the electric field at point C due to charge Q located at point A? b. What is the magnitude and direction of the electric field at point C due to charge Q located at point B? c. What is the magnitude and direction of the net electric field at point C due to two charges? d. What is the net electric force on a test charge q placed at point C?

3 4. A parallel-plate capacitor is connected to a battery with a constant voltage of 120 V. Each plate has a length of 0.1 m and they are separated by a distance of 0.05 m. An electron with an initial velocity of 2.9*10 7 m/s is moving horizontally and enters the space between the plates. Ignore gravitation. a. What is the direction of the electric field between the plates? b. Calculate the magnitude of the electric field between the plates. c. Describe the electron s path when it moves between the plates. d. What is the direction and magnitude of its acceleration? e. Will the electron leave the space between the plates?

4 5. In an oil-drop experiment, two parallel conducting plates are connected to a power supply with a constant voltage of 100 V. The separation between the plates is 0.01 m. A 4.8*10-16 kg oil drop is suspended in the region between the plates. Use g = 10 m/s 2. a. What is the direction of the electric field between the plates? b. What is the magnitude of the electric field between the plates? c. What is the sign and magnitude of the electric charge on the oil drop when it stays stationary? The mass of the drop is reduced to 3.2*10-16 kg because of vaporization. d. What is the acceleration of the drop?

5 6. Two small spheres with masses m = 20.0 g are suspended at the ends of two silk strings of length L = 1.5 m. Both spheres are charged with an equal amount of positive charge q. Each string makes an angle θ = 30 with the vertical. a. On the diagram below, draw free-body diagram showing all the applied forces on each sphere. b. Determine the magnitude of charge q on each sphere. c. Due to electric discharge, the strings reduce the angle from the vertical to θ = 20. Determine the amount of charge that left each sphere due to the electric discharge. d. If one of the strings is cut, find the instantaneous acceleration of the sphere that was hung from this string.

6 7. A nonconducting ring of radius R lies in the yz plane. The ring is charged with a positive charge Q that is uniformly distributed on the ring. a. Find the x-component of the electric field along the x-axis. b. What are the y- and z- components of the electric field along x- axis? c. Find the distance x for which the electric field is a maximum. d. Find the maximum value of the electric field. e. On the axes below, graph the x-component of the electric field as a function of distance x.

7 8. A uniformly charged disk has a radius R = 0.5 m and carries a total charge Q = C. a. What is the surface charge density on the disk? b. What is the magnitude and direction of the electric field at point P which lies on the x-axis at a distance x = 0.4 m from the disk? c. On the axes below, graph the electric field as a function of distance x. d. If instead of the disk you have an infinite sheet with the same surface charge density, is the electric field at point P the same, less, or greater that the electric field of the disk?

8 9. A positive charge Q is uniformly distributed along a thin rod of length L. The left end of the rod is placed at a distance r from the origin 0. a. What is the magnitude and direction of the electric field at the origin due to the charged rod? b. What is the electric force applied by the rod on a positive charge q placed at the origin? c. If charge q is released from the origin, describe its motion.

9 10. A positive charge is distributed uniformly around a semicircle of radius R = 0.2 m. The linear charge density is λ = C/m. a. Determine the total charge on the semicircle. b. Determine the magnitude and direction of the electric field at the center O of the semicircle. A test charge q = C is placed at the center O of the semicircle. c. Determine the magnitude and direction of the electric force applied by the semicircle on the test charge q. d. If the test charge is released at point O, describe its motion for a long time after the release.

10 11. A thin rod of length 2a is charged uniformly with a positive charge. The linear charge density is λ. Point P is a distance y meters above the rod. a. Find the net charge Q on the rod b. Find the expression for the electric field due to the charged rod at point P on the perpendicular bisector of the rod. An oil drop with a mass of m is placed at point P. The oil drop then begins to stay in place. c. Determine the expression for the charge of the oil drop that is required to keep the drop suspended in the electric field due to the rod. d. The oil drop loses some mass because of evaporation. Describe its motion in the electric field due to the charged rod.

11 Free response answers. 1. a. 0 N C b. 0 N c. 4 2kq d 2 d. 4 2kq2 d 2 2. a. kq r2 the direction is along an extension of line AC at point C b. kq r2 the direction is along an extension of line BC at point C c. 3kQ r 2 the direction is up d. 3kQq r 2 3. a. kq r2 the direction is along an extension of line AC at point C b. kq r2 the direction is towards B begining at C along line CB c. 2 2kQ r 2 the direction is right d. 2 2kQq r 2 4. a. Up b N C c. It will accelerate downwards towards the positive place. d m s2 the direction is down e. Yes

12 5. a. Down b. 10,000 N C c C Negative d. 5 m s 6. a. F T F T F E F E mg mg b μc c μc d m s 2 7. a. RQ 4πε o (R 2 +x 2 ) 3 2 b. 0 and 0 c. R 2 d. Q 6 3R 2 πε e.

13 8. a C m 2 b. σ 2ε o (1 x R 2 +x 2) c. d. It is greater 9. a. b. λ ( 1 1 ) 4πε o r r+l λq ( 1 1 ) 4πε o r r+l c. The charge will move to the left with an increasing velocity and decreasing acceleration. 10. a. Q = πr b N C c N the direction is right d. The test charge moves to the right with an increasing velocity and decreasing acceleration

14 11. a. Q = λl b. λa 2πε o y a 2 +y 2 c. Q = mg 2πε oy a 2 +y 2 λa d. The oil will move up with an increasing velocity and decreasing acceleration