REVIEW FOR MIDTERM 2

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1 Physics 2020 Summer 2011 Richard Ingebretsen REVIEW FOR MIDTERM 2 1. A If the distance between two point charges is increased by a factor of 3, the new force on either charge will be (a) decreased by a factor of 9 (d) increased by a factor of 3 (b) decreased by a factor of 3 (e) increased by a factor of 9 (c) remain the same B. If the distance between a point charge and an infinitely large charged plate is increased by a factor of 2, the new force on the point charge will (a) decrease by a factor of 4 (d) increase by a factor of 2 (b) decrease by a factor of 2 (e) increase by a factor of 4 (c) remain the same C. Two particles are held in equilibrium by the gravitational and electrostatic forces between them. Particle A has mass m A, and charge q A. Particle B has mass m B and charge q B. The distance between the charges is d. Which of the following changes will cause the charges to accelerate towards one another? (a) m A is doubled and m B is doubled. (d) q A is halved and m A is halved (b) m A is doubled and m B is halved (e) d is doubled (c) q A is doubled and q B is doubled D. Charges A, B, C and D are charged particles forming a square with 1.0 m sides as shown. A and D have a charge of +2 C; B and C have a charge of -4 C. If q is a particle with a charge of +1 C sitting directly in the middle of the square, what is the net force on q due to the other particles? (a) 0 N (d) 4 N (b) 1 N (e) 5.6 N (c) 1.4 N E. A particle with a charge of +2 C and a mass of 1 g is exposed to an electric field with strength 5 N/C. How far will the particle move in 10 seconds? (a) m (d) m (b) m (e) m (c) m 2. The drawing shows three point charges arranged in a triangle. The value of q is 2.0 :C, and d = 1.50 m. k = Nm 2 /C 2 (a) (b) Find the total potential at point P. Assume the potential of a point charge is zero at infinity. What is the electric potential energy of the 3 charge system, relative to its value when they are infinitely far away from each other?

2 3. Two charges are fixed in place along the x axis of an x-y coordinate system. A +5.0 :C charge is at the origin and a :C charge is at x = +1.0 m. k = Nm 2 /C 2 (a) Find the location along the x axis where the net electric field is zero. A third charge (-2.0 :C) is placed at x = -2.0 m. (b) (c) (d) There are now two locations where the net electric field is zero along the x axis. Region I is to the left of x = -2.0 m, Region II is between the -2.0 :C charge and the origin, Region III is between the origin and the :C charge, and Region IV is to the right of x = +1.0 m. Describe which two regions contain a point where the net electric field is zero and explain your reasoning. With all three charges in place, what is the net electric field (magnitude and direction) at a point on the y axis at y = -3.0 m? Find the acceleration (magnitude and direction) of a 6.0 g mass with a charge of -2.5 :C placed at y = -3.0 m? 4. A. Two capacitors are identical except that one is empty and the other is filled with a dielectric (6 = 4.50). The empty capacitor is connected to a 12.0 V battery. Permittivity of free space = C 2 /(Nm 2 ). (a) What must be the potential difference across the plates of the capacitor filled with a dielectric such that it stores the same amount of electrical energy as the empty capacitor? (b) Both capacitors store 2.0 : of energy and the area of the plates in each capacitor is 0.20 m 2. What is the magnitude of the electric field between the plates of the empty capacitor? B Two identical negatively charged small plastic balls (mass = 3.50 g) are suspended by 20.0 cm long strings. The balls are in equilibrium when the strings make a 15.0 angle with the vertical. How many electrons are on each ball? k = N@m 2 /C 2 ; e = C 5. A Two Styrofoam balls with the same mass m = kg and the same positive charge Q are suspended from the same point by insulating threads of length 0.98 m. The separation of the balls is 0.02 m. What is the charge Q? B. A small drop of water is suspended motionless in air by a uniform electric field that is directed upward and has a magnitude of 8310 N/C. The mass of the water drop is kg. How many excess electrons or protons reside on the drop? Specify which. C. A constant vertical electric field of magnitude N/C exists above Earth s surface on a day when a thunderstorm is brewing. A car with a rectangular size of 6.00 m by 3.00 m is traveling along a roadway as shown. What is the electric flux through the bottom of the car? D. Two protons are moving directly toward one another. When they are very far apart, their initial speeds are m/s. What is the distance of closest approach? m p = kg 6. An equilateral triangle, of sides a = 2 cm, has a point charge q =!3.6 :C at each of the three vertices (A, B, C). Another point charge Q is placed at D, the midpoint of the side BC. (a) What is Q if the total electric force on the charge at A due to charges B, C, and D is 250 N upward? (b) Calculate the electric field at point A. [Remember: An electric field is a vector.] 7. A. A total charge of C is distributed on two different small metal spheres. When the spheres are 6.00 cm apart, they feel a repulsive force of 20.0 N. How much charge is on each sphere?

3 B. A charge +q is located at the origin, while an identical charge is located on the x axis at x = m. A third charge of +9 q is located on the x axis at such a place that the net electrostatic force on the charge at the origin doubles in magnitude with its direction changing. Where should the third charge be located? (Note: This is different than your homework problem.) C. Point A is located 0.05 m away from a charge of! C. Point B is located 0.90 m away from the charge. Find the electric potential difference, V B - V A, between these two points. 8. A. The drawing shows 4 point charges. Find the total potential at point P. Assume the potential of a point charge is zero at infinity. q 1 =!42 :C; q 2 = 16 :; q 3 =!12 :C; q 4 = 21 :C; d = 1.04 m B. Determine the electric potential energy for the 3-charge configuration shown relative to its value when the charges are infinitely far away. q 1 = 8 :C; q 2 = -15 :C; q 3 = 20 :C; d = 94 cm 9. A. A plate carries a charge of -4.1 :C, while a rod carries a charge of +2.4 :C. How many electrons must be transferred from the plate to the rod, so that both objects have the same charge? B. Two charges attract each other with a force of 2.0 N. What will be the force if the distance between them is reduced to one-ninth of its original value? C. Two parallel plate capacitors have circular plates. The magnitude of the charge on these plates is the same. However, the electric field between the plates of the first capacitor is N/C, while the field within the second capacitor is N/C. Determine the ratio r 2 / r 1 of the plate radius for the second capacitor to the plate radius for the first capacitor. D. Point A is at a potential of +270 V, and point B is at a potential of -120 V. An "-particle is a helium nucleus that contains two protons and two neutrons; the neutrons are electrically neutral. An "-particle starts from rest at A and accelerates toward B. When the "-particle arrives at B, what kinetic energy (in electron volts) does it have?

4 10. A. What is the potential at point M in the figure to the right caused by the four charges? Use q = 3.0 :C and d = 10 cm. B. What is the electrostatic potential energy of the three-charge configuration shown to the right? 11. A. Two identical small insulating balls are suspended by separate 0.32 m threads that are attached to a common point on the ceiling. Each ball has a mass of kg. Initially the balls are uncharged and hang straight down. They are then given identical positive charges and, as a result, they spread apart with an angle of 50 between the threads. What is the charge on each ball? B. Two particles are in a uniform electric field whose value is N/C. The mass and charge of particle 1 are m 1 = kg and q 1 = -9.0 :C, while the corresponding values for particle 2 are m 2 = kg and q 2 = :C. Initially the particles are at rest. The particles are both located on the same electric field line but are separated from each other by a distance d. When released, they accelerate but always remain at this same distance from each other. Find the separation distance d. 12. Given the four charge configuration shown. A. What is the electric field at point P created by the four charges? Use q = 3.0 :C and d = 10 cm. Also remember that the electric field is a vector. B. What is the force on a charge q =!1.9 :C if it is placed at point P? Also remember that force is a vector. 13. A. A plate carries a charge of -3.4 :C, while a rod carries a charge of +1.8 :C. How many electrons must be transferred from the plate to the rod, so that both objects have the same charge? B. A particle of charge +13 :C and mass kg is released from rest in a region where there is a constant electric field of +440 N/C. What is the displacement of the particle after a time of s? C. During a particular thunderstorm, the electric potential difference between a cloud and the ground is V cloud - V ground = V, with the cloud being at the higher potential. What is the change in an electron's electric potential energy (in Joules) when the electron moves from the ground to the cloud? D. Two charges A and B are fixed in place, at different distances from a certain spot. At this spot the potentials due to the two charges are equal. Charge A is 0.27 m from the spot, while charge B is 0.36 m from it. Find the ratio q B / q A of the charges.

5 14. A. Four point charges have the same magnitude of C and are fixed to the corners of a square that is 1.0 cm on a side. Three of the charges are positive and one is negative. Determine the magnitude of the net electric field that exists at the center of the square. B. A charge +q is located at the origin, while an identical charge is located on the x axis at x = m. A third charge of +7 q is located on the x axis at such a place that the net electrostatic force on the charge at the origin triples, its direction remaining unchanged. Where should the third charge be located? C. Two charges are placed between the plates of a parallel plate capacitor. One charge is +q 1 and the other is q 2 = :C. The charge on each plate has a magnitude of 8.1 :C and an area of 0.03 m 2. The force on q 1 due to q 2 equals the force on q 1 due to the electric field of the parallel plate capacitor. What is the distance r between the two charges? 15. A. What is the potential at point M in the figure to the right caused by the four charges? Use q = 12.0 :C and d = 0.20 m. B. What is the electrostatic potential energy of the threecharge configuration shown to the right? Use q = 12.0 :C and d = 0.20 m. Assume the potential is zero when the charges are very far apart. 16. A. What is the electric field at point M created by the four charges? Use q = 12.0 :C and d = 0.20 m. Also remember that the electric field is a vector. B. What is the force on a charge q = -2.3 :C if it is placed at point M? Also remember that force is a vector.

6 17. A. A constant horizontal electric field of magnitude N/C exists above a large laboratory table. A metal rectangular loop 6.00 cm by 3.00 cm is at rest on the table with one 3.00 cm side resting on the table and the two 6.00 cm sides making an angle of 60 degrees with the table. What is the electric flux through the loop? B. A small drop of water is suspended motionless in air by a uniform electric field that is directed upward and has a magnitude of N/C. The mass of the water drop is kg. How many excess electrons or protons reside on the drop? Specify which. C. Two Styrofoam balls with the same mass m = kg and the same positive charge Q are suspended from the same point by insulating threads of length 0.80 m. The angle made by the two threads is 60 degrees. What is the charge Q? D. Point A is located 9.00 cm away from a charge of C. Point B is located 50.0 cm away from the charge. Find the electric potential difference, V B - V A, between these two points. 18. A. The drawing shows 4 point charges. Find the total potential at point P. Assume the potential of a point charge is zero at infinity. q 1 = -21 µc; q 2 = 32 µc; q 3 = -24 µc; q 4 = 42 µc; d = 1.04 m B. In a parallel plate capacitor there are two charged metal plates 15 cm apart as shown. There is a vacuum between the plates and a uniform electric field of strength E = 3000 N/C. An electron (q = -e, m e = kg) is released from rest at the negative plate. 1. How long will it take the electron to reach the other plate? 2. How fast will the electron be going just before it hits the positive plate? 3. How much work was done on the electron?

7 19. A. A total charge of C is distributed on two different very small metal spheres. When the spheres are 6.00 cm apart, they feel a repulsive force of 30.0 N. How much charge is on each sphere? B. A charge of +q is located at the origin, while a second identical charge is located on the x axis at x = m. At what location should a third charge of +6q be placed on the x axis to make the net electrostatic force on the second charge double in magnitude and in the opposite direction? 20. Three charges are placed on three corners of a square as shown. Each side of the square is 30.0 cm. A. What is the electric field (magnitude and direction) at the vacant corner? B. If a charge of µc is placed at the vacant corner, what would the force exerted on it be? (Magnitude and direction.) C. What is the potential energy of the 3 charge configuration assuming the potential is zero at infinity? 21. A. Four identical metallic objects carry the following charges: +1.4 µc, +5.4 µc, 8.6 µc, and 6.0 µc. The objects are brought simultaneously into contact, so that each touches the others. They are then separated. What is the final charge on each object? B. A rectangular surface (0.16 m 0.31 m) is oriented in a uniform Electric field of 578 N/C as shown. Calculate the electric flux through the surface. C. Location A is 2.70 m to the right of a point charge q. Location B lies on the same line and is 4.90 m to the left of the charge. The potential difference between the two locations is V B - V A = 45.0 V. Find the magnitude and sign of the charge. D. Two very small spheres are initially neutral and separated by a distance of m. Suppose that electrons are removed from one sphere and placed on the other sphere. What is the magnitude of the electrostatic force that acts on each sphere? 22. A. Two particles are in a uniform electric field whose value is N/C. The mass and charge of particle 1 are m 1 = kg and q 1 = 9.0 µc, while the corresponding values for particle 2 are m 2 = kg and q 2 = +8.0 µc. Initially the particles are at rest. The particles are both located on the same electric field line but are separated from each other by a distance d. When released, they accelerate but always remain at this same distance from each other. Find the separation distance d.

8 B. Two identical point charges are fixed to diagonally opposite corners of a square that is 0.2 m on a side. Each charge is +5.0 µc. How much work is done by the electric force as one of the charges moves to an empty corner? C. A charge of +q is located at the origin, while a second identical charge is located on the x-axis at x = m. A third charge of -15 q is placed somewhere on the y-axis. Where should the charge be placed if the net force on the second particle is only in the positive y direction? 23. A. What is the potential at point M in the figure to the right caused by the four charges? Take q = 7.0 μc and d = 0.12 m. B. What is the electrostatic potential energy of the threecharge configuration to the right? Assume the potential is zero when the charges are very far apart. Take q = 7.0 μc and d=0.12 m. 24. A. What is the electric field at point M created by the four charges? Remember that the electric field is a vector. Take q = 7.0 μc and d = 0.12 m. B. What is the force on a charge q = 3.7 μc if it is placed at point M? Remember that force is a vector. 25. A. Three identical metallic objects carry the following charges: A has +3.0 µc, B has +5.0 µc, and C has -2.0 µc. First A and B are brought into contact and then separated. Then B and C are brought into contact and then separated. Finally A and C are brought into contact and then separated. What is the final charge on each object? A = B = C = B. A vertical wall (7.0 m 2.7 m) in a house faces due east. A uniform electric field has a magnitude of 150 N/C. This field is parallel to the ground and points 25 north of east. What is the electric flux through the wall? C. The potential at location A is 382 V. A positively charged particle is released there from rest and arrives at location B with a speed v B. The potential at location C is 787 V, and

9 when released from rest from this spot, the particle arrives at B with twice the speed it previously had, or 2v B. Find the potential at B. D. Two spherical objects are separated by a distance of m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result, each object experiences an electrostatic force that has a magnitude of N. How many electrons did it take to produce the charge on one of the objects? 26. A. There are four charges, each with a magnitude of 2.4 µc. Two are positive and two are negative. The charges are fixed to the corners of a 0.33 m square, one to a corner, in such a way that the net force on any charge is directed toward the center of the square. Find the magnitude of the net electrostatic force experienced by any charge. B. Two particles each have a mass of kg. One has a charge of C, and the other has a charge of C. They are initially held at rest at a distance of 0.64 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-half its initial value? C. A charge of +q is located at the origin, while a second identical charge is located on the x-axis at x=+0.45 m. At what location should a third charge of -15q be placed on the x- axis to make the net electrostatic force on the second charge double in magnitude and point in the same direction? 27. A. What is the potential at point M in the figure to the right caused by the four charges? Use q = 3.0 μc and d = 0.05 m. B. What is the electrostatic potential energy of the three-charge configuration to the right? Use q = 3.0 μc and d = 0.05 m. Assume the potential is zero when the charges are very far apart. 28. A. What is the electric field at point M created by the four charges? Use q = 3.0 μc and d=0.05 m. Also remember that the electric field is a vector. B. What is the force on a charge q = -3.7 nc if it is placed at point M? Also remember that force is a vector.