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Chapter 23: Electric Potential Section 23-1: Potential Difference The voltage between the cathode and the screen of a television set is 22 kV. If we assume a speed of zero for an electron as it leaves the cathode, what is its speed just before it hits the screen? A. 8.8 × 107 m/s B. 2.8 × 106 m/s C. 6.2 × 107 m/s D. 7.7 × 1015 m/s E. 5.3 × 107 m/s The voltage between the cathode and the screen of a television set is 22 kV. If we assume a speed of zero for an electron as it leaves the cathode, what is its speed just before it hits the screen? A. 8.8 × 107 m/s B. 2.8 × 106 m/s C. 6.2 × 107 m/s D. 7.7 × 1015 m/s E. 5.3 × 107 m/s The electric field in a region is given by E = 2x2 i + 3y j where the units are in V/m. What is the change in electric potential from the origin to (x, y) = (2, 0) m? A. 8 V B. –8 V C. –16/3 V D. –24/3 V E. 11 V The electric field in a region is given by E = 2x2 i + 3y j where the units are in V/m. What is the change in electric potential from the origin to (x, y) = (2, 0) m? A. 8 V B. –8 V C. –16/3 V D. –24/3 V E. 11 V A lithium nucleus with a charge of +3e and a mass of 7 u, and an alpha particle with a charge of +2e and a mass of 4 u, are at rest. They could be accelerated to the same kinetic energy by A. accelerating them through the same electrical potential difference. B. accelerating the alpha particle through V volts and the lithium nucleus through 2V/3 volts. C. accelerating the alpha particle through V volts and the lithium nucleus through 7V/4 volts. D. accelerating the alpha particle through V volts and the lithium nucleus through 7V/6 volts. E. none of these procedures. A lithium nucleus with a charge of +3e and a mass of 7 u, and an alpha particle with a charge of +2e and a mass of 4 u, are at rest. They could be accelerated to the same kinetic energy by A. accelerating them through the same electrical potential difference. B. accelerating the alpha particle through V volts and the lithium nucleus through 2V/3 volts. C. accelerating the alpha particle through V volts and the lithium nucleus through 7V/4 volts. D. accelerating the alpha particle through V volts and the lithium nucleus through 7V/6 volts. E. none of these procedures. The concept of difference in electric potential is most closely associated with A. the mechanical force on an electron. B. the number of atoms in one gram-atom. C. the charge on one electron. D. the resistance of a certain specified column of mercury. E. the work per unit quantity of electric charge. The concept of difference in electric potential is most closely associated with A. the mechanical force on an electron. B. the number of atoms in one gram-atom. C. the charge on one electron. D. the resistance of a certain specified column of mercury. E. the work per unit quantity of electric charge. Charges Q and q (Q ≠ q), separated by a distance d, produce a potential VP = 0 at point P. This means that A. no force is acting on a test charge placed at point P. B. Q and q must have the same sign. C. the electric field must be zero at point P. D. the net work in bringing Q to distance d from q is zero. E. the net work needed to bring a charge from infinity to point P is zero. Charges Q and q (Q ≠ q), separated by a distance d, produce a potential VP = 0 at point P. This means that A. no force is acting on a test charge placed at point P. B. Q and q must have the same sign. C. the electric field must be zero at point P. D. the net work in bringing Q to distance d from q is zero. E. the net work needed to bring a charge from infinity to point P is zero. When +2.0 C of charge moves at constant speed from a point with zero potential to a point with potential +6.0 V, the amount of work done is A. 2 J. B. 3 J. C. 6 J. D. 12 J. E. 24 J. When +2.0 C of charge moves at constant speed from a point with zero potential to a point with potential +6.0 V, the amount of work done is A. 2 J. B. 3 J. C. 6 J. D. 12 J. E. 24 J. The electron volt is a unit of A. capacitance. B. charge. C. energy. D. momentum. E. potential. The electron volt is a unit of A. capacitance. B. charge. C. energy. D. momentum. E. potential. Two parallel horizontal plates are spaced 0.40 cm apart in air. You introduce an oil droplet of mass 4.9 × 10–17 kg between the plates. If the droplet carries two electronic charges and if there were no air buoyancy, you could hold the droplet motionless between the plates if you kept the potential difference between them at A. 60 V. B. 12 V. C. 3.0 V. D. 0.12 kV. E. 6.0 V. Two parallel horizontal plates are spaced 0.40 cm apart in air. You introduce an oil droplet of mass 4.9 × 10–17 kg between the plates. If the droplet carries two electronic charges and if there were no air buoyancy, you could hold the droplet motionless between the plates if you kept the potential difference between them at A. 60 V. B. 12 V. C. 3.0 V. D. 0.12 kV. E. 6.0 V. Two parallel metal plates 5.0 cm apart have a potential difference between them of 75 V. The electric force on a positive charge of 3.2 × 10–19 C at a point midway between the plates is approximately A. 4.8 × 10–18 N. B. 2.4 × 10–17 N. C. 1.6 × 10–18 N. D. 4.8 × 10–16 N. E. 9.6 × 10–17 N. Two parallel metal plates 5.0 cm apart have a potential difference between them of 75 V. The electric force on a positive charge of 3.2 × 10–19 C at a point midway between the plates is approximately A. 4.8 × 10–18 N. B. 2.4 × 10–17 N. C. 1.6 × 10–18 N. D. 4.8 × 10–16 N. E. 9.6 × 10–17 N. The electrostatic potential as a function of distance along a certain line in space is shown in graph (1). Which of the curves in graph (2) is most likely to represent the electric field as a function of distance along the same line? The electrostatic potential as a function of distance along a certain line in space is shown in graph (1). Which of the curves in graph (2) is most likely to represent the electric field as a function of distance along the same line? Which of the points shown in the diagram are at the same potential? A. 2 and 5 B. 2, 3, and 5 C. 1 and 4 D. 1 and 5 E. 2 and 4 Which of the points shown in the diagram are at the same potential? A. 2 and 5 B. 2, 3, and 5 C. 1 and 4 D. 1 and 5 E. 2 and 4 Which point in the electric field in the diagram is at the highest potential? A. 1 B. 2 C. 3 D. 4 E. 5 Which point in the electric field in the diagram is at the highest potential? A. 1 B. 2 C. 3 D. 4 E. 5 Which point in the electric field in the diagram is at the lowest potential? A. 1 B. 2 C. 3 D. 4 E. 5 Which point in the electric field in the diagram is at the lowest potential? A. 1 B. 2 C. 3 D. 4 E. 5 The figure shows two plates A and B. Plate A has a potential of 0 V and plate B a potential of 100 V. The dotted lines represent equipotential lines of 25, 50, and 75 V. A positive test charge of 1.6 × 10–19 C at point x is transferred to point z. The electric potential energy gained or lost by the test charge is A. 8 × 10–18 J, gained. B. C. D. E. 8 × 10–18 J, lost. 24 × 10–18 J, gained. 24 × 10–8 J, lost. 40 × 10–8 J, gained. The figure shows two plates A and B. Plate A has a potential of 0 V and plate B a potential of 100 V. The dotted lines represent equipotential lines of 25, 50, and 75 V. A positive test charge of 1.6 × 10–19 C at point x is transferred to point z. The electric potential energy gained or lost by the test charge is A. 8 × 10–18 J, gained. B. C. D. E. 8 × 10–18 J, lost. 24 × 10–18 J, gained. 24 × 10–8 J, lost. 40 × 10–8 J, gained. Chapter 23: Electric Potential Section 23-2: Potential Due to a System of Point Charges Charges +Q and –Q are arranged at the corners of a square as shown. When the magnitude of the electric field E and the electric potential V are determined at P, the center of the square, we find that A. E ≠ 0 and V > 0. B. E = 0 and V = 0. C. E = 0 and V > 0. D. E ≠ 0 and V < 0. E. None of these is correct. Charges +Q and –Q are arranged at the corners of a square as shown. When the magnitude of the electric field E and the electric potential V are determined at P, the center of the square, we find that A. E ≠ 0 and V > 0. B. E = 0 and V = 0. C. E = 0 and V > 0. D. E ≠ 0 and V < 0. E. None of these is correct. Two equal positive charges are placed in an external electric field. The equipotential lines shown are at 100 V intervals. The potential for line c is 200V a b c 00V A. 100 V. B. 100 V. C. 200 V. D. 200 V. E. zero Q Q Two equal positive charges are placed in an external electric field. The equipotential lines shown are at 100 V intervals. The potential for line c is 200V a b c 00V A. 100 V. B. 100 V. C. 200 V. D. 200 V. E. zero Q Q Two equal positive charges are placed in an external electric field. The equipotential lines shown are at 100 V intervals. The work required to move a third charge, q = e, from the 100 V line to b is A. 100 eV. 200V 00V a b c B. 100 eV. C. 200 eV. D. 200 eV. E. zero Q Q Two equal positive charges are placed in an external electric field. The equipotential lines shown are at 100 V intervals. The work required to move a third charge, q = e, from the 100 V line to b is A. 100 eV. 200V 00V a b c B. 100 eV. C. 200 eV. D. 200 eV. E. zero Q Q The potential at a point due to a unit positive point charge is found to be V. If the distance between the charge and the point is tripled, the potential becomes A. V/3. B. 3V. C. V/9. D. 9V. E. 1/V 2 . The potential at a point due to a unit positive point charge is found to be V. If the distance between the charge and the point is tripled, the potential becomes A. V/3. B. 3V. C. V/9. D. 9V. E. 1/V 2 . The electric field for a charge distribution is E = 0 for 4000 V m r < 1 m, and E rˆ for r 1 m . 2 r 4 B. 2000 V. 3 E (10 V/m) Use the reference point V = 0 as r infinity. The potential for r < 1 m is A. 4000 V. 3 C. 1000 V. 2 D. Zero. E. Cannot be determined precisely. 1 0 0 1 2 3 4 r (m) The electric field for a charge distribution is E = 0 for 4000 V m r < 1 m, and E rˆ for r 1 m . 2 r 4 B. 2000 V. 3 E (10 V/m) Use the reference point V = 0 as r infinity. The potential for r < 1 m is A. 4000 V. 3 C. 1000 V. 2 D. Zero. E. Cannot be determined precisely. 1 0 0 1 2 3 4 r (m) The electric field for a charge distribution is E = 0 for 3 E (10 V/m) 4000 V m r < 1 m, and E rˆ for r 1 m . 2 r Use the reference point V = 0 as r infinity. The work required to move a charge, q = e from infinity to r = 2 m is 4 A. 4000 eV. B. 2000 eV. 3 C. 1000 eV. 2 D. −4000 eV. 1 E. Zero 0 0 1 2 3 4 r (m) The electric field for a charge distribution is E = 0 for 3 E (10 V/m) 4000 V m r < 1 m, and E rˆ for r 1 m . 2 r Use the reference point V = 0 as r infinity. The work required to move a charge, q = e from infinity to r = 2 m is 4 A. 4000 eV. B. 2000 eV. 3 C. 1000 eV. 2 D. −4000 eV. 1 E. Zero 0 0 1 2 3 4 r (m) Chapter 23: Electric Potential Section 23-3: Computing the Electric Field from the Potential, and Concept Checks 23-1 and 23-2 In what direction can you move relative to an electric field so that the electric potential does not change? A. parallel to the electric field B. perpendicular to the electric field In what direction can you move relative to an electric field so that the electric potential does not change? A. parallel to the electric field B. perpendicular to the electric field In what direction can you move relative to an electric field so that the electric potential increases at the greatest rate? A. in the direction of the electric field B. opposite to the direction of the electric field C. perpendicular to the electric field In what direction can you move relative to an electric field so that the electric potential increases at the greatest rate? A. in the direction of the electric field B. opposite to the direction of the electric field C. perpendicular to the electric field The figure depicts a uniform electric field. Along which direction is there no change in the electric potential? The figure depicts a uniform electric field. Along which direction is there no change in the electric potential? The figure depicts a uniform electric field. Along which direction is the increase in the electric potential a maximum? The figure depicts a uniform electric field. Along which direction is the increase in the electric potential a maximum? The electric potential in a region of space is given by V = 2xy + 3y2 in units of V. The electric field, in V/m, in this region is A. B. C. D. E. 2 yiˆ (2 x 6 y ) ˆj 2 y (iˆ 3 ˆj ) 2 y (iˆ 3 ˆj ) 2 yiˆ (2 x 6 y ) ˆj Noneof theabove. The electric potential in a region of space is given by V = 2xy + 3y2 in units of V. The electric field, in V/m, in this region is A. B. C. D. E. 2 yiˆ (2 x 6 y ) ˆj 2 y (iˆ 3 ˆj ) 2 y (iˆ 3 ˆj ) 2 yiˆ (2 x 6 y ) ˆj Noneof theabove. If the potential V of an array of charges versus the distance from the charges is as shown in graph 1, which graph A, B, C, D, or E shows the electric field E as a function of distance r? If the potential V of an array of charges versus the distance from the charges is as shown in graph 1, which graph A, B, C, D, or E shows the electric field E as a function of distance r? Which of the following statements is true? A. The gradient of the potential must have a larger magnitude at a place where the electric field is stronger. B. The gradient of the potential must have a smaller magnitude at a place where the electric field is stronger. C. The potential must be larger at a place where the electric field is stronger. D. The potential must be smaller at a place where the electric field is stronger. Which of the following statements is true? A. The gradient of the potential must have a larger magnitude at a place where the electric field is stronger. B. The gradient of the potential must have a smaller magnitude at a place where the electric field is stronger. C. The potential must be larger at a place where the electric field is stronger. D. The potential must be smaller at a place where the electric field is stronger. Chapter 23: Electric Potential Section 23-4: Calculations of V for Continuous Charge Distributions Which graph A, B, C, D, or E that best represents the electric potential of a uniformly charged spherical shell as a function of the distance from the center of the shell? Which graph A, B, C, D, or E that best represents the electric potential of a uniformly charged spherical shell as a function of the distance from the center of the shell? Which graph A, B, C, D, or E best represents the electric potential near an infinite plane of charge? Which graph A, B, C, D, or E best represents the electric potential near an infinite plane of charge? Chapter 23: Electric Potential Section 23-5: Equipotential Surfaces Which of the following statements regarding potential is true? A. The units of potential are N/C. B. Potential is a vector quantity. C. Equipotential surfaces are at right angles to lines of electric force. D. Potential differences can be measured directly with a ballistic galvanometer. E. Equipotential surfaces for an isolated point charge are cubes concentric with the charge. Which of the following statements regarding potential is true? A. The units of potential are N/C. B. Potential is a vector quantity. C. Equipotential surfaces are at right angles to lines of electric force. D. Potential differences can be measured directly with a ballistic galvanometer. E. Equipotential surfaces for an isolated point charge are cubes concentric with the charge. The vector that best represents the direction of the electric field intensity at point x on the 20 V equipotential line is D. 1 2 3 4 E. Noneof theseis correct. A. B. C. The vector that best represents the direction of the electric field intensity at point x on the 20 V equipotential line is D. 1 2 3 4 E. Noneof theseis correct. A. B. C. The vector that best represents the direction of the electric field intensity at point x on the 200 V equipotential line is D. 1 2 3 4 E. Noneof theseis correct. A. B. C. The vector that best represents the direction of the electric field intensity at point x on the 200 V equipotential line is D. 1 2 3 4 E. Noneof theseis correct. A. B. C. Two charged metal spheres are connected by a wire. Sphere A is larger than sphere B, as shown. The magnitude of the electric potential of sphere A A. is greater than that at the surface of sphere B. B. is less than that at the surface of sphere B. C. is the same as that at the surface of sphere B. Two charged metal spheres are connected by a wire. Sphere A is larger than sphere B, as shown. The magnitude of the electric potential of sphere A A. is greater than that at the surface of sphere B. B. is less than that at the surface of sphere B. C. is the same as that at the surface of sphere B. The potential on the surface of a solid conducting sphere of radius r = 20 cm is 100 V. The potential at r = 10 cm is A. 100 V. B. 50 V. C. 25 V. D. Zero. E. Cannot be determined. The potential on the surface of a solid conducting sphere of radius r = 20 cm is 100 V. The potential at r = 10 cm is A. 100 V. B. 50 V. C. 25 V. D. Zero. E. Cannot be determined. When a small, positively charged metal ball comes in contact with the interior of a positively charged metal shell, A. the charge on the ball becomes negative. B. the amount of positive charge on the ball increases. C. the positive charge on the shell decreases. D. the charge on the shell and on the ball reach the same value. E. the ball loses all of its excess charge. When a small, positively charged metal ball comes in contact with the interior of a positively charged metal shell, A. the charge on the ball becomes negative. B. the amount of positive charge on the ball increases. C. the positive charge on the shell decreases. D. the charge on the shell and on the ball reach the same value. E. the ball loses all of its excess charge. A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius rb1 and outer radius rb2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The potential for rb1 r rb2 is A. kQ ra B. kQ rb1 C. kQ rb 2 D. E. kQ r zero A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius rb1 and outer radius rb2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The potential for rb1 r rb2 is A. kQ ra B. kQ rb1 C. kQ rb 2 D. E. kQ r zero A metal ball of charge +Q is lowered into an isolated, uncharged metal shell and allowed to rest on the bottom of the shell. When the charges reach equilibrium, A. the outside of the shell has a charge of –Q and the ball has a charge of +Q. B. the outside of the shell has a charge of +Q and the ball has a charge of +Q. C. the outside of the shell has a charge of zero and the ball has a charge of +Q. D. the outside of the shell has a charge of +Q and the ball has zero charge. E. the outside of the shell has a charge of +Q and the ball has a charge of –Q. A metal ball of charge +Q is lowered into an isolated, uncharged metal shell and allowed to rest on the bottom of the shell. When the charges reach equilibrium, A. the outside of the shell has a charge of –Q and the ball has a charge of +Q. B. the outside of the shell has a charge of +Q and the ball has a charge of +Q. C. the outside of the shell has a charge of zero and the ball has a charge of +Q. D. the outside of the shell has a charge of +Q and the ball has zero charge. E. the outside of the shell has a charge of +Q and the ball has a charge of –Q. We give the same charge to a metal sphere of radius R and a metal cone of radius R and height 2R. The shaded regions in the figure are of equal area. Which region has the greatest surface charge density? A. 1 B. 2 C. 3 D. 4 E. All have equal charge densities. We give the same charge to a metal sphere of radius R and a metal cone of radius R and height 2R. The shaded regions in the figure are of equal area. Which region has the greatest surface charge density? A. 1 B. 2 C. 3 D. 4 E. All have equal charge densities. An electric charge q is placed on an isolated metal sphere of radius r1. If an uncharged sphere of radius r2 (with r2 > r1) is then connected to the first sphere, the spheres will have equal A. and like charges on their surfaces. B. electric fields. C. potentials. D. capacitances. E. but opposite charges on their surfaces. An electric charge q is placed on an isolated metal sphere of radius r1. If an uncharged sphere of radius r2 (with r2 > r1) is then connected to the first sphere, the spheres will have equal A. and like charges on their surfaces. B. electric fields. C. potentials. D. capacitances. E. but opposite charges on their surfaces. Dielectric breakdown occurs in the air at an electric field strength of Emax = 3.0 106 V/m. What is the maximum surface charge density that can be placed on a spherical conductor of radius 1.5 m before breakdown? A. 2.7 10–5 C/m2 B. 1.2 10–5 C/m2 C. 8.1 10–5 C/m2 D. 8.6 10–6 C/m2 E. 1.8 10–5 C/m2 Dielectric breakdown occurs in the air at an electric field strength of Emax = 3.0 106 V/m. What is the maximum surface charge density that can be placed on a spherical conductor of radius 1.5 m before breakdown? A. 2.7 10–5 C/m2 B. 1.2 10–5 C/m2 C. 8.1 10–5 C/m2 D. 8.6 10–6 C/m2 E. 1.8 10–5 C/m2 Chapter 23: Electric Potential Section 23-6: Electrostatic Potential Energy Which of the curves on the graph represents the electrostatic potential energy of a small negative charge plotted as a function of its distance from a positive point charge? Which of the curves on the graph represents the electrostatic potential energy of a small negative charge plotted as a function of its distance from a positive point charge? Which of the following statements is false? A. The total work required to assemble a collection of discrete charges is the electrostatic potential energy of the system. B. The potential energy of a pair of positively charged bodies is positive. C. The potential energy of a pair of oppositely charged bodies is positive. D. The potential energy of a pair of oppositely charged bodies is negative. E. The potential energy of a pair of negatively charged bodies is negative. Which of the following statements is false? A. The total work required to assemble a collection of discrete charges is the electrostatic potential energy of the system. B. The potential energy of a pair of positively charged bodies is positive. C. The potential energy of a pair of oppositely charged bodies is positive. D. The potential energy of a pair of oppositely charged bodies is negative. E. The potential energy of a pair of negatively charged bodies is negative. The work required to bring a positively charged body from very far away is greatest for which point? The work required to bring a positively charged body from very far away is greatest for which point? The electrostatic potential energy of a positively charged body is greatest at which point? The electrostatic potential energy of a positively charged body is greatest at which point? Three charges are brought from infinity and placed at the corner of an equilateral triangle. Which of the following statements is true? A. The work required to assemble the charges is always positive. B. The electrostatic potential energy of the system is always positive. C. The electrostatic potential energy does not depend on the order the charges are placed at the corners. D. The work required to assemble the charges depends on which charge is placed at which corner. E. The electrostatic potential energy depends on which charge is placed at which corner. Three charges are brought from infinity and placed at the corner of an equilateral triangle. Which of the following statements is true? A. The work required to assemble the charges is always positive. B. The electrostatic potential energy of the system is always positive. C. The electrostatic potential energy does not depend on the order the charges are placed at the corners. D. The work required to assemble the charges depends on which charge is placed at which corner. E. The electrostatic potential energy depends on which charge is placed at which corner. Calculate the work done to bring a charge, Q = 1 mC, from infinity and place it at a distance R = 10 cm along the axis of a thin uniformly charged ring with linear charge density λ = 10 C/m and radius R. A. 564 J B. 282 J R C. 127 J D. 399 J E. zero from infinity R Q Calculate the work done to bring a charge, Q = 1 mC, from infinity and place it at a distance R = 10 cm along the axis of a thin uniformly charged ring with linear charge density λ = 10 C/m and radius R. A. 564 J B. 282 J R C. 127 J D. 399 J E. zero from infinity R Q Calculate the work done to bring a charge, Q = 1 mC, from infinity and place it at a distance R = 10 cm along the axis of a uniformly charged disk with surface charge density σ = 10 C/m2 and radius R. A. 78.9 J B. 23.4 J from infinity R C. 56.5 J D. 97.8 J E. zero R Q Calculate the work done to bring a charge, Q = 1 mC, from infinity and place it at a distance R = 10 cm along the axis of a uniformly charged disk with surface charge density σ = 10 C/m2 and radius R. A. 78.9 J B. 23.4 J from infinity R C. 56.5 J D. 97.8 J E. zero R Q