A -50 nC charged particle is in a uniform electric field .

Problem 1CQ What is the energy (in MeV) released in the alpha decay of ?

Problem 1P Moving a charge from point A, where the potential is 300 V, to point B, where the potential is 150 V, takes of work. What is the value of the charge?

Problem 2CQ Charge q is fired through a small hole in the positive plate of a capacitor, as shown in Figure Q21.2 . a. If q is a positive charge, does it speed up or slow down inside the capacitor? Answer this question twice: (i) Using the concept of force. (ii) Using the concept of energy. b. Repeat part a if q is a negative charge.

Problem 2P The graph in Figure P21.2 shows the electric potential energy as a function of separation for two point charges. If one charge is +0.44 nC, what is the other charge?

Problem 3CQ Why is the potential energy of two opposite charges a negative number? (Note: Saying that the formula gives a negative number is not an explanation.)

Problem 3P It takes 3.0 ?J of work to move a 15 nC charge from point A to B. It takes -5.0 ?J of work to move the charge from C to B. What is the potential difference ?

Problem 4CQ An electron (q = -e) completes half of a circular orbit of radius r around a nucleus with Q = +3e, as shown in Figure Q21.4 . a. How much work is done on the electron as it moves from i to f? Give either a numerical value or an expression from which you could calculate the value if you knew the radius. Justify your answer. b. By how much does the electric potential energy change as the electron moves from i to f? c. Is the electron’s speed at f greater than, less than, or equal to its speed at i? d. Are your answers to parts a and c consistent with each other?

Problem 4P A 20 nC charge is moved from a point where V = 150 V to a point where V = -50 V . How much work is done by the force that moves the charge?

Problem 5CQ An electron moves along the trajectory from i to f in Figure Q21.5 . a. Does the electric potential energy increase, decrease, or stay the same? Explain. b. Is the electron’s speed at f greater than, less than, or equal to its speed at i? Explain.

Problem 5P At one point in space, the electric potential energy of a 15 nC charge is 45 ? J. a. What is the electric potential at this point? b. If a 25 nC charge were placed at this point, what would its electric potential energy be?

Problem 6CQ The graph in Figure Q21.6 shows the electric potential along the x -axis. Draw a graph of the potential energy of a 0.10 C charged particle in this region of space, providing a numerical scale on the energy axis.

Problem 6P An electron has been accelerated from rest through a potential difference of 1000 V. a. What is its kinetic energy, in electron volts? b. What is its kinetic energy, in joules? c. What is its speed?

Problem 7CQ As shown in Figure Q21.7 , two protons are launched with the same speed from point 1 inside a parallel-plate capacitor. One proton moves along the path from 1 to 2, the other from 1 to 3. Points 2 and 3 are the same distance from the positive plate.

Problem 8CQ Figure Q21.9 shows two points inside a capacitor. Let V = 0 V at the negative plate. a. What is the ratio of the electric potential at these two points? Explain. b. What is the ratio of the electric field strength at these two points? Explain.

Problem 7P A proton has been accelerated from rest through a potential difference of -1000 V. a. What is its kinetic energy, in electron volts? b. What is its kinetic energy, in joules? c. What is its speed?

Problem 8P What potential difference is needed to accelerate a He+ ion (charge +e, mass 4 u) from rest to a speed of ?

Problem 9CQ A capacitor with plates separated by distance d is charged to a potential difference . All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a new separation of distance 2 d . a. Does the capacitor charge Q change as the separation increases? If so, by what factor? If not, why not? b. Does the electric field strength E change as the separation increases? If so, by what factor? If not, why not? c. Does the potential difference change as the separation increases? If so, by what factor? If not, why not?

Problem 9P An electron with an initial speed of 500,000 m/s is brought to rest by an electric field. a. Did the electron move into a region of higher potential or lower potential? b. What was the potential difference that stopped the electron? c. What was the initial kinetic energy of the electron, in electron volts?

Problem 10CQ Rank in order, from most positive to most negative, the electric potentials at points 1 to 5 in Figure Q21.11 . Explain.

Problem 10P A proton with an initial speed of 800,000 m/s is brought to rest by an electric field. a. Did the proton move into a region of higher potential or lower potential? b. What was the potential difference that stopped the proton? c. What was the initial kinetic energy of the proton, in electron volts?

Problem 11CQ Figure Q21.12 shows two points near a positive point charge. a. What is the ratio of the electric potentials at these two points? Explain. b. What is the ratio of the electric field strengths at these two points? Explain.

Problem 11P The electric potential at a point that is halfway between two identical charged particles is 300 V. What is the potential at a point that is 25% of the way from one particle to the other?

Problem 12CQ Each part of Figure Q21.13 shows three points in the vicinity of two point charges. The charges have equal magnitudes. Rank in order, from largest to smallest, the potentials .

Problem 12P A 2.0 cm × 2.0 cm parallel-plate capacitor has a 2.0 mm spacing. The electric field strength inside the capacitor is 1.0 × 105 V/m. a. What is the potential difference across the capacitor? b. How much charge is on each plate?

Problem 13CQ a. Suppose that throughout some region of space. Can you conclude that V = 0 V in this region? Explain. b. Suppose that V = 0 V throughout some region of space. Can you conclude that in this region? Explain.

Problem 13P Two 2.00 cm × 2.00 cm plates that form a parallel-plate capacitor are charged to ±0.708 nC. What are the electric field strength inside and the potential difference across the capacitor if the spacing between the plates is (a) 1.00 mm and (b) 2.00 mm?

Problem 14CQ Rank in order, from largest to smallest, the electric field strengths at the four labeled points in Figure Q21.15. Explain.

Problem 14P a. In Figure P21.14, which capacitor plate, left or right, is the positive plate? b. What is the electric field strength inside the capacitor? c. What is the potential energy of a proton at the midpoint of the capacitor?

Problem 15CQ Figure 15 shows an electric field diagram. Dotted lines 1 and 2 are two surfaces in space, not physical objects. a. Is the electric potential at point a higher than, lower than, or equal to the electric potential at point b? Explain. ________________ b. Rank in order, from largest to smallest, the potential differences ?Vab, ?Vcd, and ?Vef. Explain. ________________ c. Is surface 1 an equipotential surface? What about surface 2? Explain why or why not.

Problem 15P A +25 nC charge is at the origin. a. What are the radii of the 1000 V, 2000 V, 3000 V, and 4000 V equipotential surfaces? ________________ b. Draw an equipotential map in the xy-plane showing the charge and these four surfaces.

Problem 16CQ Figure Q21.17 shows a negatively charged electroscope. The gold leaf stands away from the rigid metal post. Is the electric potential of the leaf higher than, lower than, or equal to the potential of the post? Explain.

Problem 16P a. What is the electric potential at points A, B, and C in Figure P21.16? b. What is the potential energy of an electron at each of these points? c. What are the potential differences ?

Problem 17CQ Rank in order, from largest to smallest, the energies stored in each of the capacitors in Figure Q21.18. Explain.

Problem 17P A 1.0-mm-diameter ball bearing has 2.0 × 109 excess electrons. What is the ball bearing’s potential?

Problem 18CQ A parallel-plate capacitor with plate separation d is connected to a battery that has potential difference . Without breaking any of the connections, insulating handles are used to increase the plate separation to 2d. a. Does the potential difference change as the separation increases? If so, by what factor? If not, why not? b. Does the capacitance change? If so, by what factor? If not, why not? c. Does the capacitor charge Q change? If so, by what factor? If not, why not?

Problem 18P What is the electric potential at the point indicated with the dot in Figure P21.18?

Problem 19CQ The gap between the capacitor plates shown in Figure 19 is partially filled with a dielectric. The capacitor was charged by a 9 V battery, then disconnected from the battery. Rank in order, from smallest to largest, the electric field strengths E1,E2,and E3 at the points labeled in the figure, as well as the field strength E4between the plates if the dielectric is removed. Explain. FIGURE 19

Problem 19P a. What is the potential difference between the terminals of an ordinary AA or AAA battery? (If you’re not sure, find one and look at the label.) b. An AA battery is connected to a parallel-plate capacitor having 4.0-cm-diameter plates spaced 2 mm apart. How much charge does the battery move from one plate to the other?

Problem 20MCQ A 1.0 nC positive point charge is located at point A in Figure Q21.21. The electric potential at point B is A. 9.0 V B. 9.0 sin 30° V C. 9.0 cos 30° V D. 9.0 tan 30° V

Problem 20P a. In Figure P21.20, which point, A or B, has a higher electric potential? b. What is the potential difference between A and B?

Problem 21MCQ For the capacitor shown in Figure 21, the potential difference ?Vab between points a and b is A. 6 V ________________ B. 6sin 30° V ________________ C. 6cos 30° V ________________ D. 6/sin30° V ________________ E. 6/cos30°V FIGURE 21

Problem 21P In Figure P21.21, the electric potential at point A is -300 V. What is the potential at point B, which is 5.0 cm to the right of A?

Problem 22MCQ The electric potential is 300 V at x = 0 cm, is -100 V at x = 5 cm, and varies linearly with x. If a positive charge is released from rest at x = 2.5 cm, and is subject only to electric forces, the charge will A. Move to the right. B. Move to the left. C. Stay at x = 2.5 cm. D. Not enough information to tell.

Problem 22P What is the potential difference between ?

Problem 23MCQ Question refer to Figure Q21.24, which shows equipotential lines in a region of space. The equipotential lines are spaced by the same difference in potential, and several of the potentials are given. What is the potential at point c? A. -400 V B. -350 V C. -100 V D. 350 V E. 400 V

Problem 23P What are the magnitude and direction of the electric field at the dot in Figure P21.23?

Problem 24MCQ Question refer to Figure Q21.24, which shows equipotential lines in a region of space. The equipotential lines are spaced by the same difference in potential, and several of the potentials are given. At which point, a, b, or c, is the magnitude of the electric field the greatest?

Problem 24P What are the magnitude and direction of the electric field at the dot in Figure P21.24?

Problem 25 MCQ Question refer to Figure Q21.24, which shows equipotential lines in a region of space. The equipotential lines are spaced by the same difference in potential, and several of the potentials are given. What is the approximate magnitude of the electric field at point c? A. 100 V/m B. 300 V/m C. 800 V/m D. 1500 V/m E. 3000 V/m

Problem 25P One standard location for a pair of electrodes during an EKG is shown in Figure P21.25. The potential difference is recorded. For each of the three instants a, b, and c during the heart’s cycle shown in Figure 21.29, will be positive or negative? Explain.

Problem 26MCQ Question refer to Figure Q21.24, which shows equipotential lines in a region of space. The equipotential lines are spaced by the same difference in potential, and several of the potentials are given.

Problem 26P Three electrodes, 1–3, are attached to a patient as shown in Figure P21.26. During ventricular depolarization (see Figure 21.29), across which pair of electrodes is the magnitude of the potential difference likely to be the smallest? Explain.

Problem 27 MCQ Question refer to Figure Q21.24, which shows equipotential lines in a region of space. The equipotential lines are spaced by the same difference in potential, and several of the potentials are given.

Problem 27P Two 2.0 cm × 2.0 cm square aluminum electrodes, spaced 0.50 mm apart, are connected to a 100 V battery. a. What is the capacitance? b. What is the charge on the positive electrode?

Problem 28MCQ A bug zapper consists of two metal plates connected to a high-voltage power supply. The voltage between the plates is set to give an electric field slightly less than . When a bug flies between the two plates, it increases the field enough to initiate a spark that incinerates the bug. If a bug zapper has a 4000 V power supply, what is the approximate separation between the plates? A. 0.05 cm B. 0.5 cm C. 5 cm D. 50 cm

Problem 28P An uncharged capacitor is connected to the terminals of a 3.0 V battery, and 6.0 mC flows to the positive plate. The 3.0 V battery is then disconnected and replaced with a 5.0 V battery, with the positive and negative terminals connected in the same manner as before. How much additional charge flows to the positive plate?

Problem 29 MCQ An atom of helium and one of argon are singly ionized—one electron is removed from each. The two ions are then accelerated from rest by the electric field between two plates with a potential difference of 150 V. After accelerating from one plate to the other, A. The helium ion has more kinetic energy. B. The argon ion has more kinetic energy. C. Both ions have the same kinetic energy. D. There is not enough information to say which ion has more kinetic energy.

Problem 30 MCQ The dipole moment of the heart is shown at a particular instant in Figure Q21.31 . Which of the following potential differences will have the largest positive value?

Problem 30 MCQ The dipole moment of the heart is shown at a particular instant in Figure Q21.31 . Which of the following potential differences will have the largest positive value?

Problem 30P A switch that connects a battery to a 10 ? F capacitor is closed. Several seconds later you find that the capacitor plates are charged to ±30 ? C. What is the battery voltage?

Problem 31P What is the voltage of a battery that will charge a 2.0 mF capacitor to ±48 ?C?

Problem 32P Two electrodes connected to a 9.0 V battery are charged to ±45 nC. What is the capacitance of the electrodes?

Problem 33P Initially, the switch in Figure P21.33 is open and the capacitor is uncharged. How much charge flows through the switch after the switch is closed?

Problem 35P A science-fair radio uses a homemade capacitor made of two 35 cm × 35 cm sheets of aluminum foil separated by a 0.25-mm-thick sheet of paper. What is its capacitance?

Problem 34P A 1.2 nF parallel-plate capacitor has an air gap between its plates. Its capacitance increases by 3.0 nF when the gap is filled by a dielectric. What is the dielectric constant of that dielectric?

Problem 36P A 25 pF parallel-plate capacitor with an air gap between the plates is connected to a 100 V battery. A Teflon slab is then inserted between the plates and completely fills the gap. What is the change in the charge on the positive plate when the Teflon is inserted?

Problem 37P Two 2.0-cm-diameter electrodes with a 0.10-mm-thick sheet of Teflon between them are attached to a 9.0 V battery. Without disconnecting the battery, the Teflon is removed. What are the charge, potential difference, and electric field (a) before and (b) after the Teflon is removed?

Problem 38P A capacitor with its plates separated by paper stores 4.4 nC of charge when it is connected to a particular battery. An otherwise identical capacitor, but with its plates separated by Pyrex glass, is connected to the same battery. How much charge does that capacitor store?

Problem 39P To what potential should you charge a 1.0 ?F capacitor to store 1.0 J of energy? Step-by-step solution Step 1 of 1

Problem 40P A pair of 10 ?F capacitors in a high-power laser are charged to 1.7 kV. a. What charge is stored in each capacitor? b. How much energy is stored in each capacitor?

Problem 41P Capacitor 2 has half the capacitance and twice the potential difference as capacitor 1. What is the ratio ?

Problem 42P Two uncharged metal spheres, spaced 15.0 cm apart, have a capacitance of 24.0 pF. How much work would it take to move 12.0 nC of charge from one sphere to the other?

Problem 50 pJ of energy is stored in a 2.0 cm × 2.0 cm × 2.0 cm region of uniform electric field. What is the electric field strength?

Problem 45 GP What is the change in electric potential energy of a 3.0 nC point charge when it is moved from point A to point B in Figure P21.46?

Problem 44 GP A 2.0-cm-diameter parallel-plate capacitor with a spacing of 0.50 mm is charged to 200 V. What are (a) the total energy stored in the electric field and (b) the energy density?

Problem 46GP Problem What is the potential difference in Figure P21.47?

Problem 47GP A -50 nC charged particle is in a uniform electric field . An external force moves the particle 1.0 m north, then 5.0 m east, then 2.0 m south, and finally 3.0 m west. The particle begins and ends its motion with zero velocity. a. How much work is done on it by the external force? b. What is the potential difference between the particle’s final and initial positions?

Problem 48GP At a distance r from a point charge, the electric potential is 3000 V and the magnitude of the electric field is . a. What is the distance r? b. What are the electric potential and the magnitude of the electric field at distance r/2 from the charge?

Problem 49GP What is the electric potential energy of the electron in Figure P21.51? The protons are fixed and can’t move.

Problem 50GP Two point charges 2.0 cm apart have an electric potential energy -180 ?J. The total charge is 30 nC. What are the two charges?

Problem 51GP Two positive point charges are 5.0 cm apart. If the electric potential energy is 72 ?J, what is the magnitude of the force between the two charges?

Problem 52GP A +3.0 nC charge is at x = 0 cm and a -1.0 nC charge is at x = 4 cm. At what point or points on the x-axis is the electric potential zero?

Problem 53GP A -3.0 nC charge is on the x-axis at x = -9 cm and a + 4.0 nC charge is on the x-axis at x = 16 cm. At what point or points on the y-axis is the electric potential zero?

Problem 55GP A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. a. What is the electric potential at the point on the x-axis where the electric field is zero? b. What are the magnitude and direction of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

Problem 54 GP A -2.0 nC charge and a +2.0 nC charge are located on the x-axis at x = -1.0 cm and x = +1.0 cm, respectively. a. At what position or positions on the x-axis is the electric field zero? b. At what position or positions on the x-axis is the electric potential zero? c. Draw graphs of the electric field strength and the electric potential along the x-axis.

Problem 56 GP A 2.0-mm-diameter glass bead is positively charged. The potential difference between a point 2.0 mm from the bead and a point 4.0 mm from the bead is 500 V. What is the charge on the bead?

Problem 57 GP In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. a. What is the electric potential of the proton at the position of the electron? b. What is the electron’s potential energy?

Problem 59 GP a. What is the electric potential at point A in Figure P21.61? b. What is the potential energy of a proton at point A?

Problem 58GP What is the electric potential at the point indicated with the dot in Figure P21.60?

Problem 60GP A proton’s speed as it passes point A is 50,000 m/s. It follows the trajectory shown in Figure P21.62. What is the proton’s speed at point B?

Problem 61 GP Electric outlets have a voltage of approximately 120 V between the two parallel slots. Estimate the electric field strength between these two slots.

Problem 62 GP Estimate the magnitude of the electric field in a cell membrane with a thickness of 8 nm.

Problem 64GP Suppose that a molecular ion with charge -10e is embedded within the 5.0-nm-thick cell membrane of a cell with membrane potential -70 mV. What is the electric force on the molecule?

Problem 65GP The electric field strength is 50,000 V/m inside a parallel plate capacitor with a 2.0 mm spacing. A proton is released from rest at the positive plate. What is the proton’s speed when it reaches the negative plate?

Problem 66 GP An alpha particle (the nucleus of a helium atom, with charge +2e and a mass four times that of a proton) and an antiproton (which has the same mass as a proton but charge ? e) are released from rest a great distance apart. They are oppositely charged, so each accelerates toward the other. What are the speeds of the two particles when they are 2.5 nm apart? Hint:You’ll need to use two conservation laws. And what does “a great distance” suggest about the initial value of r?

Problem 67GP A proton is released from rest at the positive plate of a parallel- plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the proton’s final speed if the experiment is repeated with double the amount of charge on each capacitor plate?

Problem 68GP The electric field strength is 20,000 V/m inside a parallelplate capacitor with a 1.0 mm spacing. An electron is released from rest at the negative plate. What is the electron’s speed when it reaches the positive plate?

Problem 69GP In the early 1900s, Robert Millikan used small charged drop lets of oil, suspended in an electric field, to make the first quantitative measurements of the electron’s charge. A 0.70-?m-diameter droplet of oil, having a charge of +e, is suspended in midair between two horizontal plates of a parallel-plate capacitor. The upward electric force on the droplet is exactly balanced by the downward force of gravity. The oil has a density of , and the capacitor plates are 5.0 mm apart. What must the potential difference between the plates be to hold the droplet in equilibrium?

Problem 70GP Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is . a. What is the voltage across the capacitor? b. How much charge is on each disk? c. An electron is launched from the negative plate. It strikes the positive plate at a speed of . What was the electron’s speed as it left the negative plate?

Problem 71GP In proton-beam therapy, a high-energy beam of protons is fired at a tumor. The protons come to rest in the tumor, depositing their kinetic energy and breaking apart the tumor’s DNA, thus killing its cells. For one patient, it is desired that 0.10 J of proton energy be deposited in a tumor. To create the proton beam, the protons are accelerated from rest through a 10 MV potential difference. What is the total charge of the protons that must be fired at the tumor to deposit the required energy?

Problem 72GP A 2.5-mm-diameter sphere is charged to -4.5 nC. An electron fired directly at the sphere from far away comes to within 0.30 mm of the surface of the target before being reflected. a. What was the electron’s initial speed? b. At what distance from the surface of the sphere is the electron’s speed half of its initial value? c. What is the acceleration of the electron at its turning point?

Problem 73GP A proton is fired from far away toward the nucleus of an iron atom. Iron is element number 26, and the diameter of the nucleus is 9.0 fm. What initial speed does the proton need to just reach the surface of the nucleus? Assume the nucleus remains at rest.

Problem 74 GP Two 10.0-cm-diameter electrodes 0.50 cm apart form a parallel- plate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. After a long time, the capacitor is disconnected from the battery but is not discharged. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes

Problem 75 GP Two 10.0-cm-diameter electrodes 0.50 cm apart form a parallel- plate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. What are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes a. While the capacitor is attached to the battery? b. After insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apart? The electrodes remain connected to the battery during this process.

Problem 76GP Determine the magnitude and direction of the electric field at points 1 and 2 in Figure P21.79.

Problem 77 GP Figure P21.80 shows a series of equipotential curves. a. Is the electric field strength at point A larger than, smaller than, or equal to the field strength at point B? Explain. b. Is the electric field strength at point C larger than, smaller than, or equal to the field strength at point D? Explain. c. Determine the electric field at point D. Express your answer as a magnitude and direction.