Chapter 19: Electric Potential and Electric Field

19.1 Electric Potential Energy: Potential Difference

• 
  2:58
  Problem 1Free

  Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be $1.67\times 10^{-27}\text{ kg}$.
• 
  1:47Preview
  Problem 2Full video with free trial

  An evacuated tube uses an accelerating voltage of 40 kV to accelerate electrons to hit a copper plate and produce x rays. Non-relativistically, what would be the maximum speed of these electrons?
• 
  3:16Preview
  Problem 3Full video with free trial

  A bare helium nucleus has two positive charges and a mass of $6.64\times 10^{-27}\text{ kg}$ (a) Calculate its kinetic energy in joules at 2.00% of the speed of light. (b) What is this in electron volts? (c) What voltage would be needed to obtain this energy?
• 
  1:41Preview
  Problem 4Full video with free trial

  Singly charged gas ions are accelerated from rest through a voltage of 13.0 V. At what temperature will the average kinetic energy of gas molecules be the same as that given these ions?
• 
  1:33Preview
  Problem 5Full video with free trial

  The temperature near the center of the Sun is thought to be 15 million degrees Celsius ($1.5\times 10^7{}^{\circ }\text{C}$). Through what voltage must a singly charged ion be accelerated to have the same energy as the average kinetic energy of ions at this temperature?
• 
  2:08Preview
  Problem 6Full video with free trial

  (a) What is the average power output of a heart defibrillator that dissipates 400 J of energy in 10.0 ms? (b) Considering the high-power output, why doesn’t the defibrillator produce serious burns?
• 
  2:34Preview
  Problem 7Full video with free trial

  A lightning bolt strikes a tree, moving 20.0 C of charge through a potential difference of $1.00\times 10^2\text{ MV}$. (a) What energy was dissipated? (b) What mass of water could be raised from $15^{\circ }\text{C}$ to the boiling point and then boiled by this energy? (c) Discuss the damage that could be caused to the tree by the expansion of the boiling steam.
• 
  4:00Preview
  Problem 8Full video with free trial

  A $12.0\text{ V}$ battery operated bottle warmer heats 50.0 g of glass, $2.50\times 10^2\text{ g}$ of baby formula, and $2.00\times 10^2\text{ g}$ of aluminum from $20.0^{\circ }\text{ C}$ to $90.0^{\circ }\text{C}$. (a) How much charge is moved by the battery? (b) How many electrons per second flow if it takes 5.00 min to warm the formula? (Hint: Assume that the specific heat of baby formula is about the same as the specific heat of water.)
• 
  2:17Preview
  Problem 9Full video with free trial

  A battery-operated car utilizes a 12.0 V system. Find the charge the batteries must be able to move in order to accelerate the 750 kg car from rest to 25.0 m/s, make it climb a $2.00\times 10^2\text{ m}$ high hill, and then cause it to travel at a constant 25.0 m/s by exerting a $5.00\times 10^2\text{ N}$ force for an hour.
• 
  3:19Preview
  Problem 10Full video with free trial

  Fusion probability is greatly enhanced when appropriate nuclei are brought close together, but mutual Coulomb repulsion must be overcome. This can be done using the kinetic energy of high-temperature gas ions or by accelerating the nuclei toward one another. (a) Calculate the potential energy of two singly charged nuclei separated by $1.00\times 10^{-12}\text{ m}$ by finding the voltage of one at that distance and multiplying by the charge of the other. (b) At what temperature will atoms of a gas have an average kinetic energy equal to this needed electrical potential energy?
• 
  1:42Preview
  Problem 11Full video with free trial

  (a) Find the voltage near a 10.0 cm diameter metal sphere that has 8.00 C of excess positive charge on it. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

19.2 Electric Potential in a Uniform Electric Field

• 
  1:07Preview
  Problem 13Full video with free trial

  Show that units of V/m and N/C for electric field strength are indeed equivalent.
• 
  0:40Preview
  Problem 14Full video with free trial

  What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of $1.50\times 10^4\text{ V}$?
• 
  1:05Preview
  Problem 15Full video with free trial

  The electric field strength between two parallel conducting plates separated by 4.00 cm is $7.50\times 10^4\text{ V/m}$. (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be at zero volts. What is the potential 1.00 cm from that plate (and 3.00 cm from the other)?
• 
  0:39Preview
  Problem 16Full video with free trial

  How far apart are two conducting plates that have an electric field strength of $4.50\times 10^3\text{ V/m}$ between them, if their potential difference is 15.0 kV?
• 
  0:52Preview
  Problem 17Full video with free trial

  (a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength for air ($3.0\times 10^6\text{ V/m}$) if the plates are separated by 2.00 mm and a potential difference of $5.0\times 10^3\text{ V}$ is applied? (b) How close together can the plates be with this applied voltage?
• 
  0:36Preview
  Problem 18Full video with free trial

  The voltage across a membrane forming a cell wall is 80.0 mV and the membrane is 9.00 nm thick. What is the electric field strength? (The value is surprisingly large, but correct. Membranes are discussed in Capacitors and Dielectrics and Nerve Conduction—Electrocardiograms.) You may assume a uniform electric field.
• 
  0:56Preview
  Problem 19Full video with free trial

  Membrane walls of living cells have surprisingly large electric fields across them due to separation of ions. (Membranes are discussed in some detail in Nerve Conduction—Electrocardiograms.) What is the voltage across an 8.00 nm–thick membrane if the electric field strength across it is 5.50 MV/m? You may assume a uniform electric field.
• 
  1:13Preview
  Problem 20Full video with free trial

  Two parallel conducting plates are separated by 10.0 cm, and one of them is taken to be at zero volts. (a) What is the electric field strength between them, if the potential 8.00 cm from the zero volt plate (and 2.00 cm from the other) is 450 V? (b) What is the voltage between the plates?
• 
  0:38Preview
  Problem 21Full video with free trial

  Find the maximum potential difference between two parallel conducting plates separated by 0.500 cm of air, given the maximum sustainable electric field strength in air to be $3.0\times 10^6\text{ V/m}$
• 
  2:43Preview
  Problem 22Full video with free trial

  A doubly charged ion is accelerated to an energy of 32.0 keV by the electric field between two parallel conducting plates separated by 2.00 cm. What is the electric field strength between the plates?
• 
  2:44Preview
  Problem 23Full video with free trial

  An electron is to be accelerated in a uniform electric field having a strength of $2.00\times 10^6\text{ V/m}$. (a) What energy in keV is given to the electron if it is accelerated through 0.400 m? (b) Over what distance would it have to be accelerated to increase its energy by 50.0 GeV?

19.3 Electrical Potential Due to a Point Charge

• 
  1:09Preview
  Problem 24Full video with free trial

  A 0.500 cm diameter plastic sphere, used in a static electricity demonstration, has a uniformly distributed 40.0 pC charge on its surface. What is the potential near its surface?
• 
  0:41Preview
  Problem 25Full video with free trial

  What is the potential $0.530\times 10^{-10}\text{ m}$ from a proton (the average distance between the proton and electron in a hydrogen atom)?
• 
  0:57Preview
  Problem 26Full video with free trial

  (a) A sphere has a surface uniformly charged with 1.00 C. At what distance from its center is the potential 5.00 MV? (b) What does your answer imply about the practical aspect of isolating such a large charge?
• 
  0:40Preview
  Problem 27Full video with free trial

  How far from a $1.00\mu \text{C}$ point charge will the potential be 100 V? At what distance will it be $2.00\times 10^2\text{ V}$?
• 
  0:42Preview
  Problem 28Full video with free trial

  What are the sign and magnitude of a point charge that produces a potential of –2.00 V at a distance of 1.00 mm?
• 
  0:46Preview
  Problem 29Full video with free trial

  If the potential due to a point charge is $5.00\times 10^2\text{ V}$ at a distance of 15.0 m, what are the sign and magnitude of the charge?
• 
  1:16Preview
  Problem 30Full video with free trial

  In nuclear fission, a nucleus splits roughly in half. (a) What is the potential $2.00\times 10^{-14}\text{ m}$ from a fragment that has 46 protons in it? (b) What is the potential energy in MeV of a similarly charged fragment at this distance?
• 
  2:38Preview
  Problem 31Full video with free trial

  A research Van de Graaff generator has a 2.00-m- diameter metal sphere with a charge of 5.00 mC on it. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (c) An oxygen atom with three missing electrons is released near the Van de Graaff generator. What is its energy in MeV at this distance?
• 
  2:36Preview
  Problem 32Full video with free trial

  An electrostatic paint sprayer has a 0.200-m-diameter metal sphere at a potential of 25.0 kV that repels paint droplets onto a grounded object. (a) What charge is on the sphere? (b) What charge must a 0.100-mg drop of paint have to arrive at the object with a speed of 10.0 m/s?
• 
  2:41Preview
  Problem 33Full video with free trial

  In one of the classic nuclear physics experiments at the beginning of the 20th century, an alpha particle was accelerated toward a gold nucleus, and its path was substantially deflected by the Coulomb interaction. If the energy of the doubly charged alpha nucleus was 5.00 MeV, how close to the gold nucleus (79 protons) could it come before being deflected?
• 
  4:01Preview
  Problem 34Full video with free trial

  (a) What is the potential between two points situated 10 cm and 20 cm from a $3.0\mu \text{C}$ point charge? (b) To what location should the point at 20 cm be moved to increase this potential difference by a factor of two?
• 
  1:45Preview
  Problem 35Full video with free trial

  (a) What is the final speed of an electron accelerated from rest through a voltage of 25.0 MV by a negatively charged Van de Graaff terminal? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

19.4 Equipotential Lines

• 
  3:52Preview
  Problem 36Full video with free trial

  (a) Sketch the equipotential lines near a point charge $+q$. Indicate the direction of increasing potential. (b) Do the same for a point charge $-3q$.
• 
  2:32Preview
  Problem 37Full video with free trial

  Sketch the equipotential lines for the two equal positive charges shown in Figure 19.26. Indicate the direction of increasing potential.
• 
  3:27Preview
  Problem 38Full video with free trial

  Figure 19.34 shows the electric field lines near two charges $q_1$ and $q_2$ , the first having a magnitude four times that of the second. Sketch the equipotential lines for these two charges, and indicate the direction of increasing potential.
• 
  2:01Preview
  Problem 39Full video with free trial

  Sketch the equipotential lines a long distance from the charges shown in Figure 19.27. Indicate the direction of increasing potential.
• 
  2:50Preview
  Problem 40Full video with free trial

  Sketch the equipotential lines in the vicinity of two opposite charges, where the negative charge is three times as great in magnitude as the positive. See Figure 19.34 for a similar situation. Indicate the direction of increasing potential.
• 
  1:25Preview
  Problem 41Full video with free trial

  Sketch the equipotential lines in the vicinity of the negatively charged conductor in Figure 19.28. How will these equipotentials look a long distance from the object?
• 
  2:10Preview
  Problem 42Full video with free trial

  Sketch the equipotential lines surrounding the two conducting plates shown in Figure 19.36, given the top plate is positive and the bottom plate has an equal amount of negative charge. Be certain to indicate the distribution of charge on the plates. Is the field strongest where the plates are closest? Why should it be?
• 
  1:05Preview
  Problem 43Full video with free trial

  (a) Sketch the electric field lines in the vicinity of the charged insulator in Figure 19.30. Note its non-uniform charge distribution. (b) Sketch equipotential lines surrounding the insulator. Indicate the direction of increasing potential.
• 
  1:45Preview
  Problem 44Full video with free trial

  The naturally occurring charge on the ground on a fine day out in the open country is –1.00 nC/m2 . (a) What is the electric field relative to ground at a height of 3.00 m? (b) Calculate the electric potential at this height. (c) Sketch electric field and equipotential lines for this scenario.
• 
  1:24Preview
  Problem 45Full video with free trial

  The lesser electric ray (Narcine bancroftii) maintains an incredible charge on its head and a charge equal in magnitude but opposite in sign on its tail (Figure 19.31). (a) Sketch the equipotential lines surrounding the ray. (b) Sketch the equipotentials when the ray is near a ship with a conducting surface. (c) How could this charge distribution be of use to the ray?

19.5 Capacitors and Dielectrics

• 
  0:33Preview
  Problem 46Full video with free trial

  What charge is stored in a $180\mu \text{F}$ capacitor when 120 V is applied to it?
• 
  0:28Preview
  Problem 47Full video with free trial

  Find the charge stored when 5.50 V is applied to an 8.00 pF capacitor.
• 
  1:30Preview
  Problem 48Full video with free trial

  What charge is stored on a parallel plate capacitor with metal plates, each of area $1.00{\text{ m}}^2$, separated by 1.00 mm, when $3.00\times 10^3\text{ V}$ is applied across it?
• 
  0:43Preview
  Problem 49Full video with free trial

  Calculate the voltage applied to a $2.00\mu \text{F}$ capacitor when it holds $3.10\mu \text{C}$ of charge.
• 
  0:46Preview
  Problem 50Full video with free trial

  What voltage must be applied to an 8.00 nF capacitor to store 0.160 mC of charge?
• 
  0:22Preview
  Problem 51Full video with free trial

  What capacitance is needed to store $3.00\mu \text{C}$ of charge at a voltage of 120 V?
• 
  0:30Preview
  Problem 52Full video with free trial

  What is the capacitance of a large Van de Graaff generator’s terminal, given that it stores 8.00 mC of charge at a voltage of 12.0 MV?
• 
  0:50Preview
  Problem 53Full video with free trial

  Find the capacitance of a parallel plate capacitor having plates of area $5.00{\text{ m}}^2$ that are separated by 0.100 mm of Teflon.
• 
  1:15Preview
  Problem 54Full video with free trial

  (a) What is the capacitance of a parallel plate capacitor having plates of area $1.50{\text{ m}}^2$ that are separated by 0.0200 mm of neoprene rubber? (b) What charge does it hold when 9.00 V is applied to it?
• 
  2:09Preview
  Problem 55Full video with free trial

  A prankster applies 450 V to an $80.0\mu \text{F}$ capacitor and then tosses it to an unsuspecting victim. The victim’s finger is burned by the discharge of the capacitor through 0.200 g of flesh. What is the temperature increase of the flesh? Is it reasonable to assume no phase change?
• 
  2:49Preview
  Problem 56Full video with free trial

  (a) A certain parallel plate capacitor has plates of area $4.00{\text{ m}}^2$, separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?

19.6 Capacitors in Series and Parallel

• 
  1:12Preview
  Problem 57Full video with free trial

  Find the total capacitance of the combination of capacitors in Figure 19.32.
• 
  1:10Preview
  Problem 58Full video with free trial

  Suppose you want a capacitor bank with a total capacitance of 0.750 F and you possess numerous 1.50 mF capacitors. What is the smallest number you could hook together to achieve your goal, and how would you connect them?
• 
  1:33Preview
  Problem 59Full video with free trial

  What total capacitances can you make by connecting a $5.00\mu \text{F}$ and an $8.00\mu \text{F}$ capacitor together?
• 
  3:10Preview
  Problem 60Full video with free trial

  Find the total capacitance of the combination of capacitors shown in Figure 19.33.
• 
  2:28Preview
  Problem 61Full video with free trial

  Find the total capacitance of the combination of capacitors shown in Figure 19.34.
• 
  1:03Preview
  Problem 62Full video with free trial

  (a) An $8.00\mu \text{F}$ capacitor is connected in parallel to another capacitor, producing a total capacitance of $5.00\mu \text{F}$ . What is the capacitance of the second capacitor? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

19.7 Energy Stored in Capacitors

• 
  0:52Preview
  Problem 63Full video with free trial

  (a) What is the energy stored in the $10.0\mu \text{F}$ capacitor of a heart defibrillator charged to $9.00\times 10^3\text{ V}$? (b) Find the amount of stored charge.
• 
  1:17Preview
  Problem 64Full video with free trial

  In open heart surgery, a much smaller amount of energy will defibrillate the heart. (a) What voltage is applied to the $8.00\mu \text{F}$ capacitor of a heart defibrillator that stores 40.0 J of energy? (b) Find the amount of stored charge.
• 
  0:27Preview
  Problem 65Full video with free trial

  A $165\mu \text{F}$ capacitor is used in conjunction with a motor. How much energy is stored in it when 119 V is applied?
• 
  2:28Preview
  Problem 66Full video with free trial

  Suppose you have a 9.00 V battery, a $2.00\mu \text{F}$ capacitor, and a $7.40\mu \text{F}$ capacitor. (a) Find the charge and energy stored if the capacitors are connected to the battery in series. (b) Do the same for a parallel connection.
• 
  2:48Preview
  Problem 67Full video with free trial

  A nervous physicist worries that the two metal shelves of his wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. (a) What is the capacitance of the empty shelves if they have area $1.00\times 10^2{\text{ m}}^2$ and are 0.200 m apart? (b) What is the voltage between them if opposite charges of magnitude 2.00 nC are placed on them? (c) To show that this voltage poses a small hazard, calculate the energy stored.
• 
  2:43Preview
  Problem 68Full video with free trial

  Show that for a given dielectric material the maximum energy a parallel plate capacitor can store is directly proportional to the volume of dielectric ( $\text{Volume}=A\cdot d$). Note that the applied voltage is limited by the dielectric strength.
• 
  2:12Preview
  Problem 70Full video with free trial

  (a) On a particular day, it takes $9.60\times 10^3\text{ J}$ of electric energy to start a truck’s engine. Calculate the capacitance of a capacitor that could store that amount of energy at 12.0 V. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

Test Prep for AP® Courses