Content check — College Physics, Chapter 19: Electric Potential and Electric Field

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 19: Electric Potential and Electric Field

32 problems · 2 figures

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} kg .

Answer

42.8

19-4 §19.1 source ↗

Integrated Concepts

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?

Answer

1.00 \times 10^{5} K

19-6 §19.1 source ↗

Integrated Concepts

(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?

Answer

(a) $4 \times 10^{4} W$

(b) A defibrillator does not cause serious burns because the skin conducts electricity well at high voltages, like those used in defibrillators. The gel used aids in the transfer of energy to the body, and the skin doesn’t absorb the energy, but rather lets it pass through to the heart.

19-8 §19.1 source ↗

Integrated Concepts

A 12.0 V battery-operated bottle warmer heats 50.0 g of glass, $2.50 \times 10^{2} g$ of baby formula, and $2.00 \times 10^{2} g$ of aluminum from $20 . 0ºC$ to $90.0ºC$ . (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.)

Answer

(a) $7.40 \times 10^{3} C$

(b) $1.54 \times 10^{20} electrons per second$

19-9 §19.1 source ↗

Integrated Concepts

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 $2.00 \times 10^{2} m$ high hill, and then cause it to travel at a constant 25.0 m/s by exerting a $5.00 \times 10^{2} N$ force for an hour.

Answer

3.89 \times 10^{6} C

19-11 §19.1 source ↗

Unreasonable Results

(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?

Answer

(a) $1.44 \times 10^{12} V$

(b) This voltage is very high. A 10.0 cm diameter sphere could never maintain this voltage; it would discharge.

19-15 §19.2 source ↗

The electric field strength between two parallel conducting plates separated by 4.00 cm is

7.50 \times 10^{4} 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)?

Answer

(a) $3 . 00 kV$

(b) $750 V$

19-17 §19.2 source ↗

(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength for air (

3.0 \times 10^{6} V/m

) if the plates are separated by 2.00 mm and a potential difference of

5.0 \times 10^{3} V

is applied? (b) How close together can the plates be with this applied voltage?

Answer

(a) No. The electric field strength between the plates is $2.5 \times 10^{6} V/m,$ which is lower than the breakdown strength for air ( $3.0 \times 10^{6} V/m$ ).

(b) 1.7 mm

19-19 §19.2 source ↗

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.

Answer

44.0 mV

19-21 §19.2 source ↗

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} V/m

Answer

15 kV

19-23 §19.2 source ↗

An electron is to be accelerated in a uniform electric field having a strength of

2 . 00 \times 10^{6} 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?

Answer

(a) $800 KeV$

(b) $25.0 km$

19-24 §19.3 source ↗

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?

Answer

144 V

19-26 §19.3 source ↗

(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?

Answer

(a) 1.80 km

(b) A charge of 1 C is a very large amount of charge; a sphere of radius 1.80 km is not practical.

19-28 §19.3 source ↗

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?

Answer

–2 . 22 \times 10^{- 13} C

19-30 §19.3 source ↗

In nuclear fission, a nucleus splits roughly in half. (a) What is the potential

2 . 00 \times 10^{- 14} 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?

Answer

(a) $3 . 31 \times 10^{6} V$

(b) 152 MeV

19-32 §19.3 source ↗

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?

Answer

(a) $2 . 78 \times 10^{- 7} C$

(b) $2 . 00 \times 10^{- 10} C$

19-35 §19.3 source ↗

Unreasonable Results

(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?

Answer

(a) $2.96 \times 10^{9} m/s$

(b) This velocity is far too great. It is faster than the speed of light.

(c) The assumption that the speed of the electron is far less than that of light and that the problem does not require a relativistic treatment produces an answer greater than the speed of light.

19-46 §19.5 source ↗

What charge is stored in a

180 µF

capacitor when 120 V is applied to it?

Answer

21.6 mC

19-48 §19.5 source ↗

What charge is stored in the capacitor in Example 19.8?

Example 19.8 View it in the book ↗

Answer

80.0 mC

19-50 §19.5 source ↗

What voltage must be applied to an 8.00 nF capacitor to store 0.160 mC of charge?

Answer

20.0 kV

19-52 §19.5 source ↗

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?

Answer

667 pF

19-54 §19.5 source ↗

(a)What is the capacitance of a parallel plate capacitor having plates of area

{1.50 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?

Answer

(a) $4 . 4 µF$

(b) $4 . 0 \times 10^{- 5} C$

19-56 §19.5 source ↗

Unreasonable Results

(a) A certain parallel plate capacitor has plates of area ${4.00 m}^{2}$ , 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?

Answer

(a) 14.2 kV

(b) The voltage is unreasonably large, more than 100 times the breakdown voltage of nylon.

19-57 §19.6 source ↗

Find the total capacitance of the combination of capacitors in Figure 19.31.

A circuit is shown with three capacitors. Two capacitors, of ten microfarad and two point five microfarad capacitance, are in parallel to each other, and their combination is in series with a zero point three zero microfarad capacitor. — Figure 19.31 in the book ↗

Answer

0.293 μF

19-59 §19.6 source ↗

What total capacitances can you make by connecting a

5 . 00 µF

and an

8 . 00 µF

capacitor together?

Answer

3 . 08 µF

in series combination,

13 . 0 µF

in parallel combination

19-60 §19.6 source ↗

Find the total capacitance of the combination of capacitors shown in Figure 19.32.

The circuit includes three capacitors. A zero point three zero microfarad capacitor and a ten microfarad capacitor are connected in series, and together they are connected in parallel with a two point five microfarad capacitor. — Figure 19.32 in the book ↗

Answer

2 . 79 µF

19-62 §19.6 source ↗

Unreasonable Results

(a) An $8 . 00 µF$ capacitor is connected in parallel to another capacitor, producing a total capacitance of $5 . 00 µF$ . What is the capacitance of the second capacitor? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Answer

(a) $–3 . 00 µF$

(b) You cannot have a negative value of capacitance.

(c) The assumption that the capacitors were hooked up in parallel, rather than in series, was incorrect. A parallel connection always produces a greater capacitance, while here a smaller capacitance was assumed. This could happen only if the capacitors are connected in series.

19-63 §19.7 source ↗

(a) What is the energy stored in the

10.0 μF

capacitor of a heart defibrillator charged to

9.00 \times 10^{3} V

? (b) Find the amount of stored charge.

Answer

(a) $405 J$

(b) $90.0 mC$

19-64 §19.7 source ↗

In open heart surgery, a much smaller amount of energy will defibrillate the heart. (a) What voltage is applied to the

8.00 μF

capacitor of a heart defibrillator that stores 40.0 J of energy? (b) Find the amount of stored charge.

Answer

(a) 3.16 kV

(b) 25.3 mC

19-66 §19.7 source ↗

Suppose you have a 9.00 V battery, a

2.00 μF

capacitor, and a

7.40 μF

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.

Answer

(a) $1.42 \times 10^{−5} C$ , $6.38 \times 10^{−5} J$

(b) $8.46 \times 10^{−5} C$ , $3.81 \times 10^{−4} J$

19-67 §19.7 source ↗

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} 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.

Answer

(a) $4.43 \times 10^{- 9} F$

(b) $0.452 V$

19-70 §19.7 source ↗

Unreasonable Results

(a) On a particular day, it takes $9.60 \times 10^{3} J$ 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?

Answer

(a) $133 F$

(b) Such a capacitor would be too large to carry with a truck. The size of the capacitor would be enormous.

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Problems and answers are adapted from College Physics 2e by Paul Peter Urone, Roger Hinrichs, Kim Dirks and Manjula Sharma, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/college-physics-2e/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.