Content check — College Physics (AP), 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

54 problems · 4 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.

AP Test Prep 19.1 §19.1 source ↗

An electron is placed in an electric field of 12.0 N/C to the right. What is the resulting force on the electron?

a.
1.33×10^-20 N right
b.
1.33×10^-20 N left
c.
1.92×10^-18 N right
d.
1.92×10^-18 N left

Answer

D. 1.92×10^-18 N left

AP Test Prep 19.3 §19.1 source ↗

A −5.0 C charge is being forced south by a 60 N force. What are the magnitude and direction of the local electric field?

a.
12 N/C south
b.
12 N/C north
c.
300 N/C south
d.
300 N/C north

Answer

B. 12 N/C north

AP Test Prep 19.5 §19.1 source ↗

How many electrons have to be moved by a car battery containing 7.20×10⁵J at 12 V to reduce the energy by 1%?

a.
4.80×10²⁷
b.
4.00×10²⁶
c.
3.75×10²¹
d.
3.13×10²⁰

Answer

C. 3.75×10²¹

AP Test Prep 19.7 §19.1 source ↗

A typical AAA battery can move 2000 C of charge at 1.5 V. How long will this run a 50 mW LED?

a.
1000 minutes
b.
120,000 seconds
c.
15 hours
d.
250 minutes

Answer

A. 1000 minutes

AP Test Prep 19.9 §19.1 source ↗

What is the internal energy of a system consisting of two point charges, one 2.0 µC, and the other −3.0 µC, placed 1.2 m away from each other?

a.
−3.8×10^-2 J
b.
−4.5×10^-2 J
c.
4.5×10^-2 J
d.
3.8×10^-2 J

Answer

B. −4.5×10^-2 J

AP Test Prep 19.11 §19.1 source ↗

A system has 2.00 µC charges at (50 cm, 0) and (−50 cm, 0) and a −1.00 µC charge at (0, 70 cm). As the y-coordinate of the −1.00 µC charge increases, the potential energy ___. As the y-coordinate of the −1.00 µC charge decreases, the potential energy ___.

a.
increases, increases
b.
increases, decreases
c.
decreases, increases
d.
decreases, decreases

Answer

B. increases, decreases

AP Test Prep 19.13 §19.1 source ↗

Take a square configuration of point charges, two positive and two negative, all of the same magnitude, with like charges sharing diagonals. What will happen to the internal energy of this system if one of the negative charges becomes a positive charge of the same magnitude?

a.
increase
b.
decrease
c.
no change
d.
not enough information

Answer

A. increase

AP Test Prep 19.15 §19.1 source ↗

A system has 2.00 µC charges at (50 cm, 0) and (−50 cm, 0) and a −1.00 µC charge at (0, 70 cm), with a velocity in the –y-direction. When the −1.00 µC charge is at (0, 0) the potential energy is at a ___ and the kinetic energy is ___.

a.
maximum, maximum
b.
maximum, minimum
c.
minimum, maximum
d.
minimum, minimum

Answer

C. minimum, maximum

AP Test Prep 19.17 §19.2 source ↗

A negatively charged massive particle is dropped from above the two plates in Figure 19.5 into the space between them. Which best describes the trajectory it takes?

a.
A rightward-curving parabola
b.
A leftward-curving parabola
c.
A rightward-curving section of a circle
d.
A leftward-curving section of a circle

The figure shows two vertically oriented parallel plates A and B separated by a distance d. The plate A is positively charged and B is negatively charged. Electric field lines are parallel between the plates and curved at the ends of the plates. A charge q is moved from A to B. The work done W equals q times V sub A B, and the electric field intensity E equals V sub A B over d and potential difference delta V equals q times V sub A B. — Figure 19.5 in the book ↗

Answer

B. A leftward-curving parabola

AP Test Prep 19.19 §19.2 source ↗

Two plates are lying horizontally, but stacked with one 10.0 cm above the other. If the upper plate is held at +100 V, what is the magnitude and direction of the electric field between the plates if the lower is held at +50.0 V? -50.0 V?

a.
500 V/m, 1500 V/m, down
b.
500 V/m, 1500 V/m, up
c.
1500 V/m, 500 V/m, down
d.
1500 V/m, 500 V/m, up

Answer

A. 500 V/m, 1500 V/m, down

AP Test Prep 19.21 §19.2 source ↗

Consider three parallel conducting plates, with a space of 3.0 cm between them. The leftmost one is at a potential of +45 V, the middle one is held at ground, and the rightmost is at a potential of -75 V. What is the magnitude of the average electric field on an electron traveling between the plates? (Assume that the middle one has holes for the electron to go through.)

a.
1500 V/m
b.
2500 V/m
c.
4000 V/m
d.
2000 V/m

Answer

D. 2000 V/m

AP Test Prep 19.23 §19.2 source ↗

A certain electric potential isoline graph has isolines every 5.0 V. If six of these lines cross a 40 cm path drawn between two points of interest, what is the (magnitude of the average) electric field along this path?

a.
750 V/m
b.
150 V/m
c.
38 V/m
d.
75 V/m

Answer

D. 75 V/m

AP Test Prep 19.25 §19.4 source ↗

How would Figure 19.10 be different with two positive charges replacing the two negative charges?

a.
The equipotential lines would have positive values.
b.
It would actually resemble Figure 19.9.
c.
no change
d.
not enough information

Figure (a) shows two circles, called equipotential lines, along which the potential is negative ten volts. A dumbbell-shaped surface encloses the two circles and is labeled negative five volts. This surface is surrounded by another surface labeled negative two volts. Figure (b) shows the same equipotential lines, each set with a negative charge at its center. Blue electric field lines curve toward the negative charges from all directions. — Figure 19.10 in the book ↗

Answer

A. The equipotential lines would have positive values.

AP Test Prep 19.27 §19.4 source ↗

As isolines of electric potential get closer together, the electric field gets stronger. What shape would a hill have as the isolines of gravitational potential get closer together?

a.
constant slope
b.
steeper slope
c.
shallower slope
d.
a U-shape

Answer

B. steeper slope

AP Test Prep 19.29 §19.4 source ↗

How much work is necessary to keep a positive point charge in orbit around a negative point charge?

a.
A lot; this system is unstable.
b.
Just a little; the isolines are far enough apart that crossing them doesn’t take much work.
c.
None; we’re traveling along an isoline, which requires no work.
d.
There’s not enough information to tell.

Answer

C. None; we’re traveling along an isoline, which requires no work.

AP Test Prep 19.31 §19.5 source ↗

Two parallel plate capacitors are otherwise identical, except the second one has twice the distance between the plates of the first. If placed in otherwise identical circuits, how much charge will the second plate have on it compared to the first?

a.
four times as much
b.
twice as much
c.
the same
d.
half as much

Answer

D. half as much

AP Test Prep 19.33 §19.5 source ↗

A parallel plate capacitor with adjustable-size square plates is placed in a circuit. How does the charge on the capacitor change as the length of the sides of the plates is increased?

a.
it grows proportional to length²
b.
it grows proportional to length
c.
it shrinks proportional to length
d.
it shrinks proportional to length²

Answer

A. it grows proportional to length²

AP Test Prep 19.35 §19.5 source ↗

A student was changing one of the dimensions of a square parallel plate capacitor and measuring the resultant charge in a circuit with a battery. However, the student forgot which dimension was being varied, and didn’t write it or any units down. Given the table, which dimension was it?

a.
The distance between the plates
b.
The area
c.
The length of a side
d.
Both the area and the length of a side

Table 19.2 in the book ↗

Dimension	Charge(µC)
1.00	0.50
1.10	0.61
1.20	0.71
1.30	0.86

Answer

C. The length of a side

AP Test Prep 19.37 §19.7 source ↗

Consider a parallel plate capacitor, with no dielectric material, attached to a battery with a fixed voltage. What happens when a dielectric is inserted into the capacitor?

a.
Nothing changes, except now there is a dielectric in the capacitor.
b.
The energy in the system decreases, making it very easy to move the dielectric in.
c.
You have to do work to move the dielectric, increasing the energy in the system.
d.
The reversed polarity destroys the battery.

Answer

C. You have to do work to move the dielectric, increasing the energy in the system.

AP Test Prep 19.39 §19.7 source ↗

What happens to the energy stored in a circuit as you increase the number of capacitors connected in parallel? Series?

a.
increases, increases
b.
increases, decreases
c.
decreases, increases
d.
decreases, decreases

Answer

B. increases, decreases

AP Test Prep 19.41 §19.7 source ↗

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. What is the energy of this capacitor with 3.00×10³ V applied to it?

a.
3.98×10^-2 J
b.
5.08×10¹⁴ J
c.
1.33×10^-5 J
d.
1.69×10¹¹ J

Answer

A. 3.98×10^-2 J

AP Test Prep 19.43 §19.7 source ↗

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. If the plates grow in area while the voltage is held fixed, the capacitance ___ and the stored energy ___.

a.
decreases, decreases
b.
decreases, increases
c.
increases, decreases
d.
increases, increases

Answer

D. increases, increases

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Problems and answers are adapted from College Physics for AP® Courses 2e by Gregg Wolfe, Erika Gasper, John Stoke, Julie Kretchman, David Anderson and others, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/college-physics-ap-courses-2e/pages/1-connection-for-ap-r-courses. 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.