College Physics

Roger A. Freedman; Todd Ruskell; Philip R. Kesten

Chapter 17 Electrostatics II: Electric Potential Energy and Electric Potential - all with Video Answers

Educators

Chapter Questions

04:02

Problem 1

What is the difference between electric potential and electric field?

Vishal Gupta

Numerade Educator

00:52

Problem 2

What is the difference between electric potential and electric potential energy?

Dading Chen

Numerade Educator

03:04

Problem 3

Explain why electric potential requires the existence of only one charge, but a finite electric potential energy requires the existence of two charges.

Vishal Gupta

Numerade Educator

02:22

Problem 4

An electron is released from rest in an electric field. Will it accelerate in the direction of increasing or decreasing potential? Why?

Vishal Gupta

Numerade Educator

01:49

Problem 5

Does it make sense to say that the voltage at some point in space is $10.3$ V? Explain your answer. SSM

Vishal Gupta

Numerade Educator

04:24

Problem 6

Explain why an electron will accelerate toward a region of lower electric potential energy but higher electric potential.

Vishal Gupta

Numerade Educator

02:24

(a) If the electric potential throughout some region of space is zero, does it necessarily follow that the electric field is zero? (b) If the electric field throughout a region is zero, does it necessarily follow that the electric potential is zero? SSM

Vishal Gupta

Numerade Educator

03:10

Problem 8

Discuss how a topographical map showing various elevations around a mountain is analogous to the equipotential lines surrounding a charged object.

Prabhu Ramji

Numerade Educator

02:04

Problem 9

How much work is required to move a charge from one end of an equipotential path to the other? Explain your answer.

Vishal Gupta

Numerade Educator

03:08

Problem 10

Explain why capacitance depends neither on the stored charge $Q$ nor on the potential difference $V$ between the plates of a capacitor.

Vishal Gupta

Numerade Educator

02:08

Problem 11

Describe three methods by which you might increase the capacitance of a parallel-plate capacitor.

Vishal Gupta

Numerade Educator

01:36

Problem 12

If the voltage across a capacitor is doubled, by how much does the stored energy change?

Vishal Gupta

Numerade Educator

04:28

Problem 13

You charge a capacitor and then remove it from the battery. The capacitor consists of large movable plates with air between them. You pull the plates a bit farther apart. What happens to the stored energy? SSM

Vishal Gupta

Numerade Educator

02:19

Problem 14

The capacitance of several capacitors in series is less than any of the individual capacitances. What, then, is the advantage of having several capacitors in series?

Vishal Gupta

Numerade Educator

01:42

Problem 15

What is the advantage to arranging several capacitors in parallel?

Vishal Gupta

Numerade Educator

02:04

Problem 16

Which way of connecting (series or parallel) three identical capacitors to a battery would store more energy?

Vishal Gupta

Numerade Educator

02:12

Problem 17

Qualitatively explain why the equivalent capacitance of a parallel combination of identical capacitors is larger than the individual capacitances.

Vishal Gupta

Numerade Educator

03:56

Problem 18

Does inserting a dielectric into a capacitor increase or decrease the energy stored in the capacitor? Explain your answer.

Vishal Gupta

Numerade Educator

02:59

Problem 19

What are the benefits, if any, of filling a capacitor with a dielectric other than air?

Vishal Gupta

Numerade Educator

02:29

Problem 20

Capacitors $A$ and $B$ are identical except that the region between the plates of capacitor $A$ is filled with a dielectric. As shown in Figure $17-19$, the plates of these capacitors are maintained at the same potential difference by a battery. Is the electric field magnitude in the region between the plates of capacitor A smaller, the same, or larger than the field in the region between the plates of capacitor $B$ ? Explain your answer.

Vishal Gupta

Numerade Educator

03:39

Problem 21

For a positive charge moving in the direction of the electric field,
A. its potential energy increases and its electric potential increases.
B. its potential energy increases and its electric potential decreases.
C. its potential energy decreases and its electric potential increases.
D. its potential energy decreases and its electric potential decreases.
E. its potential energy and its electric potential remain constant. SSM

Vishal Gupta

Numerade Educator

02:32

Problem 22

If a negative charge is released in a uniform electric field, it will move
A. in the direction of the electric field.
B. from high potential to low potential.
C. from low potential to high potential.
D. in a direction perpendicular to the electric field.
E. in circular motion.

Vishal Gupta

Numerade Educator

03:30

Problem 23

An equipotential surface must be
A. parallel to the electric field at every point.
B. equal to the electric field at every point.
C. perpendicular to the electric field at every point.
D. tangent to the electric field at every point.
E. equal to the inverse of the electric field at every point.

Vishal Gupta

Numerade Educator

01:30

Problem 24

A positive charge is moved from one point to another point along an equipotential surface. The work required to move the charge
A. is positive.
B. is negative.
C. is zero.
D. depends on the sign of the potential.
E. depends on the magnitude of the potential.

Vishal Gupta

Numerade Educator

01:35

Problem 25

The electric potential at a point equidistant from two particles that have charges $+Q$ and $-Q$ is
A. larger than zero.
B. smaller than zero.
C. equal to zero.
D. equal to the average of the two distances times the charges.
E. equal to the net electric field.

Vishal Gupta

Numerade Educator

03:26

Problem 26

Four point charges of equal magnitude but differing signs are arranged at the corners of a square (Figure $17-20$ ). The electric field $E$ and the potential $V$ at the center of the square are
A. $\mathrm{E}=0 ; \mathrm{V} \neq 0^{\mathrm{E}}=0 ; V \neq 0$
B. $\mathrm{E}=0 ; \mathrm{V}=0 \mathrm{E}=0 ; V=0$
C. $\mathrm{E} \neq 0 ; \mathrm{V} \neq 0^{\mathrm{E}} \neq 0 ; V \neq 0$
D. $\mathrm{E} \neq 0 ; \mathrm{V}=0^{\mathrm{E}} \neq 0 ; V=0$
E. $\mathrm{E}=2 \mathrm{~V} 1 / 2 \mathrm{E}=2 V^{1 / 2}$

Vishal Gupta

Numerade Educator

02:31

Problem 27

An isolated parallel-plate capacitor carries a charge Q. If the separation between the plates is doubled, the electrical energy stored in the capacitor will be
A. halved.
B. doubled.
C. unchanged.
D. quadrupled.
E. quartered.

Vishal Gupta

Numerade Educator

02:05

Problem 28

A parallel-plate capacitor is connected to a battery that maintains a constant potential difference across the plates. If the separation between the plates is doubled, the electrical energy stored in the capacitor will be
A. halved.
B. doubled.
C. unchanged.
D. quadrupled.
E. quartered.

Vishal Gupta

Numerade Educator

02:27

Problem 29

Capacitors connected in series have the same
A. charge.
B. voltage.
C. dielectric.
D. surface area.
E. separation.

Vishal Gupta

Numerade Educator

02:09

Problem 30

Capacitors connected in parallel have the same
A. charge.
B. voltage.
C. dielectric.
D. surface area.
E. separation.

Vishal Gupta

Numerade Educator

01:49

Problem 31

A pollen grain has a maximum electric charge limit it can carry before the electric field it generates exceeds the dielectric limit for air of $3 \times 106 \mathrm{~N} / \mathrm{C}$ $3 \times 10^{6} \mathrm{~N} / \mathrm{C}$. Estimate the maximum voltage at the surface of a pollen grain that is carrying its maximum electric charge, assuming $\mathrm{V}=0 \mathrm{~V}=0$ at infinity.

Prabhu Ramji

Numerade Educator

01:42

Problem 32

Estimate the amount of energy released in a typical "finger-to-door knob" spark.

Prabhu Ramji

Numerade Educator

01:21

Problem 33

Estimate the amount of energy released in a cloud-to-ground lightning strike.

Prabhu Ramji

Numerade Educator

02:13

Problem 34

If a source charge is in the microcoulomb range, how far from the charge should you be to have an electric potential in the millivolt range as compared to the potential a long way from the charge?

Prabhu Ramji

Numerade Educator

02:36

Problem 35

Estimate the number of $100 \mu \mathrm{F}$ capacitors, connected in parallel, that would provide enough energy to get an electric car moving at $20 \mathrm{~m} / \mathrm{s}$ (the mass of a $1 \mu \mathrm{F}$ capacitor equals $0.005 \mathrm{~g}$ ).

Ze-Han Lee

Numerade Educator

04:00

Problem 36

A point charge $q_{0}$ that has a charge of $0.500 \mu \mathrm{C}$ is at the origin. (a) $\mathrm{A}$ second particle $q$ that has a charge of $1.00 \mu \mathrm{C}$ and a mass of $0.0800 \mathrm{~g}$ is placed at $\mathrm{x}=0.800 \mathrm{~m} x=0.800 \mathrm{~m}$. What is the potential energy of this system of charges? (b) If the particle with charge $q$ is released from rest, what will its speed be when it reaches $\mathrm{x}=2.00 \mathrm{~m} x=2.00 \mathrm{~m} ?$ Example $17-2$

Prabhu Ramji

Numerade Educator

04:04

Problem 37

A uniform electric field of $2.00 \mathrm{kN} / \mathrm{C}$ points in the $+x$ direction. (a) What is the change in potential energy $U_{\text {electric, } b}-U_{\text {electric, } a}$ of a $+2.00 \mathrm{nC}$ test charge as it is moved from point $a$ at $\mathrm{x}=-30.0 \mathrm{~cm}^{x}=-30.0 \mathrm{~cm}$ to point $b$ at $x=+50.0 \mathrm{~cm} x=+50.0 \mathrm{~cm}$ ? (b) The same test charge is released from rest at point $a$. What is its kinetic energy when it passes through point $b$ ? (c) If a negative charge instead of a positive charge were used in this problem, qualitatively how would your answers change? SSM Example $17-1$

Prabhu Ramji

Numerade Educator

04:00

Problem 38

Two red blood cells each have a mass of $9.0 \times 10-14 \mathrm{~kg}$ $9.0 \times 10^{-14} \mathrm{~kg}$ and carry a negative charge spread uniformly over their surfaces. The repulsion arising from the excess charge prevents the cells from clumping together. One cell carries $-2.50 \mathrm{pC}$ of charge and the other $-3.10$ pC, and each cell can be modeled as a sphere $7.5 \mu \mathrm{m}$ in diameter. (a) What speed would they need when very far away from each other to get close enough to just touch? Ignore viscous drag from the surrounding liquid. (b) What is the magnitude of the maximum acceleration of each cell in part (a)?

Prabhu Ramji

Numerade Educator

02:53

Problem 39

Three charges lie on the $x$ axis. Charge q1=+2.20 \muC $q_{1}=+2.20 \mu \mathrm{C}$ is at $\mathrm{x}=-30.0 \mathrm{~cm}^{x}=-30.0 \mathrm{~cm}$, charge $\mathrm{q} 2=-3.10 \mu \mathrm{C}^{q_{2}}=-3.10 \mu \mathrm{C}$ is at the origin,
and charge $\mathrm{q} 3=+1.70 \mu \mathrm{C}^{q_{3}}=+1.70 \mu \mathrm{C}$ is at $\mathrm{x}=25.0 \mathrm{~cm} x=25.0 \mathrm{~cm} .$ Calculate
the potential energy of the system of charges. Example $17-3$

Prabhu Ramji

Numerade Educator

03:37

Problem 40

Calculate the potential energy of the system of charges in Figure $17-20$, if the magnitude of each charge is $|\mathrm{Q}|=4.40 \mu \mathrm{C}^{|Q|}=4.40 \mu \mathrm{C}$ and the length of each side of the large square connecting each charge is $60.0 \mathrm{~cm} .$ Example $17-3$

Prabhu Ramji

Numerade Educator

01:45

Problem 41

A uniform electric field of magnitude $28.0 \mathrm{~V} / \mathrm{m}$ makes an angle of $30.0^{\circ}$ with a displacement of length $10.0 \mathrm{~m}$. What is the potential difference of the final position relative to the initial position of this displacement? Example $\underline{17}-5$

Prabhu Ramji

Numerade Educator

01:47

Problem 42

At a certain point in space, there is a potential of $800 \mathrm{~V}$ relative to zero. What is the potential energy of the system when a $+1.0 \mu \mathrm{C}$ charge is placed at that point in space? Example $17-6$

Prabhu Ramji

Numerade Educator

01:55

Problem 43

How much work is required to move a 2.0-C positive charge from the negative terminal of a 9.0-V battery to the positive terminal? SSM Example

Prabhu Ramji

Numerade Educator

01:27

Problem 44

A potential difference exists between the inner and outer surfaces of the membrane of a cell. The inner surface is negative relative to the outer surface. If $1.5 \times 10-20 \mathrm{~J} 1.5 \times 10^{-20} \mathrm{~J}$ of work is required to eject a positive sodium ion ( $\mathrm{Na}^{+}$ ) from the interior of the cell, what is the potential difference between the inner and outer surfaces of the cell?Example $17-6$

Prabhu Ramji

Numerade Educator

01:14

Problem 45

What is the electric potential due to the nucleus of hydrogen at a distance of $5.00 \times 10-11 \mathrm{~m} 5.00 \times 10^{-11} \mathrm{~m}$ ? Assume the potential is equal to zero as $\mathrm{r} \rightarrow \infty r \rightarrow \infty$

Prabhu Ramji

Numerade Educator

02:23

Problem 46

(a) What is the electric potential due to a point charge of $+2.00 \mu \mathrm{C}$ at a distance of $0.500 \mathrm{~cm} ?$ (b) How will the answer change if the charge has a value of $-2.00 \mu \mathrm{C}$ ? Assume the potential is equal to zero as $\mathrm{r} \rightarrow \infty r \rightarrow \infty$.

Prabhu Ramji

Numerade Educator

01:30

Problem 47

The electric potential has a value of $-200 \mathrm{~V}$ at a distance of $1.25 \mathrm{~m}$ from a point charge. What is the value of that charge? Assume the potential is equal to zero as $\mathrm{r} \rightarrow \infty r \rightarrow \infty$.

Prabhu Ramji

Numerade Educator

04:14

Problem 48

At point $P$ in Figure $17-21$ the electric potential is zero. (As usual, we take the potential to be zero at infinite distance.) (a) What can you say about the two charges? (b) Are there any other points of zero potential on the line connecting $P$ and the two charges?

Prabhat Tyagi

Numerade Educator

03:11

Problem 49

Two point charges are placed on the $x$ axis: $+0.500 \mu$ C at $x=0 x=0$ and $-0.200 \mu \mathrm{C}$ at $\mathrm{x}=10.0 \mathrm{~cm} x=10.0 \mathrm{~cm}$. At what point(s), if any, on the $x$ axis is the electric potential equal to zero? SSM

Prabhu Ramji

Numerade Educator

05:34

Problem 50

A charge of $+2.00 \mu \mathrm{C}$ is at the origin and a charge of $-3.00 \mu \mathrm{C}$ is on the $y$ axis at $\mathrm{y}=40.0 \mathrm{~cm}^{y}=40.0 \mathrm{~cm} .$ (a) What is the potential at point $a$, which is on the $x$ axis at $x=40.0 \mathrm{~cm} x=40.0 \mathrm{~cm}$ ? (b) What is the potential difference $\mathrm{Vb}-\mathrm{Va} V_{b}-V_{a}$ when point $b$ is at $(40.0 \mathrm{~cm}, 30.0 \mathrm{~cm}) ?(\mathrm{c})$ How much work is required to move an electron at rest from point $a$ to rest at point $b$ ?

Prabhu Ramji

Numerade Educator

02:43

Problem 51

Calculate the electric potential at the origin $O$ due to the point charges in $\underline{\text { Figure } 17-22 .}$

Prabhu Ramji

Numerade Educator

02:33

Problem 52

In the Bohr model of the hydrogen atom, an electron in the lowest energy state moves around the nucleus at a speed of $2.19 \times 106 \mathrm{~m} / \mathrm{s}$ $2.19 \times 10^{6} \mathrm{~m} / \mathrm{s}$ at a distance of $0.529 \times 10-10 \mathrm{~m} 0.529 \times 10^{-10} \mathrm{~m}$ from the nucleus. (a) What is the electric potential due to the hydrogen nucleus at this distance? (b) How much energy is required to ionize a hydrogen atom, whose electron is in this lowest energy state? Assume the electric potential goes to zero as $\mathrm{r} \rightarrow \infty r \rightarrow \infty$.

Prabhu Ramji

Numerade Educator

01:58

Problem 53

As shown in Figure $17-23$, two large parallel plates, which are aligned along the $y$ axis, are separated by a distance $\mathrm{d}=30.0 \mathrm{~cm} d=30.0 \mathrm{~cm}$ and are at different electric potentials. The center of each plate has a small opening that lies on the $x$ axis. A proton, traveling on the $x$ axis, passes through the first plate with a speed of $2.50 \times 105 \mathrm{~m} / \mathrm{s}^{2.50 \times 10^{5} \mathrm{~m} / \mathrm{s}}$, and then leaves through the second plate with a speed of $7.80 \times 105 \mathrm{~m} / \mathrm{s} 7.80 \times 10^{5} \mathrm{~m} / \mathrm{s}$. Calculate the potential difference, $\mathrm{V} 2-\mathrm{V} 1^{V}_{2}-V_{1}$, between the two plates. Note that a positive potential difference indicates the second plate is at a higher potential than the first plate. Example $17-4$

Prabhu Ramji

Numerade Educator

01:22

Problem 54

Electric field lines for a system of two point charges are shown in Figure 17-24. Reproduce the figure and draw on it some equipotential lines for the system.

Keshav Singh

Numerade Educator

01:43

Problem 55

In \underline{Figure } 1 7 - 2 5 , equipotential lines are shown at 1-m intervals. What is the electric field at (a) point $A$ and
(b) point $B$ ?

Prabhu Ramji

Numerade Educator

01:43

Problem 56

Equipotential lines for some region of space are shown in Figure $17-26 .$ What is the approximate electric field at (a) point $A$ and (b) point $B$ ?

Prabhu Ramji

Numerade Educator

02:43

Problem 57

Draw the equipotential lines and electric field lines surrounding (a) two positive charges; (b) two negative charges (Figure 17-27). SSM

Zulfiqar Ali

Numerade Educator

01:03

Problem 58

Draw the equipotential lines and electric field lines surrounding a dipole $(+q$ is a distance $L$ from $-q)(\underline{\text { Figure } 17-28})$.

Keshav Singh

Numerade Educator

01:22

Problem 59

Draw the electric field lines and the electric equipotential lines for the charge distribution in Figure $17-29 .$

Keshav Singh

Numerade Educator

01:12

Problem 60

Using a single 10.0-V battery, what capacitance do you need to store $10.0 \mu \mathrm{C}$ of charge?

Prabhu Ramji

Numerade Educator

01:17

Problem 61

A $2.00-\mu \mathrm{F}$ capacitor is connected to a $12.0$ - $\mathrm{V}$ battery. What is the magnitude of the charge on each plate of the capacitor?

Prabhu Ramji

Numerade Educator

01:43

Problem 62

A parallel-plate capacitor has a plate separation of $1.00 \mathrm{~mm}$. If the material between the plates is air, what plate area is required to provide a capacitance of $2.00 \mathrm{pF}$ ? Example $17-7$

Prabhu Ramji

Numerade Educator

01:30

Problem 63

A parallel-plate capacitor has square plates that have edge lengths equal to $1.00 \times 102 \mathrm{~cm} 1.00 \times 10^{2} \mathrm{~cm}$ and are separated by $1.00 \mathrm{~mm}$. What is the capacitance of this device? Example $17-7$

Prabhu Ramji

Numerade Educator

01:29

Problem 64

An air-filled parallel-plate capacitor has plates measuring $10.0 \mathrm{~cm} \times 10.0 \mathrm{~cm} 10.0 \mathrm{~cm} \times 10.0 \mathrm{~cm}$ and a plate separation of $1.00 \mathrm{~mm}$. If you
want to construct a parallel-plate capacitor of the same capacitance but with plates measuring $5.00 \mathrm{~cm} \times 5.00 \mathrm{~cm}, 5.00 \mathrm{~cm} \times 5.00 \mathrm{~cm}$, what plate separation do you need? Example $17-7$

Prabhu Ramji

Numerade Educator

01:19

Problem 65

A parallel-plate capacitor has square plates that have edge length equal to $1.00 \mathrm{~m}$. If the material between the plates is air, what separation distance is required to provide a capacitance of 8850 pF? SSM Example $17-7$

Prabhu Ramji

Numerade Educator

00:56

Problem 66

Using a single 10.0-V battery, what capacitance do you need to store $1.00 \times 10-4 \mathrm{~J} 1.00 \times 10^{-4} \mathrm{~J}$ of electric potential energy? $\underline{\text { Example } 17-9}$

Prabhu Ramji

Numerade Educator

02:03

Problem 67

A parallel-plate capacitor has square plates that have edge length equal to $1.00 \times 102 \mathrm{~cm} 1.00 \times 10^{2} \mathrm{~cm}$ and are separated by $1.00 \mathrm{~mm}$. It is connected to a battery and is charged to $12.0 \mathrm{~V}$. How much energy is stored in the capacitor? Example $17-9$

Prabhu Ramji

Numerade Educator

01:39

Problem 68

You charge a $2.00-\mu \mathrm{F}$ capacitor to $50.0 \mathrm{~V}$. How much additional energy must you add to charge it to $100 \mathrm{~V}$ ? Example $17-9$

Prabhu Ramji

Numerade Educator

01:05

Problem 69

A capacitor has a capacitance of $80.0 \mu \mathrm{F}$. If you want to store $160 \mathrm{~J}$ of electric energy in this capacitor, what potential difference do you need to apply to the plates? Example $17-9$

Prabhu Ramji

Numerade Educator

01:48

Problem 70

a) You want to store $1.00 \times 10-5 \mathrm{C} 1.00 \times 10^{-5} \mathrm{C}$ of charge on a capacitor, but you only have a $100-\mathrm{V}$ voltage source with which to charge it. What must be the value of the capacitance? (b) You want to store $1.00 \times 10-3 \mathrm{~J} 1.00 \times 10^{-3} \mathrm{~J}$ of energy on a capacitor, and you only have a $100-$ $\mathrm{V}$ voltage source with which to charge it. What must be the value of the capacitance? Example $17-9$

Prabhu Ramji

Numerade Educator

01:37

Problem 71

A defibrillator containing a $20.0-\mu \mathrm{F}$ capacitor is used to shock the heart of a patient by holding it to the patient's chest. Just prior to discharging, the capacitor has a voltage of $10.0 \mathrm{kV}$ across its plates. How much energy is released into the patient, assuming no energy losses? SSM Example 17-9

Prabhu Ramji

Numerade Educator

02:55

Problem 72

How should four $1.0$ -pF capacitors be connected to have a total capacitance of $0.75 \mathrm{pF} ? \underline{\text { Example } 17-11}$

Prabhu Ramji

Numerade Educator

01:37

Problem 73

Three capacitors have capacitances $10.0 \mu \mathrm{F}, 15.0 \mu \mathrm{F}$, and $30.0 \mu \mathrm{F}$. What is their effective capacitance if the three are connected (a) in parallel and (b) in series? Example $17-10$

Prabhu Ramji

Numerade Educator

01:49

Problem 74

A series circuit consists of a $0.50-\mu \mathrm{F}$ capacitor, a $0.10-\mu \mathrm{F}$ capacitor, and a 220-V battery. Determine the charge on each of the capacitors. Example $17-$ 10

Prabhu Ramji

Numerade Educator

02:13

Problem 75

Two capacitors provide an equivalent capacitance of $8.00 \mu \mathrm{F}$ when connected in parallel and $2.00 \mu \mathrm{F}$ when connected in series. What is the capacitance of each capacitor? SSM Example $17-10$

Prabhu Ramji

Numerade Educator

02:44

Problem 76

$A 2.00-\mu \mathrm{F}$ capacitor is first charged by being connected across a $6.00 \mathrm{-V}$ battery. It is then disconnected from the battery and connected across an uncharged $4.00-\mu \mathrm{F}$ capacitor. Calculate the final charge on each of the capacitors. Example $17-10$

Prabhu Ramji

Numerade Educator

01:24

Problem 77

A $0.0500-\mu F$ capacitor and a $0.100-\mu F$ capacitor are connected in parallel across a 220-V battery. Determine the charge on each of the capacitors. Example $17-10$

Prabhu Ramji

Numerade Educator

01:35

Problem 78

What is the equivalent capacitance of the network of three capacitors shown in Figure 17-30? Example $17-11$

Prabhu Ramji

Numerade Educator

01:41

Problem 79

Calculate the equivalent capacitance between $a$ and $b$ for the combination of capacitors shown in Figure 17-31. Example $17-11$

Prabhu Ramji

Numerade Educator

03:04

Problem 80

A $10.0-\mu \mathrm{F}$ capacitor, a $40.0-\mu \mathrm{F}$ capacitor, and a $100.0-\mu \mathrm{F}$ capacitor are connected in parallel across a 12.0-V battery. (a) What is the equivalent capacitance of the combination? (b) What is the charge on each capacitor? (c) What is the potential difference across each capacitor? Example $17-10$

Prabhu Ramji

Numerade Educator

03:27

Problem 81

A $10.0-\mu \mathrm{F}$ capacitor, a $40.0-\mu \mathrm{F}$ capacitor, and a $100.0-\mu \mathrm{F}$ capacitor are connected in series across a 12.0-V battery. (a) What is the equivalent capacitance of the combination? (b) What is the charge on each capacitor? (c) What is the potential difference across each capacitor? SSM Example $17-10$

Prabhu Ramji

Numerade Educator

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Problem 82

For the capacitor network shown in Figure $17-32$, the potential difference across $a b$ is $75.0 \mathrm{~V}$. How much charge and how much energy are stored in this system? Example $17-11$

Prabhu Ramji

Numerade Educator

02:48

Problem 83

What is the dielectric constant of the material that fills the gap between a parallel-plate capacitor with plate area of $20.0 \mathrm{~cm}^{2}$ and plate separation of $1.00 \mathrm{~mm}$ if the capacitance is measured to be $0.0142 \mu \mathrm{F}$ ? Example $17-12$

Prabhu Ramji

Numerade Educator

01:26

Problem 84

A parallel-plate capacitor has plates of $1.00 \mathrm{~cm}$ by $2.00 \mathrm{~cm}$. The plates are separated by a 1.00-mm-thick piece of paper. What is the capacitance of this capacitor? The dielectric constant for paper is 2.7. Example $17-12$

Prabhu Ramji

Numerade Educator

01:13

Problem 85

A 2800-pF air-filled capacitor is connected to a 16-V battery. If you now insert a ceramic dielectric material $(\mathrm{k}=5.8 k=5.8)$ that fills the space between the plates, how much charge will flow from the battery? SSM

Prabhu Ramji

Numerade Educator

02:05

Problem 86

A parallel-plate capacitor has square plates $1.00 \times 102 \mathrm{~cm} 1.00 \times 10^{2} \mathrm{~cm}$ on a side that are separated by $1.00 \mathrm{~mm}$. It is connected to a battery and charged to $12.0 \mathrm{~V}$. How much energy is stored in the capacitor if a ceramic dielectric material ( $\kappa$ is $5.8$ ) fills the space between the plates? Example $17-$ 12

Prabhu Ramji

Numerade Educator

05:29

Problem 87

(a) Determine the capacitance of the parallel-plate capacitor shown in Figure 17-33. The dielectric with constant $\kappa_{1}$ fills up one-quarter of the area, but the full separation of the plates. The materials with constants $\kappa_{2}$ and $\kappa_{3}$ fill the other three-quarters of the area, and divide the separation of the plates in half. (b) What happens to the capacitance if the material with constant $\kappa_{3}$ is replaced by air? Example $17-12$

Prabhu Ramji

Numerade Educator

03:05

Problem 88

A parallel-plate capacitor that has a plate separation of $0.50 \mathrm{~cm}$ is filled halfway with a slab of dielectric material ( ? is $5.0$ ) (Figure 17-34). If the plates are $1.25 \mathrm{~cm}$ by $1.25 \mathrm{~cm}$ in area, what is the capacitance of this capacitor? Example $17-12$

Keshav Singh

Numerade Educator

02:07

Problem 89

A parallel-plate capacitor has a plate separation of $1.5 \mathrm{~mm}$ and is charged to $600 \mathrm{~V}$. If an electron leaves the negative plate, starting from rest, how fast is it going when it hits the positive plate? Example $17-6$

Keshav Singh

Numerade Educator

03:11

Problem 90

As shown in Figure $17-35$, three particles, each with charge $q$, are at different corners of a rhombus with sides of length $a$ and with one diagonal of length $a$ and the other of length $b$. (a) What is the electric potential energy of the charge distribution? (b) What is the electric potential at the vacant corner of the rhombus? (c) How much work by an external agent is required to bring a fourth particle, also of charge $q$, from rest at infinity to rest at the vacant corner? (d) What is the total electric potential energy of the four charges? SSM Example $17-3$

Anand Jangid

Numerade Educator

01:54

Problem 91

A lightning bolt transfers 20 C of charge to Earth through an average potential difference of $30 \mathrm{MV}$. (a) How much energy is dissipated in the bolt? (b) What mass of water at $100^{\circ} \mathrm{C}$ could this energy turn into steam? Example $\underline{17-6}$

Keshav Singh

Numerade Educator

03:20

Problem 92

In 2004, physicists at the SLAC National Accelerator Laboratory fired electrons toward each other at very high speeds so that they came within $1.0 \times 10-15 \mathrm{~m} 1.0 \times 10^{-15} \mathrm{~m}$ of each other (approximately the diameter of a proton). (a) What was the electric force on each electron at closest approach?
(b) Would you be able to feel a force of this magnitude acting on you? (c) What kinetic energy must each electron have had when they were far apart to be able to get this close? Example $17-2$

Keshav Singh

Numerade Educator

01:29

Problem 93

Potassium ions $\left(\mathrm{K}^{+}\right)$ move across a $8.0$ -nm-thick cell membrane from the inside to the outside. The potential inside the cell is $-70.0 \mathrm{mV}$, and the potential outside is zero. (a) What is the change in the electrical potential energy of the potassium ions as they move across the membrane? Does their potential energy increase or decrease? Example $17-6$

Keshav Singh

Numerade Educator

02:41

Problem 94

Calculate the equivalent capacitance of the combination in Figure $17-36 .$ SSM Example $17-11$

Keshav Singh

Numerade Educator

12:48

Problem 95

Suppose you are supplied with five identical capacitors (each with a capacitance of $10.0 \mu \mathrm{F}$ ). Determine all of the unique combinations that use all five capacitors and the equivalent capacitance of each combination. Example

Ivan Kochetkov

Numerade Educator

02:48

Problem 96

96. $^{\circ \circ}$ Determine the equivalent capacitance of the combination in Figure 17
37. Example 17-11

Keshav Singh

Numerade Educator

03:06

Problem 97

The arrangement of four capacitors in Figure $17-38$ has an equivalent capacitance of $8.00 \mu \mathrm{F}$. Calculate the value of $C_{x} . \underline{\text { Example } 17-11}$

Keshav Singh

Numerade Educator

02:11

Problem 98

Calculate the charge stored on each capacitor in the circuit shown in Figure $17-39 .$ Example $17-10$

Keshav Singh

Numerade Educator

02:14

Problem 99

A parallel-plate capacitor is made by sandwiching $0.100-\mathrm{mm}$ sheets of paper (dielectric constant $2.7$ ) between three sheets of aluminum foil (A, B, and $\mathrm{C}$ in $\underline{\text { Figure } 17-40}$ ) and rolling the layers into a cylinder. A capacitor that has an area of $10 \mathrm{~m}^{2}$ is fabricated this way. What is the capacitance of this capacitor? Example $17-12$

Keshav Singh

Numerade Educator

03:18

Problem 100

A parallel-plate capacitor with a capacitance of $5.00 \mu \mathrm{F}$ is fully charged with a 12.0-V battery. The battery is then removed. How much work is required to triple the separation between the plates? Example $17-9$

Keshav Singh

Numerade Educator

02:40

Problem 101

An air-filled parallel-plate capacitor is connected to a battery with a voltage $V$. (a) The plates are pulled apart, doubling the gap width, while they remain connected to the battery. By what factor does the potential energy of the capacitor change? (b) If the capacitor is removed from the battery, what happens to the stored potential energy when the gap width is doubled? Explain your answer. Example $17-9$

Supratim Pal

Numerade Educator

03:49

Problem 102

An air-filled parallel-plate capacitor is attached to a battery with a voltage $V$. While attached to the battery, the area of the plates is doubled and the separation of the plates is halved. During this process, what happens to (a) the capacitance, (b) the charge on the positive plate, (c) the potential across the plates, and (d) the potential energy stored in the capacitor? (e) How would your answers change if, once the capacitor was charged, it was disconnected from the battery while the area and separation were changed as above?

Keshav Singh

Numerade Educator

02:34

Problem 103

A honey bee of mass $130 \mathrm{mg}$ has accumulated a static charge of $+1.8$ pC. The bee is returning to her hive by following the path shown in Figure 17-41. Because Earth has a naturally occurring electric field near ground level of around $100 \mathrm{~V} / \mathrm{m}$ pointing vertically downward, the bee experiences an electric force as she flies. (a) What is the change in the bee's electric potential energy, $\Delta U_{\text {electric }}$, as she flies from point A to point B? (b) Compute the ratio of the bee's change in electric potential energy to her change in gravitational potential energy, $\Delta U_{\text {electric }} / \Delta U_{\text {grav }} .$ Example $17-4 .$

Sachin Rao

Numerade Educator

03:45

Problem 104

A parallel-plate capacitor has area $A$ and separation $d$. (a) What is its new capacitance if a conducting slab of thickness $\mathrm{d}^{\prime}<\mathrm{d} d^{\prime}<d$ is inserted between, and parallel to, the plates as shown in Figure $17-42 ?$ (b) Does your answer depend on where the slab is positioned vertically between the plates?

Keshav Singh

Numerade Educator

03:27

Problem 105

Three $0.18-\mu \mathrm{F}$ capacitors are connected in parallel across a 12-V battery (Figure 17-43). The battery is then disconnected. Next, one capacitor is carefully disconnected so that it doesn't lose any charge and is reconnected with its positively charged and negatively charged sides reversed. (a) What is the potential difference across the capacitors now? (b) By how much has the stored energy of the combination of capacitors changed in the process?

Keshav Singh

Numerade Educator

06:34

Problem 106

(a) Calculate the charge and energy stored on the $25-\mu \mathrm{F}$ capacitor when the switch $S$ is placed at position $A$ in Figure $17-44$. (b) Repeat for both the $25-\mu \mathrm{F}$ and the $20-\mu \mathrm{F}$ capacitors after the switch is then placed at position B. Example $17-10$

Keshav Singh

Numerade Educator

04:37

Problem 107

Figure $17-45$ shows equipotential curves for $30 \mathrm{~V}, 10 \mathrm{~V}$, and $-10 \mathrm{~V}$. A proton follows the path shown in the figure. If the proton's speed at point $A$ is $80 \mathrm{~km} / \mathrm{s}$, what is its speed at point $B$ ? Example $17-6$

Sheh Lit Chang

University of Washington

04:26

Problem 108

A parallel-plate, air-filled capacitor has a charge of $20.0 \mu \mathrm{C}$ and a gap width of $0.100 \mathrm{~mm}$. The potential difference between the plates is $200 \mathrm{~V}$.
(a) What is the electric field between the plates? (b) What is the surface charge density on the positive plate? (c) If the plates are moved closer together while the charge remains constant, how do the electric field, surface charge density, and potential difference change, if at all? Explain your answers. Example 17-7

Sarah Mccrumb

Numerade Educator