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University Physics Volume 2

Samuel J. Ling, Jeff Sanny, William Moebs

Chapter 7

Electric Potential - all with Video Answers

Educators


Chapter Questions

01:24

Problem 1

Would electric potential energy be meaningful if the electric field were not conservative?

Luis Rios
Luis Rios
Numerade Educator
01:11

Problem 2

Why do we need to be careful about work done on the system versus work done by the system in calculations?

Luis Rios
Luis Rios
Numerade Educator
00:45

Problem 3

Does the order in which we assemble a system of point charges affect the total work done?

Luis Rios
Luis Rios
Numerade Educator
02:30

Problem 4

Discuss how potential difference and electric field strength are related. Give an example.

Luis Rios
Luis Rios
Numerade Educator
00:45

Problem 5

What is the strength of the electric field in a region where the electric potential is constant?

Luis Rios
Luis Rios
Numerade Educator
01:02

Problem 6

If a proton is released from rest in an electric field, will it move in the direction of increasing or decreasing potential? Also answer this question for an electron and a neutron. Explain why.

Luis Rios
Luis Rios
Numerade Educator
00:36

Problem 7

Voltage is the common word for potential difference. Which term is more descriptive, voltage or potential difference?

Luis Rios
Luis Rios
Numerade Educator
01:38

Problem 8

If the voltage between two points is zero, can a test charge be moved between them with zero net work being done? Can this necessarily be done without exerting a force? Explain.

Luis Rios
Luis Rios
Numerade Educator
01:03

Problem 9

What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential energy?

Luis Rios
Luis Rios
Numerade Educator
01:13

Problem 10

Voltages are always measured between two points. Why?

Luis Rios
Luis Rios
Numerade Educator
00:48

Problem 11

How are units of volts and electron-volts related? How do they differ?

Luis Rios
Luis Rios
Numerade Educator
00:37

Problem 12

Can a particle move in a direction of increasing electric potential, yet have its electric potential energy decrease? Explain

Luis Rios
Luis Rios
Numerade Educator
01:35

Problem 13

Compare the electric dipole moments of charges $\pm Q$ separated by a distance $d$ and charges $\pm Q / 2$ separated by a distance $d / 2$.

Luis Rios
Luis Rios
Numerade Educator
01:19

Problem 14

Would Gauss's law be helpful for determining the electric field of a dipole? Why? a Van de Graaff generator, many practical applications of electrostatics exist, including photocopiers, laser printers, ink jet printers, and electrostatic air filters.

Luis Rios
Luis Rios
Numerade Educator
04:30

Problem 15

In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? In what region does it differ from that of a point charge?

Luis Rios
Luis Rios
Numerade Educator
01:02

Problem 16

Can the potential of a nonuniformly charged sphere be the same as that of a point charge? Explain.

Luis Rios
Luis Rios
Numerade Educator
01:42

Problem 17

If the electric field is zero throughout a region, must the electric potential also be zero in that region?

Luis Rios
Luis Rios
Numerade Educator
01:35

Problem 18

Explain why knowledge of $\overrightarrow{\mathbf{E}}(x, y, z)$ is not sufficient to determine $V(x, y, z)$. What about the other way around?

Luis Rios
Luis Rios
Numerade Educator
01:21

Problem 19

If two points are at the same potential, are there any electric field lines connecting them?

Luis Rios
Luis Rios
Numerade Educator
01:01

Problem 20

Suppose you have a map of equipotential surfaces spaced 1.0 V apart. What do the distances between the surfaces in a particular region tell you about the strength of the $\overrightarrow{\mathbf{E}}$ in that region?

Luis Rios
Luis Rios
Numerade Educator
01:26

Problem 21

Is the electric potential necessarily constant over the surface of a conductor?

Luis Rios
Luis Rios
Numerade Educator
01:26

Problem 22

Under electrostatic conditions, the excess charge on a conductor resides on its surface. Does this mean that all of the conduction electrons in a conductor are on the surface?

Luis Rios
Luis Rios
Numerade Educator
01:02

Problem 23

Can a positively charged conductor be at a negative potential? Explain.

Luis Rios
Luis Rios
Numerade Educator
View

Problem 24

Can equipotential surfaces intersect?

Luis Rios
Luis Rios
Numerade Educator
00:29

Problem 25

Why are the metal support rods for satellite network dishes generally grounded?

Luis Rios
Luis Rios
Numerade Educator
00:41

Problem 26

(a) Why are fish reasonably safe in an electrical storm? (b) Why are swimmers nonetheless ordered to get out of the water in the same circumstance?

Luis Rios
Luis Rios
Numerade Educator
01:19

Problem 27

What are the similarities and differences between the processes in a photocopier and an electrostatic precipitator?

Ankur S
Ankur S
Numerade Educator
00:25

Problem 28

About what magnitude of potential is used to charge the drum of a photocopy machine? A

Luis Rios
Luis Rios
Numerade Educator
06:14

Problem 29

Consider a charge $Q_1(+5.0 \mu \mathrm{C})$ fixed at a site with another charge $Q_2$ (charge $+3.0 \mu \mathrm{C}$, mass $6.0 \mu \mathrm{g}$ ) moving in the neighboring space. (a) Evaluate the potential energy of $Q_2$ when it is $4.0 \mathrm{~cm}$ from $Q_1$. (b) If $Q_2$ starts from rest from a point $4.0 \mathrm{~cm}$ from $Q_1$, what will be its speed when it is $8.0 \mathrm{~cm}$ from $Q_1$ ? (Note: $Q_1$ is held fixed in its place.)

Luis Rios
Luis Rios
Numerade Educator
05:49

Problem 30

Two charges $Q_1(+2.00 \mu \mathrm{C})$ and $Q_2(+2.00 \mu \mathrm{C})$ are placed symmetrically along the $x$-axis at $x= \pm 3.00 \mathrm{~cm}$. Consider a charge $Q_3$ of charge $+4.00 \mu \mathrm{C}$ and mass $10.0 \mathrm{mg}$ moving along the $y$-axis. If $Q_3$ starts from rest at $y=2.00 \mathrm{~cm}$, what is its speed when it reaches $y=4.00 \mathrm{~cm}$ ?

Luis Rios
Luis Rios
Numerade Educator
03:42

Problem 31

To form a hydrogen atom, a proton is fixed at a point and an electron is brought from far away to a distance of $0.529 \times 10^{-10} \mathrm{~m}$, the average distance between proton and electron in a hydrogen atom. How much work is done?

Luis Rios
Luis Rios
Numerade Educator
00:52

Problem 32

(a) What is the average power output of a heart defibrillator that dissipates $400 \mathrm{~J}$ of energy in $10.0 \mathrm{~ms}$ ? (b) Considering the high-power output, why doesn't the defibrillator produce serious burns?

Luis Rios
Luis Rios
Numerade Educator
02:34

Problem 33

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
$$
1.67 \times 10^{-27} \mathrm{~kg} \text {. }
$$

Ze-Han Lee
Ze-Han Lee
Numerade Educator
03:48

Problem 34

An evacuated tube uses an accelerating voltage of $40 \mathrm{kV}$ to accelerate electrons to hit a copper plate and produce X-rays. Non-relativistically, what would be the maximum speed of these electrons?

cm
Charles Magnusen
Numerade Educator
01:32

Problem 35

Show that units of $\mathrm{V} / \mathrm{m}$ and $\mathrm{N} / \mathrm{C}$ for electric field strength are indeed equivalent.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:10

Problem 36

What is the strength of the electric field between two parallel conducting plates separated by $1.00 \mathrm{~cm}$ and having a potential difference (voltage) between them of $1.50 \times 10^4 \mathrm{~V}$ ?

cm
Charles Magnusen
Numerade Educator
03:18

Problem 37

The electric field strength between two parallel conducting plates separated by $4.00 \mathrm{~cm}$ is web search for "xerography" may be of use.
$7.50 \times 10^4 \mathrm{~V} / \mathrm{m}$. (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be zero volts. What is the potential $1.00 \mathrm{~cm}$ from that plate and $3.00 \mathrm{~cm}$ from the other?

Luis Rios
Luis Rios
Numerade Educator
01:12

Problem 38

The voltage across a membrane forming a cell wall is $80.0 \mathrm{mV}$ and the membrane is $9.00 \mathrm{~nm}$ thick. What is the electric field strength? (The value is surprisingly large, but correct.) You may assume a uniform electric field.

Luis Rios
Luis Rios
Numerade Educator
03:59

Problem 39

Two parallel conducting plates are separated by $10.0 \mathrm{~cm}$, and one of them is taken to be at zero volts. (a) What is the electric field strength between them, if the potential $8.00 \mathrm{~cm}$ from the zero volt plate (and $2.00 \mathrm{~cm}$ from the other) is $450 \mathrm{~V}$ ? (b) What is the voltage between the plates?

cm
Charles Magnusen
Numerade Educator
00:46

Problem 40

Find the maximum potential difference between two parallel conducting plates separated by $0.500 \mathrm{~cm}$ of air, given the maximum sustainable electric field strength in air to be $3.0 \times 10^6 \mathrm{~V} / \mathrm{m}$.

Ze-Han Lee
Ze-Han Lee
Numerade Educator
02:04

Problem 41

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

Ze-Han Lee
Ze-Han Lee
Numerade Educator
02:43

Problem 42

Use the definition of potential difference in terms of electric field to deduce the formula for potential difference between $r=r_a$ and $r=r_b$ for a point charge located at the origin. Here $r$ is the spherical radial coordinate.

Luis Rios
Luis Rios
Numerade Educator
01:20

Problem 43

The electric field in a region is pointed away from the $z$-axis and the magnitude depends upon the distance $s$ from the axis. The magnitude of the electric field is given as $E=\frac{a}{s}$ where $\alpha$ is a constant. Find the potential difference between points $P_1$ and $P_2$, explicitly stating the path over which you conduct the integration for the line integral.
FIGURE CANT COPY

Luis Rios
Luis Rios
Numerade Educator
02:37

Problem 44

Singly charged gas ions are accelerated from rest through a voltage of $13.0 \mathrm{~V}$. At what temperature will the average kinetic energy of gas molecules be the same as that given these ions?

Luis Rios
Luis Rios
Numerade Educator
03:18

Problem 45

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?

cm
Charles Magnusen
Numerade Educator
02:21

Problem 46

How far from a $1.00-\mu \mathrm{C}$ point charge is the potential $100 \mathrm{~V}$ ? At what distance is it $2.00 \times 10^2 \mathrm{~V}$ ?

Luis Rios
Luis Rios
Numerade Educator
01:10

Problem 47

If the potential due to a point charge is $5.00 \times 10^2 \mathrm{~V}$ at a distance of $15.0 \mathrm{~m}$, what are the sign and magnitude of the charge?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
04:41

Problem 48

In nuclear fission, a nucleus splits roughly in half. (a) What is the potential $2.00 \times 10^{-14} \mathrm{~m}$ 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?

cm
Charles Magnusen
Numerade Educator
02:57

Problem 49

A research Van de Graaff generator has a 2.00-m-diameter metal sphere with a charge of $5.00 \mathrm{mC}$ on it. Assume the potential energy is zero at a reference point infinitely far away from the Van de Graaff. (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 kinetic energy in MeV when the atom is at the distance found in part b?

Luis Rios
Luis Rios
Numerade Educator
02:26

Problem 50

An electrostatic paint sprayer has a $0.200-\mathrm{m}$ diameter metal sphere at a potential of $25.0 \mathrm{kV}$ 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 $10.0 \mathrm{~m} / \mathrm{s}$ ?

cm
Charles Magnusen
Numerade Educator
05:17

Problem 51

(a) What is the potential between two points situated $10 \mathrm{~cm}$ and $20 \mathrm{~cm}$ from a $3.0-\mu \mathrm{C}$ point charge? (b) To what location should the point at $20 \mathrm{~cm}$ be moved to increase this potential difference by a factor of two?

cm
Charles Magnusen
Numerade Educator
12:34

Problem 52

Find the potential at points $P_1, P_2, P_3$, and $P_4$ in the diagram due to the two given charges.
FIGURE CANT COPY

Vishal Gupta
Vishal Gupta
Numerade Educator
19:13

Problem 53

Two charges $-2.0 \mu \mathrm{C}$ and $+2.0 \mu \mathrm{C}$ are separated by $4.0 \mathrm{~cm}$ on the $z$-axis symmetrically about origin, with the positive one uppermost. Two space points of interest $P_1$ and $P_2$ are located $3.0 \mathrm{~cm}$ and $30 \mathrm{~cm}$ from origin at an angle $30^{\circ}$ with respect to the $z$-axis. Evaluate electric potentials at $P_1$ and $P_2$ in two ways: (a) Using the exact formula for point charges, and (b) using the approximate dipole potential formula.

Vishal Gupta
Vishal Gupta
Numerade Educator
14:20

Problem 54

(a) Plot the potential of a uniformly charged 1-m rod with $1 \mathrm{C} / \mathrm{m}$ charge as a function of the perpendicular distance from the center. Draw your graph from $\mathrm{s}=0.1 \mathrm{~m}$ to $\mathrm{s}=1.0 \mathrm{~m}$. (b) On the same graph, plot the potential of a point charge with a 1-C charge at the origin. (c) Which potential is stronger near the rod? (d) What happens to the difference as the distance increases? Interpret your result.

Vedad Babic
Vedad Babic
Numerade Educator
01:47

Problem 55

Throughout a region, equipotential surfaces are given by $z=$ constant. The surfaces are equally spaced with $V=100 \mathrm{~V}$ for $z=0.00 \mathrm{~m}, V=200 \mathrm{~V}$ for $z=0.50 \mathrm{~m}, V=300 \mathrm{~V}$ for $z=1.00 \mathrm{~m}$. What is the electric field in this region?

Luis Rios
Luis Rios
Numerade Educator
05:41

Problem 56

In a particular region, the electric potential is given by $V=-x y^2 z+4 x y$. What is the electric field in this region?

Luis Rios
Luis Rios
Numerade Educator
03:13

Problem 57

Calculate the electric field of an infinite line charge, throughout space.

Luis Rios
Luis Rios
Numerade Educator
09:52

Problem 58

Two very large metal plates are placed $2.0 \mathrm{~cm}$ apart, with a potential difference of $12 \mathrm{~V}$ between them. Consider one plate to be at $12 \mathrm{~V}$, and the other at $0 \mathrm{~V}$. (a) Sketch the equipotential surfaces for $0,4,8$, and $12 \mathrm{~V}$. (b) Next sketch in some electric field lines, and confirm that they are perpendicular to the equipotential lines.

Vishal Gupta
Vishal Gupta
Numerade Educator
09:42

Problem 59

A very large sheet of insulating material has had an excess of electrons placed on it to a surface charge density of $-3.00 \mathrm{nC} / \mathrm{m}^2$, (a) As the distance from the sheet increases, does the potential increase or decrease? Can you explain why without any calculations? Does the location of your reference point matter? (b) What is the shape of the equipotential surfaces? (c) What is the spacing between surfaces that differ by 1.00 $\mathrm{V}$ ?

Vishal Gupta
Vishal Gupta
Numerade Educator
09:10

Problem 60

A metallic sphere of radius $2.0 \mathrm{~cm}$ is charged with $+5.0-\mu \mathrm{C}$ charge, which spreads on the surface of the sphere uniformly. The metallic sphere stands on an insulated stand and is surrounded by a larger metallic spherical shell, of inner radius $5.0 \mathrm{~cm}$ and outer radius $6.0 \mathrm{~cm}$. Now, a charge of $-5.0-\mu \mathrm{C}$ is placed on the inside of the spherical shell, which spreads out uniformly on the inside surface of the shell. If potential is zero at infinity, what is the potential of (a) the spherical shell, (b) the sphere, (c) the space between the two, (d) inside the sphere, and $(\mathrm{e})$ outside the shell?
FIGURE CANT COPY

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:49

Problem 61

Two large charged plates of charge density $\pm 30 \mu \mathrm{C} / \mathrm{m}^2$ face each other at a separation of $5.0 \mathrm{~mm}$. (a) Find the electric potential everywhere. (b) An electron is released from rest at the negative plate; with what speed will it strike the positive plate?

Luis Rios
Luis Rios
Numerade Educator
04:20

Problem 62

A long cylinder of aluminum of radius $R$ meters is charged so that it has a uniform charge per unit length on its surface of $\lambda$.
(a) Find the electric field inside and outside the cylinder. (b) Find the electric potential inside and outside the cylinder. (c) Plot electric field and electric potential as a function of distance from the center of the rod.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:43

Problem 63

Two parallel plates $10 \mathrm{~cm}$ on a side are given equal and opposite charges of magnitude $5.0 \times 10^{-9} \mathrm{C}$. The plates are $1.5 \mathrm{~mm}$ apart. What is the potential difference between the plates?

Luis Rios
Luis Rios
Numerade Educator
02:10

Problem 64

The surface charge density on a long straight metallic pipe is $\sigma$. What is the electric potential outside and inside the pipe? Assume the pipe has a diameter of $2 a$.
FIGURE CANT COPY

Prashant Bana
Prashant Bana
Numerade Educator
06:39

Problem 65

Concentric conducting spherical shells carry charges $Q$ and $-Q$, respectively. The inner shell has negligible thickness. What is the potential difference between the shells?
FIGURE CANT COPY

Rashmi Sinha
Rashmi Sinha
Numerade Educator
06:39

Problem 66

66. Shown below are two concentric spherical shells of negligible thicknesses and radii $R_1$ and $R_2$. The inner and outer shell carry net charges $q_1$ and $q_2$, respectively, where both $q_1$ and $q_2$ are positive. What is the electric potential in the regions (a) $r<R_1$, (b) $R_1<r<R_2$, and (c) $r>R_2$ ?
FIGURE CANT COPY

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:38

Problem 67

A solid cylindrical conductor of radius $a$ is surrounded by a concentric cylindrical shell of inner radius $b$. The solid cylinder and the shell carry charges $Q$ and - $Q$, respectively. Assuming that the length $L$ of both conductors is much greater than $a$ or $b$, what is the potential difference between the two conductors?

Suhas Katkar
Suhas Katkar
Numerade Educator
02:03

Problem 68

(a) What is the electric field $5.00 \mathrm{~m}$ from the center of the terminal of a Van de Graaff with a $3.00-\mathrm{mC}$ charge, noting that the field is equivalent to that of a point charge at the center of the terminal? (b) At this distance, what force does the field exert on a $2.00-\mu \mathrm{C}$ charge on the Van de Graaff's belt?

Luis Rios
Luis Rios
Numerade Educator
08:48

Problem 69

(a) What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? (b) Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces.

cm
Charles Magnusen
Numerade Educator
02:27

Problem 70

A simple and common technique for accelerating electrons is shown in Eigure 7.46. where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. (a) Calculate the acceleration of the electron if the field strength is $2.50 \times 10^4 \mathrm{~N} / \mathrm{C}$. (b) Explain why the electron will not be pulled back to the positive plate once it moves through the hole.
FIGURE CANT COPY
Figure 7.46 Parallel conducting plates with opposite charges on them create a relatively uniform electric field used to accelerate electrons to the right. Those that go through the hole can be used to make a TV or computer screen glow or to produce $\mathrm{X}$ - rays.

Luis Rios
Luis Rios
Numerade Educator
08:52

Problem 71

In a Geiger counter, a thin metallic wire at the center of a metallic tube is kept at a high voltage with respect to the metal tube. Ionizing radiation entering the tube knocks electrons off gas molecules or sides of the tube that then accelerate towards the center wire, knocking off even more electrons. This process eventually leads to an avalanche that is detectable as a current. A particular Geiger counter has a tube of radius $R$ and the inner wire of radius $a$ is at a potential of $V_0$ volts with respect to the outer metal tube. Consider a point $P$ at a distance $s$ from the center wire and far away from the ends. (a) Find a formula for the electric field at a point $P$ inside using the infinite wire approximation. (b) Find a formula for the electric potential at a point $P$ inside. (c) Use $V_0=900 \mathrm{~V}, a=3.00 \mathrm{~mm}, R=2.00 \mathrm{~cm}$, and find the value of the electric field at a point 1.00 $\mathrm{cm}$ from the center.
FIGURE CANT COPY

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
03:58

Problem 72

The practical limit to an electric field in air is about $3.00 \times 10^6 \mathrm{~N} / \mathrm{C}$. Above this strength, sparking takes place because air begins to ionize. (a) At this electric field strength, how far would a proton travel before hitting the speed of light (ignore relativistic effects)? (b) Is it practical to leave air in particle accelerators?

Luis Rios
Luis Rios
Numerade Educator
01:51

Problem 73

To form a helium atom, an alpha particle that contains two protons and two neutrons is fixed at one location, and two electrons are brought in from far away, one at a time. The first electron is placed at $0.600 \times 10^{-10} \mathrm{~m}$ from the alpha particle and held there while the second electron is brought to $0.600 \times 10^{-10} \mathrm{~m}$ from the alpha particle on the other side from the first electron. See the final configuration below. (a) How much work is done in each step? (b) What is the electrostatic energy of the alpha particle and two electrons in the final configuration?
Alpha particle
Electron
Electron
$$
\uparrow-0.6 \times 10^{-10} \mathrm{~m} \rightarrow-0.6 \times 10^{-10} \mathrm{~m} \rightarrow
$$

Anand Jangid
Anand Jangid
Numerade Educator
08:46

Problem 74

Find the electrostatic energy of eight equal charges $(+3 \mu \mathrm{C})$ each fixed at the corners of a cube of side $2 \mathrm{~cm}$.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:47

Problem 75

The probability of fusion occurring 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 $1.00 \times 10^{-12} \mathrm{~m}$.
(b) At what temperature will atoms of a gas have an average kinetic energy equal to this needed electrical potential energy?

Luis Rios
Luis Rios
Numerade Educator
03:23

Problem 76

A bare helium nucleus has two positive charges and a mass of $6.64 \times 10^{-27} \mathrm{~kg}$. (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?

Luis Rios
Luis Rios
Numerade Educator
10:55

Problem 77

An electron enters a region between two large parallel plates made of aluminum separated by a distance of $2.0 \mathrm{~cm}$ and kept at a potential difference of $200 \mathrm{~V}$. The electron enters through a small hole in the negative plate and moves toward the positive plate. At the time the electron is near the negative plate, its speed is $4.0 \times 10^5 \mathrm{~m} / \mathrm{s}$. Assume the electric field between the plates to be uniform, and find the speed of electron at (a) $0.10 \mathrm{~cm}$, (b) $0.50 \mathrm{~cm}$, (c) $1.0 \mathrm{~cm}$, and (d) $1.5 \mathrm{~cm}$ from the negative plate, and (e) immediately before it hits the positive plate.
FIGURE CANT COPY

Vishal Gupta
Vishal Gupta
Numerade Educator
01:40

Problem 78

How far apart are two conducting plates that have an electric field strength of $4.50 \times 10^3 \mathrm{~V} / \mathrm{m}$ between them, if their potential difference is $15.0 \mathrm{kV}$ ?

cm
Charles Magnusen
Numerade Educator
02:23

Problem 79

(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength of dry air, which is $3.00 \times 10^6 \mathrm{~V} / \mathrm{m}$, if the plates are separated by $2.00 \mathrm{~mm}$ and a potential difference of $5.0 \times 10^3 \mathrm{~V}$ is applied? (b) How close together can the plates be with this applied voltage?

Luis Rios
Luis Rios
Numerade Educator
01:11

Problem 80

Membrane walls of living cells have surprisingly large electric fields across them due to separation of ions. What is the voltage across an 8.00-nm-thick membrane if the electric field strength across it is $5.50 \mathrm{MV} / \mathrm{m}$ ? You may assume a uniform electric field.

Luis Rios
Luis Rios
Numerade Educator
02:41

Problem 81

A double charged ion is accelerated to an energy of $32.0 \mathrm{keV}$ by the electric field between two parallel conducting plates separated by $2.00 \mathrm{~cm}$. What is the electric field strength between the plates?

Luis Rios
Luis Rios
Numerade Educator
01:54

Problem 82

The temperature near the center of the Sun is thought to be 15 million degrees Celsius $\left(1.5 \times 10^7{ }^{\circ} \mathrm{C}\right)$ (or kelvin). 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?

Luis Rios
Luis Rios
Numerade Educator
06:08

Problem 83

A lightning bolt strikes a tree, moving $20.0 \mathrm{C}$ of charge through a potential difference of $1.00 \times 10^2 \mathrm{MV}$. (a) What energy was dissipated? (b) What mass of water could be raised from $15^{\circ} \mathrm{C}$ 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.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:04

Problem 84

What is the potential $0.530 \times 10^{-10} \mathrm{~m}$ from a proton (the average distance between the proton and electron in a hydrogen atom)?

Ze-Han Lee
Ze-Han Lee
Numerade Educator
02:13

Problem 85

(a) A sphere has a surface uniformly charged with $1.00 \mathrm{C}$. 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?

cm
Charles Magnusen
Numerade Educator
01:53

Problem 86

What are the sign and magnitude of a point charge that produces a potential of $-2.00 \mathrm{~V}$ at a distance of $1.00 \mathrm{~mm}$ ?

cm
Charles Magnusen
Numerade Educator
04:43

Problem 87

In one of the classic nuclear physics experiments at the beginning of the twentieth 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 $5.00 \mathrm{MeV}$, how close to the gold nucleus ( 79 protons) could it come before being deflected?

Vishal Gupta
Vishal Gupta
Numerade Educator
07:06

Problem 88

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

Vishal Gupta
Vishal Gupta
Numerade Educator
06:15

Problem 89

A battery-operated car uses a $12.0-\mathrm{V}$ system. Find the charge the batteries must be able to move in order to accelerate the $750 \mathrm{~kg}$ car from rest to $25.0 \mathrm{~m} / \mathrm{s}$, make it climb a $2.00 \times 10^2-\mathrm{m}$ high hill, and finally cause it to travel at a constant $25.0 \mathrm{~m} / \mathrm{s}$ while climbing with $5.00 \times 10^2-\mathrm{N}$ force for an hour.

Vishal Gupta
Vishal Gupta
Numerade Educator
04:08

Problem 90

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

Vishal Gupta
Vishal Gupta
Numerade Educator
01:46

Problem 91

A uniformly charged half-ring of radius $10 \mathrm{~cm}$ is placed on a nonconducting table. It is found that $3.0 \mathrm{~cm}$ above the center of the half-ring the potential is $-3.0 \mathrm{~V}$ with respect to zero potential at infinity. How much charge is in the half-ring?

Luis Rios
Luis Rios
Numerade Educator
03:22

Problem 92

A glass ring of radius $5.0 \mathrm{~cm}$ is painted with a charged paint such that the charge density around the ring varies continuously given by the following function of the polar angle $\theta, \lambda=\left(3.0 \times 10^{-6} \mathrm{C} / \mathrm{m}\right) \cos ^2 \theta$. Find the potential at a point $15 \mathrm{~cm}$ above the center.

Ajay Singhal
Ajay Singhal
Numerade Educator
03:22

Problem 93

A CD disk of radius $(R=3.0 \mathrm{~cm})$ is sprayed with a charged paint so that the charge varies continually with radial distance $r$ from the center in the following manner:
$$
\sigma=-(6.0 \mathrm{C} / \mathrm{m}) r / R \text {. }
$$
Find the potential at a point $4 \mathrm{~cm}$ above the center.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:56

Problem 94

(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 Graff terminal? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

Luis Rios
Luis Rios
Numerade Educator
02:08

Problem 95

A large metal plate is charged uniformly to a density of $\sigma=2.0 \times 10^{-9} \mathrm{C} / \mathrm{m}^2$. How far apart are the equipotential surfaces that represent a potential difference of $25 \mathrm{~V}$ ?

Vishal Gupta
Vishal Gupta
Numerade Educator
06:17

Problem 96

Your friend gets really excited by the idea of making a lightning rod or maybe just a sparking toy by connecting two spheres as shown in Figure 7.39, and making $R_2$ so small that the electric field is greater than the dielectric strength of air, just from the usual $150 \mathrm{~V} / \mathrm{m}$ electric field near the surface of the Earth. If $\boldsymbol{R}_1$ is $10 \mathrm{~cm}$, how small does $R_2$ need to be, and does this seem practical? (Hint: recall the calculation for electric field at the surface of a conductor from Gauss's Law.)

Vishal Gupta
Vishal Gupta
Numerade Educator
06:06

Problem 97

(a) Find $x>>L$ limit of the potential of a finite uniformly charged rod and show that it coincides with that of a point charge formula.
(b) Why would you expect this result?

Narayan Hari
Narayan Hari
Numerade Educator
09:10

Problem 98

A small spherical pith ball of radius $0.50 \mathrm{~cm}$ is painted with a silver paint and then $-10 \mu \mathrm{C}$ of charge is placed on it. The charged pith ball is put at the center of a gold spherical shell of inner radius $2.0 \mathrm{~cm}$ and outer radius $2.2 \mathrm{~cm}$. (a) Find the electric potential of the gold shell with respect to zero potential at infinity. (b) How much charge should you put on the gold shell if you want to make its potential $100 \mathrm{~V}$ ?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:24

Problem 99

Two parallel conducting plates, each of crosssectional area $400 \mathrm{~cm}^2$, are $2.0 \mathrm{~cm}$ apart and uncharged. If $1.0 \times 10^{12}$ electrons are transferred from one plate to the other, (a) what is the potential difference between the plates?
(b) What is the potential difference between the positive plate and a point $1.25 \mathrm{~cm}$ from it that is between the plates?

Luis Rios
Luis Rios
Numerade Educator
07:38

Problem 100

A point charge of $q=5.0 \times 10^{-8} \mathrm{C}$ is placed at the center of an uncharged spherical conducting shell of inner radius $6.0 \mathrm{~cm}$ and outer radius $9.0 \mathrm{~cm}$. Find the electric potential at (a) $r=4.0 \mathrm{~cm}$, (b) $r=8.0 \mathrm{~cm}$, (c) $r=12.0 \mathrm{~cm}$.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:03

Problem 101

Earth has a net charge that produces an electric field of approximately $150 \mathrm{~N} / \mathrm{C}$ downward at its surface. (a) What is the magnitude and sign of the excess charge, noting the electric field of a conducting sphere is equivalent to a point charge at its center? (b) What acceleration will the field produce on a free electron near Earth's surface? (c) What mass object with a single extra electron will have its weight supported by this field?

Simran Hiranandani
Simran Hiranandani
Numerade Educator
04:37

Problem 102

Point charges of $25.0 \mu \mathrm{C}$ and $45.0 \mu \mathrm{C}$ are placed $0.500 \mathrm{~m}$ apart.
(a) At what point along the line between them is the electric field zero?
(b) What is the electric field halfway between them?

Simran Hiranandani
Simran Hiranandani
Numerade Educator
04:10

Problem 103

What can you say about two charges $q_1$ and $q_2$, if the electric field one-fourth of the way from $q_1$ to $q_2$ is zero?

cm
Charles Magnusen
Numerade Educator
02:13

Problem 104

Calculate the angular velocity $\omega$ of an electron orbiting a proton in the hydrogen atom, given the radius of the orbit is $0.530 \times 10^{-10} \mathrm{~m}$. You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.

Simran Hiranandani
Simran Hiranandani
Numerade Educator
11:09

Problem 105

An electron has an initial velocity of $5.00 \times 10^6 \mathrm{~m} / \mathrm{s}$ in a uniform $2.00 \times 10^5-\mathrm{N} / \mathrm{C}$ electric field. The field accelerates the electron in the direction opposite to its initial velocity. (a) What is the direction of the electric field? (b) How far does the electron travel before coming to rest? (c) How long does it take the electron to come to rest? (d) What is the electron's velocity when it returns to its starting point?

Vishal Gupta
Vishal Gupta
Numerade Educator
04:12

Problem 106

Three $\mathrm{Na}^{+}$and three $\mathrm{Cl}^{-}$ions are placed alternately and equally spaced around a circle of radius $50 \mathrm{~nm}$. Find the electrostatic energy stored.

Narayan Hari
Narayan Hari
Numerade Educator
02:50

Problem 107

Look up (presumably online, or by dismantling an old device and making measurements) the magnitude of the potential deflection plates (and the space between them) in an ink jet printer. Then look up the speed with which the ink comes out the nozzle. Can you calculate the typical mass of an ink drop?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:13

Problem 109

Calculate the electric field of a dipole throughout space from the potential.

Luis Rios
Luis Rios
Numerade Educator