• Home
  • Textbooks
  • Matter & Interactions
  • Electric Field

Matter & Interactions

Ruth W. Chabay, Bruce A. Sherwood

Chapter 13

Electric Field - all with Video Answers

Educators

Chapter Questions

01:13

Problem 1

What is the relationship between the terms "ficld" and force"? What are their units?

Ma Ednelyn Lim
Ma Ednelyn Lim
Numerade Educator
02:30

Problem 2

You are the captain of a spaceship. You need to measure the electric field at a specified location $P$ in space outside your ship. You send a crew member outside with a meter stick, a stopwatch. and a small ball of known mass $M$ and net charge $+Q$ (held by insulating strings while being carried). (a) Write down the instructions you will give to the crew member, explaining what observations to make. (b) Explain how you will analyze the data that the crew member brings you to determine the magnitude and direction of the electric field at location $P$.

Adriano Chikande
Adriano Chikande
Numerade Educator
01:14

Problem 3

Criticize the following statement: "A proton can never be at rest, because it makes a very large electric ficld near itself that accelerates it."

Adriano Chikande
Adriano Chikande
Numerade Educator
01:35

Problem 4

Draw a diagram showing two separated point charges placed in such a way that the electric field is zero somewhere, and indicate that position. Explain your reasons.

Adriano Chikande
Adriano Chikande
Numerade Educator
01:14

Problem 5

At location $A$ there is an electric field in the direction shown by the orange arrow in Figure $13.56 .$ This electric field is due to charged particles that are not shown in the diagram. (a) If a proton is placed at location $A,$ which of the arrows $(a-h)$ best indicates the direction of the electric force on the proton? (b) If the proton is removed and an electron is placed at location $A$ which of the arrows in Figure 13.56 best indicates the direction of the electric force on the electron?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:30

Problem 6

We found that the force exerted on a distant charged object by a dipole is given by
$$F_{\text {on }} Q \text { by dipole } \approx Q\left(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q s}{r^{3}}\right)$$
In this equation, what is the meaning of the symbols $q, Q, s,$ and $r ?$

Adriano Chikande
Adriano Chikande
Numerade Educator
01:16

Problem 7

At a given instant in time, three charged objects are located near each other, as shown in Figure 13.57 . Explain why the equation
$$F_{\mathrm{on}} Q_{\mathrm{by}} \text { dipole } \approx Q\left(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q s}{r^{3}}\right)$$
cannot be used to calculate the electric force on the ball of charge $+Q$

Adriano Chikande
Adriano Chikande
Numerade Educator
01:19

Problem 8

Where could you place one positive charge and one negative charge to produce the pattern of electric field shown in Figure $13.58 ?$ (As usual, each electric field vector is drawn with its tail at the location where the electric field was measured.) Briefly explain your choices.

Adriano Chikande
Adriano Chikande
Numerade Educator
01:54

Problem 9

Consider Figure 13.59 . Assume that the dipole is fixed in position. (a) What is the direction of the electric field at location $A$ due to the dipole? (b) At location $B ?$ (c) If an electron were placed at location $A,$ in which direction would it begin to move? (d) If a proton were placed at location $B$, in which direction would it begin to move? (e) Now suppose that an electron is placed at location $A$ and held there, while the dipole is free to move. When the dipole is released, in what direction will it begin to move?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:42

Problem 10

Which of these statements about a dipole are correct? Select all that are true.
(1) At a distance $d$ from a dipole, where $d \gg s$ (the separation between the charges), the magnitude of the electric field due to the dipole is proportional to $1 / d^{3}$
(2) A dipole consists of two particles whose charges are equal in magnitude but opposite in sign.
(3) The net electric field due to a dipole is zero, since the contribution of the negative charge cancels out the contribution of the positive charge.
(4) At a distance $d$ from a dipole, where $d \gg s$ (the separation between the charges, the magnitude of the electric field due to the dipole is proportional to $1 / d^{2}$. (5) The electric field at any location in space, due to a dipole, is the vector sum of the electric field due to the positive charge and the electric field due to the negative charge.

Adriano Chikande
Adriano Chikande
Numerade Educator
01:15

Problem 11

If we triple the distance $d$, by what factor is the force on the point charge due to the dipole in Figure 13.60 reduced? (Note that the factor is smaller than one if the force is reduced and larger than one if the force is increased.)

Adriano Chikande
Adriano Chikande
Numerade Educator
01:09

Problem 12

If the charge of the point charge in Figure 13.60 were $-9 Q$ (instead of $Q$ ): (a) By what factor would the magnitude of the force on the point charge due to the dipole change? Express your answer as the ratio (magnitude of new force / magnitude of $F v$ ).
(b) Would the direction of the force change?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:06

Problem 13

The distance between the dipole and the point charge in Figure 13.60 is $d .$ If the distance between them were changed to $0.5 d,$ by what factor would the force on the point charge due to the dipole change? Express your answer as the ratio (magnitude of new force / magnitude of $F v$ ).

Adriano Chikande
Adriano Chikande
Numerade Educator
01:20

Problem 14

Draw a diagram like the one in Figure 13.61
On your diagram, draw vectors showing: (a) the electric field of the dipole at the location of the negatively charged ball, (b) the net force on the ball due to the dipole, (c) the electric field of the ball at the center of the dipole, (d) the net force on the dipole due to the ball.

Adriano Chikande
Adriano Chikande
Numerade Educator
01:08

Problem 15

If the distance between the ball and the dipole in Figure 13.61 were doubled, what change would there be in the force on the ball due to the dipole?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:10

Problem 16

An electron in a region in which there is an electric field experiences a force of magnitude $3.8 \times 10^{-16} \mathrm{N}$. What is the magnitude of the electric field at the location of the electron?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:09

Problem 17

The electric field at a particular location is measured to be $\langle 0,-280,0\rangle \mathrm{N} / \mathrm{C}$. What force would a positron experience if placed at this particular location?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:06

Problem 18

An electron in a region in which there is an electric field experiences a force of magnitude $3.7 \times 10^{-16} \mathrm{N}$. What is the magnitude of the electric field at the location of the electron?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:12

Problem 19

If the particle in Figure 13.62 is a proton, and the electric field $\vec{E}_{1}$ has the value $\left\langle 2 \times 10^{4}, 2 \times 10^{4}, 0\right\rangle \mathrm{N} / \mathrm{C},$ what is the force $\vec{F}_{2}$ on the proton?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:19

Problem 20

An electron in a region in which there is an electric field experiences a force of $\left\langle 8.0 \times 10^{-17},-3.2 \times 10^{-16},-4.8 \times\right.$ $\left.10^{-16}\right\rangle \mathrm{N} .$ What is the electric field at the location of the electron?

Adriano Chikande
Adriano Chikande
Numerade Educator
02:36

Problem 21

In the region shown in Figure 13.63 there is an electric field due to a point charge located at the center of the dashed circle. The arrows indicate the magnitude and direction of the electric field at the locations shown.
(a) What is the sign of the source charge?
(b) Now a particle whose charge is $-7 \times 10^{-9} \mathrm{C}$ is placed at location $B$. What is the direction of the electric force on the $-7 \times 10^{-9} \mathrm{C}$ charge?
(c) The electric field at location $B$ has the value \langle 2000,2000,0\rangle
N/C. What is the unit vector in the direction of $\vec{E}$ at this location?
(d) What is the electric force on the $-7 \times 10^{-9} \mathrm{C}$ charge?
(e) What is the unit vector in the direction of this electric force?

Adriano Chikande
Adriano Chikande
Numerade Educator
02:18

Problem 22

In the region shown in Figure 13.64 there is an electric field due to charged objects not shown in the diagram. A tiny glass ball with a charge of $5 \times 10^{-9} \mathrm{C}$ placed at location $A$ experiences a force of $\left\langle 4 \times 10^{-5},-4 \times 10^{5}, 0\right\rangle \mathrm{N},$ as shown in the figure. (a) Which arrow in Figure 13.65 best indicates the direction of the electric field at location $A$ ? (b) What is the electric field at location $A$ ? (c) What is the magnitude of this electric field? (d) Now the glass ball is moved very far away. A tiny plastic ball with charge $-6 \times 10^{-9} \mathrm{C}$ is placed at location $A$ Which arrow in Figure 13.65 best indicates the direction of the electric force on the negatively charged plastic ball? (e) What is the force on the negative plastic ball? (f) You discover that the source of the electric field at location $A$ is a negatively charged particle. Which of the numbered locations in Figure 13.64 shows the location of this negatively charged particle, relative to location $A$ ?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:31

Problem 23

An electron is observed to accelerate in the $+z$ direction with an acceleration of $1.6 \times 10^{16} \mathrm{m} / \mathrm{s}^{2} .$ Explain how to use the definition of electric field to determine the electric field at this location, and give the direction and magnitude of the field.

Adriano Chikande
Adriano Chikande
Numerade Educator
01:10

Problem 24

An object falling in a vacuum near a planet has a charge of $-4 \times 10^{-8} \mathrm{C}$ and a mass of $0.3 \mathrm{kg} .$ In this region of space there is an electric field $\left\langle 2 \times 10^{7}, 0,0\right\rangle \mathrm{N} / \mathrm{C}$ and a gravitational field \langle 0,5,0\rangle N/kg. What is the net force acting on the object?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:13

Problem 25

$A$ proton is observed to have an instantaneous acceleration of $9 \times 10^{11} \mathrm{m} / \mathrm{s}^{2} .$ What is the magnitude of the electric field at the proton's location?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:27

Problem 26

In Figure 13.66 a proton at location $A$ makes an electric field $\vec{E}_{1}$ at location $B .$ A different proton, placed at location $B$ experiences a force $\vec{F}_{1}$ Now the proton at $B$ is removed and replaced by a lithium nucleus, containing three protons and four neutrons. (a) Now what is the value of the electric field at location $B$ due to the proton? (b) What is the force on the lithium nucleus? (c) The lithium nucleus is removed, and an electron is placed at location $B$. Now what is the value of the electric field at location $B$ due to the proton? (d) What is the magnitude of the force on the electron? (e) Which arrow in Figure 13.65 best indicates the direction of the force on the electron due to the electric field?

Adriano Chikande
Adriano Chikande
Numerade Educator
03:01

Problem 27

You want to calculate the electric field at location $\langle 0.5,-0.1,-0.5\rangle \mathrm{m},$ due to a particle with charge $+9 \mathrm{n} \mathrm{C}$ located at $\langle-0.6,-0.7,-0.2\rangle \mathrm{m} .$ (a) What is the source location? (b) What is the observation location? (c) What is the vector $\vec{r}$ that points from the source location to the observation location? (d) What is $|\vec{r}| ?$ (e) What is the vector $\dot{r} ?$ (f) What is the value of $\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{|\vec{r}|^{2}} ?$ (g) Finally, what is the electric field, expressed as a vector?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:06

Problem 28

A particle with charge $+5 \mathrm{nC}$ (a nanocoulomb is $1 \times 10^{-9}$ C) is located at the origin. What is the electric field due to this particle at a location \langle 0.4,0,0\rangle $\mathrm{m} ?$

Adriano Chikande
Adriano Chikande
Numerade Educator
01:44

Problem 29

What is the electric field at a location $\langle-0.1,-0.1,0\rangle \mathrm{m},$ due to a particle with charge +4 nC located at the origin?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:06

Problem 30

In a hydrogen atom in its ground state, the electron is on average a distance of about $0.5 \times 10^{-10} \mathrm{m}$ from the proton. What is the magnitude of the electric field due to the proton at this distance from the proton?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:31

Problem 31

A sphere with radius 1 $\mathrm{cm}$ has a charge of $2 \times 10^{-9} \mathrm{C}$ spread out uniformly over its surface. What is the magnitude of the electric field due to the sphere at a location $4 \mathrm{cm}$ from the center of the sphere?

Ajay Singhal
Ajay Singhal
Numerade Educator
02:24

Problem 32

A sphere with radius $2 \mathrm{cm}$ is placed at a location near a point charge. The sphere has a charge of $-9 \times 10^{-10}$ C spread uniformly over its surface. The electric field due to the point charge has a magnitude of $470 \mathrm{N} / \mathrm{C}$ at the center of the sphere. What is the magnitude of the force on the sphere due to the point charge?

Supratim Pal
Supratim Pal
Numerade Educator
01:23

Problem 33

What are the magnitude and direction of the electric field $\vec{E}$ at location \langle 20,0,0\rangle $\mathrm{cm}$ if there is a negative point charge of $1 \mathrm{nC}$ $\left(1 \times 10^{-9} \mathrm{C}\right)$ at location \langle 40,0,0\rangle $\mathrm{cm} ?$ Include units.

Ajay Singhal
Ajay Singhal
Numerade Educator
05:27

Problem 34

A sphere with radius $2 \mathrm{cm}$ is placed at a location near a point charge. The sphere has a charge of $-8 \times 10^{-10} \mathrm{C}$ spread uniformly over its surface. The electric field due to the point charge has a magnitude of $500 \mathrm{N} / \mathrm{C}$ at the center of the sphere. What is the magnitude of the force on the sphere due to the point charge?

Katie Mcalpine
Katie Mcalpine
Numerade Educator
03:01

Problem 35

An electron is located at $\langle 0.8,0.7,-0.8\rangle \mathrm{m} .$ You need to find the electric field at location $\langle 0.5,1,-0.5\rangle \mathrm{m},$ due to the electron.
(a) What is the source location?
(b) What is the observation location?
(c) What is the vector $\vec{r}$ ?
(d) What is $|\vec{r}|$ ?
(e) What is the vector $\dot{r}$ ? (f) What is the value of $\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{|\vec{r}|^{2}} ?$
(g) Finally, what is the electric field at the observation location, expressed as a vector?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:06

Problem 36

A charged particle located at the origin creates an electric field of $\left\langle-1.2 \times 10^{3}, 0,0\right\rangle \mathrm{N} / \mathrm{C}$ at a location $\langle 0.12,0,0\rangle \mathrm{m} .$ What is the particle's charge?

Adriano Chikande
Adriano Chikande
Numerade Educator
12:17

Problem 37

At a particular location in the room there is an electric field $=\langle 1000,0,0\rangle \mathrm{N} / \mathrm{C}$. Where would you place a single negative point particle of charge $1 \mu \mathrm{C}$ in order to produce this electric field?

DM
Debra Mangion
Numerade Educator
07:56

Problem 38

The electric field at a location $C$ points north, and the magnitude is $1 \times 10^{6} \mathrm{N} / \mathrm{C}$. Give numerical answers to the following questions: (a) Where relative to $C$ should you place a single proton to produce this field? (b) Where relative to $C$ should you place a single electron to produce this field? (c) Where should you place a proton and an electron, at equal distances from $C,$ to produce this field?

Brandy Heflin
Brandy Heflin
Numerade Educator
07:56

Problem 39

You want to create an electric field $=\langle 0,4104,0\rangle \mathrm{N} / \mathrm{C}$ at location $\langle 0,0,0\rangle .$ (a) Where would you place a proton to produce this field at the origin? (b) Instead of a proton, where would you place an electron to produce this field at the origin? (Hint: This problem will be much easier if you draw a diagram.)

Brandy Heflin
Brandy Heflin
Numerade Educator
01:06

Problem 40

A $\pi^{-}(" \text { pi-minus" ) particle, which has charge }-e$, is at location $\left\langle 7 \times 10^{-9},-4 \times 10^{-9},-5 \times 10^{-9}\right\rangle$. $\mathrm{m}$. (a) What is the electric field at location $\left\langle-5 \times 10^{-9}, 5 \times 10^{-9}, 4 \times 10^{-9}\right\rangle \mathrm{m},$ due to the $\pi^{-}$ particle? (b) At a particular moment an antiproton (same mass as the proton, charge $-e$ ) is at the observation location. At this moment what is the force on the antiproton, due to the $\pi^{-?}$

Adriano Chikande
Adriano Chikande
Numerade Educator
01:44

Problem 41

What is the electric field at a location $\vec{b}=$ $\langle-0.1,-0.1,0\rangle \mathrm{m},$ due to a particle with charge $+3 \mathrm{nC}$ located at the origin?

Adriano Chikande
Adriano Chikande
Numerade Educator
01:05

Problem 42

At a particular location in the room there is an electric field $\vec{E}=\langle 1000,0,0\rangle \mathrm{N} / \mathrm{C}$. Figure out where to place a single positive point particle, and how much charge it should have, in order to produce this electric field (there are many possible answers!). Do the same for a single negatively charged point particle. Be sure to draw diagrams to explain the geometry of the situation.

Penny Riley
Penny Riley
Numerade Educator
07:56

Problem 43

Where must an electron be to create an electric field of $\langle 0,160,0\rangle \mathrm{N} / \mathrm{C}$ at a location in space? Calculate its displacement from the observation location and show its location on a diagram.

Brandy Heflin
Brandy Heflin
Numerade Educator
07:56

Problem 44

The electric field at a location $C$ points west, and the magnitude is $2 \times 10^{6} \mathrm{N} / \mathrm{C}$. Give numerical answers to the following questions: (a) Where relative to $C$ should you place a single proton to produce this field? (b) Where relative to $C$ should you place a single electron to produce this field? (c) Where should you place a proton and an electron, at equal distances from $C,$ to produce this field?

Brandy Heflin
Brandy Heflin
Numerade Educator
01:04

Problem 45

A lithium nucleus consisting of three protons and four neutrons accelerates to the right due to electric forces, and the initial magnitude of the acceleration is $3 \times 10^{13} \mathrm{m} / \mathrm{s} / \mathrm{s}$. (a) What is the direction of the electric field that acts on the lithium nucleus?
(b) What is the magnitude of the electric field that acts on the lithium nucleus? Be quantitative (that is, give a number). (c) If this acceleration is due solely to a single helium nucleus (two protons and two neutrons, where is the helium nucleus initially located? Be quantitative (that is, give a number).

Raj Bala
Raj Bala
Numerade Educator
04:16

Problem 46

On a clear and carefully drawn diagram, place a helium nucleus (consisting of two protons and two neutrons) and a proton in such a way that the electric field due to these charges is zero at a location marked $\times,$ a distance $1 \times 10^{-10} \mathrm{m}$ from the helium nucleus. Explain briefly but carefully, and use diagrams to help in the explanation. Be quantitative about the relative distances. (b) On a clear and carefully drawn diagram, place a helium nucleus and an electron in such a way that the electric field due to these charges is zero at a location marked $\times$. Explain briefly but carefully, and use diagrams to help in the explanation. Be quantitative about the relative distances.

Suzanne W.
Suzanne W.
Numerade Educator
01:05

Problem 47

At a particular moment, three charged particles are located as shown in Figure $13.67 . Q_{1}=-4 \mu \mathrm{C}, Q_{2}=+3 \mu \mathrm{C},$ and $Q_{3}=-2 \mu \mathrm{C} .$ Your answers to the following questions should be vectors. (Recall that $1 \mu \mathrm{C}-1 \times 10^{-6} \mathrm{C}$.) (a) Find the electric field at the location of $Q_{3}$, due to $Q_{1}$. (b) Find the electric field at the location of $Q_{3}$, due to $Q_{2}$. (c) Find the net electric field at the location of $Q_{3}$. (d) Find the net force on $Q_{3}$. (e) Find the electric field at location $A$ due to $Q_{1}$. (f) Find the electric field at location $A$ due to $Q_{2}$. (g) Find the electric field at location $A$ due to $Q_{3}$ (h) What is the net electric field at location $A$ ? (i) If a particle with charge -3 nC were placed at location $A$, what would be the force on this particle?

Raj Bala
Raj Bala
Numerade Educator
09:38

Problem 48

At a particular moment, one negative and two positive charges are located as shown in Figure $13.68 . Q_{1}=+3 \mu \mathrm{C}, Q_{2}=$ $+8 \mu \mathrm{C},$ and $Q_{3}=-5 \mu \mathrm{C} .$ Your answers to each part of this problem should be vectors. (Recall that $1 \mu C=1 \times 10^{-6}$ C.)
(a) Find the electric field at the location of $Q_{1}$, due to $Q_{2}$ and $Q_{3} \cdot$ (b) Use the electric ficld you calculated in part (a) to find the force on $Q_{1}$. (c) Find the electric field at location $A$, due to all three charges. (d) An alpha particle (He $^{2+}$, containing two protons and two neutrons) is released from rest at location $A$.

Dading Chen
Dading Chen
Numerade Educator
04:26

Problem 49

Use your answer from the previous part to determine the initial acceleration of the alpha particle.
An $\mathrm{Fe}^{3+}$ ion is located $400 \mathrm{nm}\left(400 \times 10^{-9} \mathrm{m}, \text { about } 4000\right.$ atomic diameters) from a $\mathrm{Cl}^{-}$ ion, as shown in Figure 13.69 (ions not shown to scale).
(a) Determine the magnitude and direction of the electric field $E_{A}$ at location $A, 100 \mathrm{nm}$ to the left of the $\mathrm{Cl}^{-}$ ion. (b) Determine the magnitude and direction of the electric field $\vec{E}_{B}$ at location $B$, $100 \mathrm{nm}$ to the right of the $\mathrm{Cl}^{-}$ ion. (c) If an electron is placed at location $A,$ what are the magnitude and direction of the force on the electron?

João Gabriel Alencar Caribé
João Gabriel Alencar Caribé
Numerade Educator
11:52

Problem 50

A hollow ball with radius $R=2 \mathrm{cm}$ has a charge of $q_{1}=-3 \mathrm{nC}$ spread uniformly over its surface, as shown in Figure $13.70 .$ The center of the ball is at $\langle-3,0,0\rangle \mathrm{cm} .$ A point charge of $q_{2}=5 \mathrm{nC}$ is located at $\langle 4,0,0\rangle \mathrm{cm} .$ (a) What is the net electric field at location $A,$ when $\vec{r}_{A}=\langle 0,6,0\rangle \mathrm{cm} ?(\mathrm{b})$ Draw an arrow representing the net electric field at that location. Make sure that the arrow you drew makes sense.

Brandy Heflin
Brandy Heflin
Numerade Educator
05:27

Problem 51

Three nested hollow spheres have the same center. The innermost sphere has a radius of $2 \mathrm{cm}$ and carries a uniformly distributed charge of $6 \mathrm{nC}\left(1 \mathrm{nC}=1 \times 10^{-9} \mathrm{C}\right) .$ The middle sphere has a radius of $5 \mathrm{cm}$ and carries a uniformly distributed charge of $-4 \mathrm{nC}$. The outermost sphere has a radius of $10 \mathrm{cm}$ and carries a uniformly distributed charge of 8 nC. (a) What is the magnitude of the electric field at a distance of $1 \mathrm{cm}$ from the center? (b) What is the magnitude of the electric field at a distance of $4 \mathrm{cm}$ from the center? (c) What is the magnitude of the electric field at a distance of $9 \mathrm{cm}$ from the center?

Katie Mcalpine
Katie Mcalpine
Numerade Educator
09:03

Problem 52

A dipole is located at the origin and is composed of charged particles with charge $+e$ and $-e$, separated by a distance $6 \times 10^{-10} \mathrm{m}$ along the $x$ axis. The charge $+e$ is on the $+x$ axis. Calculate the electric field due to this dipole at a location $\langle 0,-5 x$ $\left.10^{-8}, 0\right\rangle \mathrm{m}$.

Jonathan Everett
Jonathan Everett
Numerade Educator
09:03

Problem 53

A dipole is located at the origin and is composed of charged particles with charge $+e$ and $-e$, separated by a distance $2 \times 10^{-10} \mathrm{m}$ along the $x$ axis. Calculate the magnitude of the electric field due to this dipole at a location $\left\langle 0,3 \times 10^{-8}, 0\right\rangle \mathrm{m}$.

Jonathan Everett
Jonathan Everett
Numerade Educator
02:48

Problem 54

The dipole moment of the HF (hydrogen fluoride) molecule has been measured to be $6.3 \times 10^{-30} \mathrm{C} \cdot \mathrm{m}$. If we model the dipole as having charges of $+e$ and $-e$ separated by a distance $s,$ what is $s ?$ Is this plausible?

Sima Sarker
Sima Sarker
Numerade Educator
02:02

Problem 55

A dipole is located at the origin and is composed of charged particles with charge $+e$ and $-e$, separated by a distance $6 \times 10^{-10} \mathrm{m}$ along the $y$ axis. The $+e$ charge is on the $-y$ axis Calculate the force on a proton due to this dipole at a location $\left\langle 0,4 \times 10^{-8}, 0\right\rangle \mathrm{m}$.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
02:02

Problem 56

A dipole is located at the origin and is composed of charged particles with charge $+2 e$ and $-2 e,$ separated by a distance $2 \times 10^{-10} \mathrm{m}$ along the $y$ axis. The $+2 e$ charge is on the $+y$ axis. Calculate the force on a proton at a location $\left\langle 0,0,3 \times 10^{-8}\right\rangle$ m due to this dipole.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:26

Problem 57

A dipole consists of two charges $+6 \mathrm{nC}$ and $-6 \mathrm{nC}$, held apart by a rod of length $3 \mathrm{mm}$, as shown in Figure 13.71 . (a) What is the magnitude of the electric field due to the dipole at location $A, 5 \mathrm{cm}$ from the center of the dipole? (b) What is the magnitude of the electric field due to the dipole at location $B, 5 \mathrm{cm}$ from the center of the dipole?

Ummatul Choudary
Ummatul Choudary
Numerade Educator
02:02

Problem 58

A dipole is centered at the origin and is composed of charged particles with charge $+2 e$ and $-2 e$, separated by a distance $7 \times 10^{-10} \mathrm{m}$ along the $y$ axis. The $+2 e$ charge is on the $-y$ axis, and the $-2 e$ charge is on the $+y$ axis. (a) A proton is located at $\left\langle 0,3 \times 10^{-8}, 0\right\rangle \mathrm{m}$. What is the force on the proton due to the dipole? (b) An electron is located at $\left\langle-3 \times 10^{-8}, 0,0\right\rangle$ $\mathrm{m} .$ What is the force on the electron due to the dipole? (Hint: Make a diagram. One approach is to calculate magnitudes, and get directions from your diagram.)

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
08:18

Problem 59

Two dipoles are oriented as shown in Figure $13.72 .$ Each dipole consists of two charges $+q$ and $-q,$ held apart by a rod of length $s,$ and the center of each dipole is a distance $d$ from location $A .$ If $q=2 \mathrm{nC}, s=1 \mathrm{mm},$ and $d=8 \mathrm{cm},$ what is the electric field at location $A$ ? (Hint: Draw a diagram and show the direction of each dipole's contribution to the electric field on the diagram.)

Jonathan Everett
Jonathan Everett
Numerade Educator
03:21

Problem 60

Two dipoles are oriented as shown in Figure 13.73 . Each dipole consists of charges held apart by a short rod (not shown to scale $) .$ What is the electric field at location $A$ ? Start by drawing a diagram that shows the direction of each dipole's contribution to the electric field at location $A$.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:34

Problem 61

A charge of $+1 \mathrm{nC}\left(1 \times 10^{-9} \mathrm{C}\right)$ and a dipole with charges $+q$ and $-q$ separated by $0.3 \mathrm{mm}$ contribute a net field at location $A$ that is zero, as shown in Figure 13.74 (a) Which end of the dipole is positively charged? (b) How large is the charge $q ?$

Kayla Gephart
Kayla Gephart
Numerade Educator
00:34

Problem 62

A water molecule is asvmmetrical. with one end positively charged and the other negatively charged. It has a dipole moment whose magnitude is measured to be $6.2 \times$ $10^{-30} \mathrm{C} \cdot \mathrm{m} .$ If the dipole moment is oriented perpendicular to an electric field whose magnitude is $4 \times 10^{5} \mathrm{N} / \mathrm{m}$, what is the magnitude of the torque on the water molecule? Also, show that the vector torque is equal to $\vec{p} \times \vec{E}$, where $\vec{p}$ is the dipole moment.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:32

Problem 63

Two identical permanent dipoles, each consisting of charges $+q$ and $-q$ separated by a distance $s,$ are aligned along the $x$ axis, a distance $r$ from each other, where $r \gg s$ (Figure 13.75). Show all of the steps in your work, and briefly explain each step. (a) Draw a diagram showing all individual forces acting on each particle, and draw heavier vectors showing the net force on each dipole. (b) Show that the magnitude of the net force exerted on one dipole by the other dipole is this:
$$F \approx \frac{1}{4 \pi \varepsilon_{0}} \frac{6 q^{2} s^{2}}{r^{4}}$$

Mayukh Banik
Mayukh Banik
Numerade Educator
04:17

Problem 64

You make repeated measurements of the electric field $\vec{E}$ due to a distant charge, and you find it is constant in magnitude and direction. At time $t=0$ your partner moves the charge. The electric field doesn't change for a while, but at time $t=45$ ns you observe a sudden change. How far away was the charge originally?

Ajay Singhal
Ajay Singhal
Numerade Educator
03:01

Problem 65

In Section 13.9 there is a program to calculate the electric field of a single point charge at multiple observation locations
(a) Study this program and make sure you can explain every line of code, (b) Modify the program so that the magnitude of the electric field at each observation location is the same. (There is more than one way to do this.) (c) Add an additional circle of observation locations in the $y z$ plane, centered on the point charge.

Adriano Chikande
Adriano Chikande
Numerade Educator
03:01

Problem 66

A particle with a charge of $+3 \mathrm{nC}$ is located at \langle-0.04,0,0\rangle
(a) Calculate the electric field at location \langle-0.04,0,0.05\rangle $\mathrm{m}$ due to this particle, and create an arrow to visualize the field at the observation location. Try a scale factor of about $2 \times 10^{-6}$ (b) Add an arrow representing the electric field at location \langle-0.04,0,-0.05\rangle due to this particle. (c) Add two more arrows, each representing the electric field at a location $0.05 \mathrm{m}$ from the particle in the $\pm y$ direction. (d) Add two more arrows each representing the electric field at a location $0.05 \mathrm{m}$ from the particle in the $\pm x$ direction.

Adriano Chikande
Adriano Chikande
Numerade Educator
05:21

Problem 67

Three charged spheres lie in the $x z$ plane. Sphere $a$ has a charge of $+2 \mathrm{nC}$, and is located at $\langle-0.03,0,0.03\rangle \mathrm{m} .$ Sphere $b$ has a charge of $+4 \mathrm{nC}$, and is located at $\langle 0.03,0,0.03\rangle \mathrm{m}$. Sphere $c$ has a charge of $-2 \mathrm{nC}$, and is located at $\langle 0,0,-0.011\rangle \mathrm{m}$. Write a program to calculate and display (using an arrow) the electric field of these three charged spheres at location $\langle 0,0.25,0) \mathrm{m}$.

Mayukh Banik
Mayukh Banik
Numerade Educator
06:01

Problem 68

The following code creates two objects representing a dipole oriented along the $y$ axis.
(a) Extend the program to calculate and display (using arrows) the electric field due to the dipole at 12 equally spaced observation locations located on a circle of radius $0.5 \mathrm{nm}$ in the $x y$ plane, centered on the dipole.
(b) Add a second circle of arrows representing the electric field at observation locations in the $y z$ plane.

Corinna Pena
Corinna Pena
Numerade Educator
02:18

Problem 69

The following skeleton program creates objects representing a stationary source charge and a moving antiproton.
(a) Complete the program so that the antiproton is affected by the net electric field at its current location. (b) Add two arrows, and use them to visualize the momentum of the antiproton, and the electric field at the location of the antiproton. These arrows should move with the antiproton.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:02

Problem 70

Start with the program you wrote in Problem P68 to calculate and display the electric field of a dipole. (a) Place a proton at location $\left\langle 0.3 \times 10^{-9}, 0,0\right\rangle \mathrm{m},$ and release it from rest. Compute and display the trajectory of the proton as it moves under the influence of the electric field of the dipole. You may wish to start with $\Delta t=1 \times 10^{-17} \mathrm{s}$. (b) Simultaneously compute and plot a graph showing the potential energy $U,$ kinetic energy $K,$ and $(K+U)$ vs. time for the entire system (dipole $+$ proton) Your graph will be more useful as a computational diagnostic tool if you do not include the potential energy associated with the interaction of the pair of charges making up the dipole, which does not change. (c) Explain the shape of the $K$ and $U$ graphs.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
03:21

Problem 71

Write a computer program to calculate and plot a graph of the magnitude of the electric field of the dipole from Problem P68 at locations on the $y$ axis as a function of distance from the center of the dipole. Vary $y$ from $0.2 \mathrm{nm}\left(0.2 \times 10^{-9} \mathrm{m}\right)$ to $0.5 \mathrm{nm}$ from the center of the dipole. Do the calculation two different ways, and put both plots (in different colors) on the same axes:
(a) Calculate the electric field exactly as the superposition of the fields due to the individual charges, (b) Calculate the electric field using the approximate equation for the dipole field derived in Section $13.6 .$ (c) Comment on the validity of the approximate equation. How close to the dipole (compared to $s$, the dipole separation ) do you have to get before the approximate equation no longer gives good results? What is your criterion for "good results"?

Prabhu Ramji
Prabhu Ramji
Numerade Educator