Physics

James S. Walker

Chapter 22

Magnetism - all with Video Answers

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Chapter Questions

Problem 1

Predict/Explain Proton 1 moves with a speed $v$ from the east coast to the west coast in the continental United States; proton 2 moves with the same speed from the southern United States
toward Canada, (a) Is the magnitude of the magnetic force experienced by proton 2 greater than, less than, or equal to the force experienced by proton 1$?$ (b) Choose the best explanation from
among the following:
\begin{equation}
\begin{array}{l}{\text { I. The protons experience the same force because the magnetic }} \\ {\text { field is the same and their speeds are the same. }} \\ {\text { II. Proton } 1 \text { experiences the greater force because it moves at }} \\ {\text { right angles to the magnetic field. }} \\ {\text { III. Proton } 2 \text { experiences the greater force because it moves in the }} \\ {\text { same direction as the magnetic field. }}\end{array}
\end{equation}

Timothy Richards

Timothy Richards

Numerade Educator

Problem 2

An electron moving in the positive $x$ direction, at right angles to a magnetic field, experiences a magnetic force in the positive $y$ direction. What is the direction of the magnetic field?

WL

William Liu

Numerade Educator

Problem 3

Suppose particles $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$ in FlGURE $22-41$ have identical
masses and charges of the same magnitude. Rank the particles in order of increasing speed. Indicate ties where appropriate.

Timothy Richards

Timothy Richards

Numerade Educator

Problem 4

Referring to Figure $22-41,$ what is the sign of the charge for each of the three particles? Explain.

Timothy Richards

Timothy Richards

Numerade Educator

Problem 5

What is the acceleration of a proton moving with a speed of 7.5 $\mathrm{m} / \mathrm{s}$ at right angles to a magnetic field of 1.4 $\mathrm{T}$?

Timothy Richards

Timothy Richards

Numerade Educator

Problem 6

An electron moves at right angles to a magnetic field of 0.23 $\mathrm{T}$ . What is its speed if the force exerted on it is $8.9 \times 10^{-15} \mathrm{N} ?$

Timothy Richards

Timothy Richards

Numerade Educator

Problem 7

A negatively charged ion moves due north with a speed of $1.5 \times 10^{6} \mathrm{m} / \mathrm{s}$ at the Earth's equator. What is the magnetic force exerted on this ion?

Timothy Richards

Timothy Richards

Numerade Educator

Problem 8

A proton high above the equator approaches the Earth moving straight downward with a speed of 375 $\mathrm{m} / \mathrm{s}$ . Find the acceleration of the proton, given that the magnetic field at its altitude is $4.05 \times 10^{-5} \mathrm{T} .$

Timothy Richards

Timothy Richards

Numerade Educator

Problem 9

A $0.32-\mu \mathrm{C}$ particle moves with a speed of 16 $\mathrm{m} / \mathrm{s}$ through a region where the magnetic field has a strength of 0.95 T. At what angle to the field is the particle moving if the force exerted on it is (a) $4.8 \times 10^{-6} \mathrm{N},$ (b) $3.0 \times 10^{-6} \mathrm{N},$ or $(\mathrm{c}) 1.0 \times 10^{-7} \mathrm{N} ?$

Timothy Richards

Timothy Richards

Numerade Educator

Problem 10

A particle with a charge of 18$\mu \mathrm{C}$ experiences a force of $2.8 \times 10^{-4} \mathrm{N}$ when it moves at right angles to a magnetic field with a speed of 24 $\mathrm{m} / \mathrm{s} .$ What force does this particle experience when it moves with a speed of 6.3 $\mathrm{m} / \mathrm{s}$ at an angle of $25^{\circ}$ relative to the magnetic field?

Timothy Richards

Timothy Richards

Numerade Educator

Problem 11

An ion experiences a magneticforce of $6.2 \times 10^{-16} \mathrm{N}$ when moving in the positive $x$ direction but no magnetic force when moving in the positive $y$ direction. What is the magnitude of the magnetic force exerted on the ion when it moves in the $x$ -y plane along the line $x=y ?$ Assume that the ion's speed is the same in all cases.

Timothy Richards

Timothy Richards

Numerade Educator

Problem 12

An electron moving with a speed of $4.0 \times 10^{5} \mathrm{m} / \mathrm{s}$ in the positive $x$ direction experiences zero magnetic force. When it moves in the positive $y$ direction, it experiences a force of $3.2 \times 10^{-13} \mathrm{N}$ that points in the positive $z$ direction. What are the direction and magnitude of the magnetic field?

Timothy Richards

Timothy Richards

Numerade Educator

Problem 13

Predict/Calculate Two charged particles with different speeds move one at a time through a region of uniform magnetic field. The particles move in the same direction and experience equal magnetic forces. (a) If particle 1 has four times the charge of particle $2,$ which particle has the greater speed? Explain. (b) Find the ratio of the speeds, $v_{1} / v_{2}$ .

Timothy Richards

Timothy Richards

Numerade Educator

Problem 14

A $6.60-\mu \mathrm{C}$ particle moves through a region of space where
an electric field of magnitude 1450 $\mathrm{N} / \mathrm{C}$ points in the positive $x$
direction, and a magnetic field of magnitude 1.22 $\mathrm{T}$ points in the positive $z$ direction. If the net force acting on the particle is
$6.23 \times 10^{-3} \mathrm{N}$ in the positive $x$ direction, find the magnitude and
direction of the particle's velocity. Assume the particle's velocity
is in the $x$ -y plane.

Timothy Richards

Timothy Richards

Numerade Educator

Problem 15

When at rest, a proton experiences a net electromagnetic force of magnitude $8.0 \times 10^{-13} \mathrm{N}$ pointing in the positive $x$ direction. When the proton moves with a speed of $1.5 \times 10^{6} \mathrm{m} / \mathrm{s}$ in the positive $y$ direction, the net electromagnetic force on it decreases in magnitude to $7.5 \times 10^{-13} \mathrm{N}$ , still pointing in the positive $x$ direction. Find the magnitude and direction of (a) the electric field and (b) the magnetic field.

Timothy Richards

Timothy Richards

Numerade Educator

Problem 16

A velocity selector is to be constructed using a magnetic field in the positive $y$ direction. If positively charged particles move through the selector in the positive $z$ direction, (a) what must be
the direction of the electric field? (b) Repeat part (a) for the case of negatively charged particles.

JC

John Casserino

Numerade Educator

Problem 17

Charged particles pass through a velocity selector with electric and magnetic fields at right angles to each other, as shown in FIGURE $22-42$ . If the electric field has a magnitude of 450 $\mathrm{N} / \mathrm{C}$ and the magnetic field has a magnitude of 0.18 $\mathrm{T}$ , what speed must the par-
ticles have to pass through the selector undeflected?

Timothy Richards

Timothy Richards

Numerade Educator

Problem 18

The velocity selector in FlGURE $22-43$ is designed to allow charged particles with a speed of
$4.5 \times 10^{3} \mathrm{m} / \mathrm{s}$ to pass through undeflected. Find the direction
and magnitude of the required electric field, given that the magnetic field has a magnitude of 0.96 $\mathrm{T} .$

Timothy Richards

Timothy Richards

Numerade Educator

Problem 19

Find the radius of the orbit when (a) an electron or (b) a proton moves perpendicular to a magnetic field of 0.86 T with a speed of $6.47 \times 10^{5} \mathrm{m} / \mathrm{s}$.

Timothy Richards

Timothy Richards

Numerade Educator

Problem 20

B1O Predict/Calculate The artery in Figure $22-14$ has an inside diameter of 2.75 $\mathrm{mm}$ and passes through a region where the magnetic field is 0.065 $\mathrm{T}$ (a) If the voltage difference between the electrodes is $195 \mu \mathrm{V},$ what is the speed of the blood? (b) Which electrode is at the higher potential? Does your answer depend on the sign of the ions in the blood? Explain.

Luis Mendoza

Numerade Educator

Problem 21

An electron accelerated from rest through a voltage of 750 $\mathrm{V}$ enters a region of constant magnetic field. If the electron follows a circular path with a radius of 27 $\mathrm{cm}$ , what is the magnitude of the magnetic field?

Timothy Richards

Timothy Richards

Numerade Educator

Problem 22

A $10.2-\mu \mathrm{C}$ particle with a mass of $2.80 \times 10^{-5} \mathrm{kg}$ moves perpendicular to a 0.850 - magnetic field in a circular path of radius 29.3 $\mathrm{m} .$ (a) How fast is the particle moving? (b) How much time will it take for the particle to complete one orbit?

Luis Mendoza

Numerade Educator

Problem 23

Predict/Calculate When a charged particle enters a region of uniform magnetic field, it follows a circular path, as indicated in FlGURE $22-44 .$ (a) Is this particle positively or negatively charged? Explain. (b) Suppose that the magnetic field has a magnitude of $0.180 \mathrm{T},$ the particle's speed is $6.0 \times 10^{6} \mathrm{m} / \mathrm{s},$ and the radius of its path is 52.0 $\mathrm{cm} .$ Find the mass of the particle, given that its charge has a magnitude of $1.60 \times 10^{-19} \mathrm{C}$ . Give your result in atomic mass units, u, where $1 \mathrm{u}=1.67 \times 10^{-27} \mathrm{kg}$.

Luis Mendoza

Numerade Educator

Problem 24

A proton with a kinetic energy of $4.6 \times 10^{-16} \mathrm{J}$ moves perpendicular to a magnetic field of 0.36 $\mathrm{T}$ . What is the radius of its circular path?

Ankur S

Numerade Educator

Problem 25

Predict/Calculate An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons, and has a mass of $6.64 \times 10^{-27} \mathrm{kg} .$ A horizontal beam of alpha particles is injected with a speed of $1.3 \times 10^{5} \mathrm{m} / \mathrm{s}$ into a region with a vertical magnetic field of magnitude 0.155 $\mathrm{T}$ (a) How much time does it take for an alpha particle to move halfway through a complete circle? (b) If the speed of the alpha particle is doubled, does the time found in part (a) increase, decrease, or stay the same? Explain. (c) Repeat part (a) for alpha particles with a speed of $2.6 \times 10^{5} \mathrm{m} / \mathrm{s}$ .

Luis Mendoza

Numerade Educator

Problem 26

An electron and a proton move in circular orbits in a plane perpendicular to a uniform magnetic field $\overrightarrow{\mathbf{B}}$ . Find the ratio of the radii of their circular orbits when the electron and the proton have (a) the same momentum and (b) the same kinetic energy.

Luis Mendoza

Numerade Educator

Problem 27

Helical Motion As a model of the physics of the aurora, consider a proton emitted by the Sun that encounters the magnetic field of the Earth while traveling at $4.3 \times 10^{5} \mathrm{m} / \mathrm{s}$ (a) The proton arrives at an angle of $33^{\circ}$ from the direction of $\overline{\mathbf{B}}$ (refer to Figure $22-19 ) .$ What is the radius of the circular portion of its path if $B=3.5 \times 10^{-5} \mathrm{T}$ ? (b) Calculate the time required for the proton to complete one circular orbit in the magnetic field. (c) How far parallel to the magnetic field does the proton travel during the time to complete a circular orbit? This is called the pitch of its helical motion.

Luis Mendoza

Numerade Educator

Problem 28

What is the magnetic force exerted on a $2.35-\mathrm{m}$ length of wire carrying a current of 0.819 A perpendicular to a magnetic field of 0.920 $\mathrm{T}$ ?

Luis Mendoza

Numerade Educator

Problem 29

$\cdot$ A wire with a current of 2.1 $\mathrm{A}$ is at an angle of $38.0^{\circ}$ relative to a magnetic field of 0.78 $\mathrm{T}$ . Find the force exerted on a 2.25 -m length of the wire.

Luis Mendoza

Numerade Educator

Problem 30

The magnetic force exerted on a 1.2 -m segment of straight wire is 1.6 $\mathrm{N} .$ The wire carries a current of 3.0 A in a region with a constant magnetic field of 0.50 $\mathrm{T}$ . What is the angle between the wire and the magnetic field?

Luis Mendoza

Numerade Educator

Problem 31

A $0.61-\mathrm{m}$ copper rod with a mass of 0.043 $\mathrm{kg}$ carries a current of
15 A in the positive $x$ direction. What are the magnitude and direction of the minimum magnetic field needed to levitate the rod?

Luis Mendoza

Numerade Educator

Problem 32

The long, thin wire shown in FlGURE $22-45$ is in a region of constant magnetic field $\overrightarrow{\mathbf{B}} .$ The wire carries a current of 6.2 $\mathrm{A}$ and is oriented at an angle of $7.5^{\circ}$ to the direction of the magnetic field. (a) If the magnetic force exerted on this wire per meter is 0.038 $\mathrm{N}$ what is the magnitude of the magnetic field? (b) At what angle will the force exerted on the wire per meter be equal to 0.016 $\mathrm{N} ?$

Luis Mendoza

Numerade Educator

Problem 33

A wire with a length of 3.8 $\mathrm{m}$ and a mass of 0.65 $\mathrm{kg}$ is in a region
of space with a magnetic field of 0.74 $\mathrm{T}$ . What is the minimum current needed to levitate the wire?

Luis Mendoza

Numerade Educator

Problem 34

Loudspeaker Force The coil in a loudspeaker has 50 turns and a radius of 3.8 $\mathrm{cm} .$ The magnetic field is perpendicular to the wires in the coil and has a magnitude of 0.33 T. If the current in the coil is $280 \mathrm{mA},$ what is the total force on the coil?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 35

A high-voltage power line carries a current of 110 A at a location where the Earth's magnetic field has a magnitude of 0.59 and points to the north, $72^{\circ}$ below the horizontal. Find the direction and magnitude of the magnetic force exerted on a $250-\mathrm{m}$ length of wire if the current in the wire flows (a) horizontally toward the east or (b) horizontally toward the south.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 36

A metal bar of mass $m$ and length $L$ is suspended from two conducting wires, as shown in FIGURE $22-46 .$ A uniform magnetic field of magnitude $B$ points vertically downward. Find the angle $\theta$ the suspending wires make with the vertical when the bar carries a current I.

Luis Mendoza

Numerade Educator

Problem 37

For each of the three situations shown in FlGURE $22-47,$ indicate whether there will be a tendency for the square current loop to rotate clockwise, counterclockwise, or not at all, when viewed from above the loop along the indicated axis.

Luis Mendoza

Numerade Educator

Problem 38

A rectangular loop of 280 turns is 35 $\mathrm{cm}$ wide and 19 $\mathrm{cm}$ high.
What is the current in this loop if the maximum torque in a field
of 0.48 $\mathrm{T}$ is 23 $\mathrm{N} \cdot \mathrm{m}$ ?

Luis Mendoza

Numerade Educator

Problem 39

A single circular loop of radius 0.15 $\mathrm{m}$ carries a current of 3.1 $\mathrm{A}$
in a magnetic field of 0.91 $\mathrm{T}$ . What is the maximum torque exerted
on this loop?

Luis Mendoza

Numerade Educator

Problem 40

In the previous problem, find the angle the plane of the loop must make with the field if the torque is to be half its maximum value.

Luis Mendoza

Numerade Educator

Problem 41

A square loop of wire 0.15 $\mathrm{m}$ on a side lies on a horizontal table
and carries a counterclockwise current of 4.2 $\mathrm{A}$ . The component of
Earth's magnetic field that is in the plane of the loop is $2.5 \times 10^{-5} \mathrm{T}$ and points toward the top of the loop. (a) Consider a horizontal axis of rotation that passes through the center of the loop from left to right. Does the top wire of the loop want to rotate toward you (up from the table) or away from you (down into the table)? (b) Calculate the magnitude of the torque about the axis described in (a).

Luis Mendoza

Numerade Educator

Problem 42

Predict/Calculate Each of the 10 turns of wire in a vertical, rectangular loop carries a current of 0.22 A. The loop has a height of 8.0 $\mathrm{cm}$ and a width of 15 $\mathrm{cm} . \mathrm{A}$ horizontal magnetic field of magnitude 0.050 $\mathrm{T}$ is oriented at an angle of $\theta=65^{\circ}$
relative to the normal to the plane of the loop, as indicated in FlGURE $22-48$ . Find (a) thelmagnetic force on each side of the loop, (b) the net magnetic force on the loop, and (c) the magnetic torque on the loop. (d) If the loop can rotate about a vertical axis with only a small amount of friction, will it end up with an orientation given by $\theta=0, \theta=90^{\circ},$ or $\theta=180^{\circ} ?$ Explain.

Luis Mendoza

Numerade Educator

Problem 43

Find the magnetic field 7.25 $\mathrm{cm}$ from a long, straight wire that carries a current of 6.81 $\mathrm{A} .$

Luis Mendoza

Numerade Educator

Problem 44

How much current must pass through a horizontal power transmission cable in order for the magnetic field at a location 11 $\mathrm{m}$ directly below it to be equal to the Earth's magnetic field, which is
approximately $5.0 \times 10^{-5} \mathrm{T}$ ?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 45

You travel to the north magnetic pole of the Earth, where the magnetic field points vertically downward. There, you draw a circle on the ground. Applying Ampere's law to this circle, show
that zero current passes through its area.

Luis Mendoza

Numerade Educator

Problem 46

Pacemaker Switches Some pacemakers employ magnetic reed switches to enable doctors to change their mode of operation without surgery. A typical reed switch can be switched from one position to another with a magnetic field of $5.0 \times 10^{-4} \mathrm{T}$ . What current must a wire carry if it is to produce a $5.0 \times 10^{-4} \mathrm{T}$ field at a distance of 0.50 $\mathrm{m} ?$

Luis Mendoza

Numerade Educator

Problem 47

Two power lines, each 290 $\mathrm{m}$ in length, run parallel to each other with a separation of 23 $\mathrm{cm} .$ If the lines carry parallel currents of $120 \mathrm{A},$ what are the magnitude and direction of the magnetic force each exerts on the other?

Luis Mendoza

Numerade Educator

Problem 48

Predict/Calculate Consider the long, straight, current-carrying wires shown in FlGURE $2-49 .$ One wire carries a current of 6.2 $\mathrm{A}$ in the positive $y$ direction; the other wire carries a current of 4.5 $\mathrm{A}$ in the positive $x$ direction. (a) At which of the two points, A or B, do you expect the magnitude of the net magnetic field to be greater? Explain. (b) Calculate the magnitude of the net magnetic field at points A and B.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 49

In Oersted's experiment, suppose that the compass was 0.15 $\mathrm{m}$ from the current-carrying wire. If a magnetic field of one-third the Earth's magnetic field of $5.0 \times 10^{-5} \mathrm{T}$ was required to give a noticeable deflection of the compass needle, what current must the wire have carried?

Luis Mendoza

Numerade Educator

Problem 50

Predict/Calculate Two long, straight wires are separated by a distance of 9.25 $\mathrm{cm} .$ One wire carries a current of 2.75 A, the other carries a current of 4.33 A. (a) Find the force per meter exerted on the $2.75-$ wire. (b) Is the force per meter exerted on the $4.33-\mathrm{A}$ wire greater than, less than, or the same as the force per meter exerted on the 2.75 -A wire? Explain.

Luis Mendoza

Numerade Educator

Problem 51

Two long, straight wires are oriented perpendicular to the page, as shown in FlGuRE $22-50 .$ The current in one wire is $I_{1}=3.0 \mathrm{A},$ pointing into the page, and the current in the other wire is $I_{2}=4.0 \mathrm{A},$ pointing out of the page. Find the magnitude and direction of the net magnetic field at point $\mathrm{P} .$

Luis Mendoza

Numerade Educator

Problem 52

A loop of wire is connected to the terminals of a battery, as indicated in FlGuRE $22-51 .$ If the loop is to attract the bar magnet, which of the terminals, A or B, should be the positive terminal of the battery? Explain.

Luis Mendoza

Numerade Educator

Problem 53

Predict/Explain The number of turns in a solenoid is doubled, and at the same time its length is doubled. (a) Does the magnetic field within the solenoid increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
\begin{equation}
\begin{array}{l}{\text { I. Doubling the number of turns in a solenoid doubles its magnetic field, }} \\ {\text { and hence the field increases. }} \\ {\text { II. Making a solenoid longer decreases its magnetic field, and }} \\ {\text { therefore the field decreases. }} \\ {\text { III. The magnetic field remains the same because the number of }} \\ {\text { turns per length is unchanged. }}\end{array}
\end{equation}

Luis Mendoza

Numerade Educator

Problem 54

A circular coil of wire has a radius of 7.5 $\mathrm{cm}$ and has 125 turns of wire that carries 6.6 $\mathrm{A}$ of current. What is the magnetic field at the center of the coil?

Luis Mendoza

Numerade Educator

Problem 55

The solenoid for an automobile power door lock is 2.5 $\mathrm{cm}$ long and has 190 turns of wire that carry 1.6 A of current. What is the magnitude of the magnetic field that it produces?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 56

It is desired that a solenoid 25 $\mathrm{cm}$ long and with 350 turns produce a magnetic field within it equal to the Earth's magnetic field $\left(5.0 \times 10^{-5} \mathrm{T}\right) .$ What current is required?

Luis Mendoza

Numerade Educator

Problem 57

A solenoid that is 72 $\mathrm{cm}$ long produces a magnetic field of 1.8 $\mathrm{T}$ within its core when it carries a current of 8.1 $\mathrm{A} .$ How many turns of wire are contained in this solenoid?

Luis Mendoza

Numerade Educator

Problem 58

The maximum current in a superconducting solenoid can be as large as 3.75 kA. If the number of turns per meter in such a solenoid is $3650,$ what is the magnitude of the magnetic field it produces?

Luis Mendoza

Numerade Educator

Problem 59

To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 7.6 $\mathrm{cm}$ in diameter and 33 $\mathrm{cm}$ in length. You would like a 3.0 -A current to produce a $2.5-\mathrm{kG}$ magnetic field inside your solenoid. What is the total length of wire you will need
to meet these specifications?

Luis Mendoza

Numerade Educator

Problem 60

A proton is to orbit the Earth at the equator using the Earth's
magnetic field to supply part of the necessary centripetal force.
Should the proton move eastward or westward? Explain.

Luis Mendoza

Numerade Educator

Problem 61

FIGURE $22-52$ shows an electron beam whose initial direction of motion is horizontal, from right to left. A magnetic field deflects the beam downward. What is the direction of the magnetic field?

Luis Mendoza

Numerade Educator

Problem 62

The three wires shown in FIGURE $22-53$ are long and straight, and they each carry a current of the same magnitude, I. The currents in wires 1 and 3 are out of the page; the current in wire 2 is into the page. What is the direction of the magnetic force experienced by wire 3$?$

Luis Mendoza

Numerade Educator

Problem 63

Each of the current-carrying wires in Figure $22-53$ is long and straight, and carries the current I either into or out of the page, as shown. What is the direction of the net magnetic field produced by these three wires at the center of the triangle?

Luis Mendoza

Numerade Educator

Problem 64

The four wires shown in FIGURE $2-54$ are long and straight, and they each carry a current of
the same magnitude, I. The currents in wires $1,2,$ and 3 are out of the page; the current in wire
4 is into the page. What is the direction of the magnetic force experienced by wire 2 ?

Luis Mendoza

Numerade Educator

Problem 65

Each of the current-carrying wires in Figure $22-54$ is long and straight, and carries the current I either into or out of the page, as shown. What is the direction of the net magnetic field produced
by these four wires at the center of the square?

Luis Mendoza

Numerade Educator

Problem 66

Brain Function and Magnetic Fields Experiments have shown that thought processes in the brain can be affected if the parietal lobe is exposed to a magnetic field with a strength of 1.0 T. How much current must a long, straight wire carry if it is to produce a 1.0 -T magnetic field at a distance of 0.50 $\mathrm{m} ?$ (For comparison, a typical lightning bolt carries a current of about $20,000 \mathrm{A},$ which would melt most wires.)

Luis Mendoza

Numerade Educator

Problem 67

Credit-Card Magnetic Strips Experiments carried out on the television show Mythbusters determined that a magnetic field of 1000 gauss is needed to corrupt the information on a credit card's magnetic strip. (They also busted the myth that a credit card can be demagnetized by an electric eel or an eelskin wallet. Suppose a long, straight wire carries a current of 3.5 A. How close can a credit
card be held to this wire without damaging its magnetic strip?

Vishal Gupta

Numerade Educator

Problem 68

Superconducting Solenoid Cryomagnetics, Inc., advertises a high- field, superconducting solenoid that produces a magnetic field of 17 twith a current of 105 $\mathrm{A}$ . What is the number of turns per meter in this solenoid?

Luis Mendoza

Numerade Educator

Problem 69

Consider a current loop immersed in a magnetic field, as in Figure $22-47$ (a). It is given that $B=0.42$ T and $I=8.8 \mathrm{A}$ . In addition, the loop is a square 0.38 $\mathrm{m}$ on a side. Find the magnitude of the magnetic force exerted on each side of the loop.

Luis Mendoza

Numerade Educator

Problem 70

A positively charged particle moves through a region with a uniform electric field pointing toward the top of the page and a uniform magnetic field pointing into the page. The particle can have one of the four velocities shown in FIGURE $22-55 .$ (a) Rank the four possibilities in order of increasing magnitude of the net force $(F_{1}$, $F_{2}$, $F_{3}$, and $F_{4})$ the particle experiences. Indicate ties where appropriate. (b) Which of the four velocities could potentially result in zero net force?

Luis Mendoza

Numerade Educator

Problem 71

A proton follows the path shown in FlGURE $22-56$ as it moves through three regions with different uniform magnetic fields, $B_{1}, B_{2},$ and $B_{3}$ . In each region the proton completes a half-circle, and the magnetic field is perpendicular to the page. (a) Rank the three fields in order of increasing magnitude. Indicate ties where appropriate. (b) Give the direction (into or out of the page) for each of the fields.

Luis Mendoza

Numerade Educator

Problem 72

Predict/Explain Suppose the initial speed of the proton in Figure $22-56$ is increased. (a) Does the radius of each half-circular path segment increase, decrease, or stay the same? (b) Choose the
best explanation from among the following:
$$\begin{array}{l}{\text { I. The radius of a circular orbit in a magnetic field is propor- }} \\ {\text { tional to the speed of the proton; therefore, the radius of the }} \\ {\text { half-circular path will increase. }}\end{array}$$
$$\begin{array}{l}{\text { II. A greater speed means the proton will experience more force }} \\ {\text { from the magnetic field, resulting in a decrease of the radius. }}\end{array}$$
$$\begin{array}{l}{\text { III. The increase in speed offsets the increase in magnetic force, }} \\ {\text { resulting in no change of the radius. }}\end{array}$$

Luis Mendoza

Numerade Educator

Problem 73

Magnetic Resonance Imaging An MRI (magnetic resonance imaging solenoid produces a magnetic field of 1.5 $\mathrm{T}$ . The solenoid is 2.5 $\mathrm{m}$ long, 1.0 $\mathrm{m}$ in diameter, and wound with insulated wires 2.2 $\mathrm{mm}$ in diameter. Find the current that flows in the solenoid.
(Your answer should be rather large.)

Prabhu Ramji

Numerade Educator

Problem 74

Predict/Calculate A long, straight wire carries a current of 14 A. Next to the wire is a square loop with sides 1.0 $\mathrm{m}$ in length, as shown in FlGURE $22-57 .$ The loop carries a current of 2.5 $\mathrm{A}$ in the direction indicated. (a) What is the direction of the net force
exerted on the loop? Explain. (b) Calculate the magnitude of the
net force acting on the loop.

Luis Mendoza

Numerade Educator

Problem 75

A particle with a charge of 38$\mu \mathrm{C}$ moves with a speed of 77 $\mathrm{m} / \mathrm{s}$ in the positive $x$ direction. The magnetic field in this region of space has a component of 0.45 $\mathrm{T}$ in the positive $y$ direction, and a component of 0.85 Tin the positive $z$ direction. What are the magnitude and direction of the magnetic force on the particle?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 76

Predict/Calculate $A$ beam of protons with various speeds is directed in the positive $x$ direction. The beam enters a region with a uniform magnetic field of magnitude 0.52 T pointing in the negative $z$ direction, as indicated in FIGURE $22-58 .$ It is desired to use a uniform electric field (in addition to the magnetic field) to select from this beam only those protons with a speed of $1.42 \times 10^{5} \mathrm{m} / \mathrm{s}-$ that is, only these protons should be undeflected by the two fields.
(a) Determine the magnitude and direction of the electric field that yields the desired result. (b) Suppose the electric field is to be produced by a parallel-plate capacitor with a plate separation of
2.5 $\mathrm{cm} .$ What potential difference is required between the plates?
(c) Which plate in Figure $22-58$ (top or bottom) should be positively charged? Explain.

Luis Mendoza

Numerade Educator

Problem 77

Two parallel wires, each carrying a current of 2.2 $\mathrm{A}$ in the same direction, are shown in FlGURE $22-59 .$ Find the direction and magnitude of the net magnetic field at points $\mathrm{A}, \mathrm{B},$ and C.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 78

Repeat Problem 77 for the case where the current in wire 1 is reversed in direction.

Luis Mendoza

Numerade Educator

Problem 79

Electric Motor A current of 2.4 A flows through a circular coil of wire with 52 turns and a radius of 0.64 $\mathrm{cm} .$ The coil rotates in a uniform $0.12-$ T magnetic field. (a) What is the maximum torque exerted on the loop of wire? (b) The time-averaged torque on the loop is half its maximum value. If the moment of inertia of the loop is $2.5 \times 10^{-5} \mathrm{kg} \cdot \mathrm{m}^{2}$ and the loop undergoes constant angular acceleration, in what time will it have reached its maximum
angular speed of 2500 $\mathrm{rev} / \mathrm{min}$ ?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 80

Balanced Coil A student wishes to suspend a square loop of wire at a $45^{\circ}$ angle to the verticalusing the Earth's magnetic field. The geometry is depicted in FIGURE $22-60 .$ At the student's location the Earth's magnetic field has a magnitude of $5.2 \times 10^{-5} \mathrm{T}$ and
is oriented $60.0^{\circ}$ below horizontal. All of the counterclockwise torque acting on the loop arises from the magnetic force on the bottom side of the square.l(a) Is the current in the loop clock-
wise or counterclockse as viewed from above? (b) The loop is a square with mass $m=0.0089 \mathrm{kg}$ and sides of length $L=0.10 \mathrm{m} .$ How much current must flow through the loop to suspend it as shown? (Note: The angle between the plane of the loop and the magnetic force is $105^{\circ} . )$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 81

Lightning Bolts A powerful bolt of lightning can carry a current of 225 $\mathrm{kA}$ . (a) Treating a lightning bolt as a long, thin wire, calculate the magnitude of the magnetic field produced by such a bolt of lightning at a distance of 35 $\mathrm{m}$ . (b) If two such bolts strike simultaneously at a distance of 35 $\mathrm{m}$ from each other, what is the magnetic force per meter exerted by one bolt on the other?

Luis Mendoza

Numerade Educator

Problem 82

Predict/Calculate Consider the two current-carrying wires shown in $\mathrm{FlGURE} 22-61 .$ The current in wire 1 is 3.7 $\mathrm{A}$ ; the current in wire 2 is adjusted to make the net magnetic field at point A equal to zero.(a) Is the magnitude of the current in wire 2 greater than, less than, or the same as that in wire 1$?$ Explain. (b) Find the magnitude and direction of the current in wire 2.

Luis Mendoza

Numerade Educator

Problem 83

Magnetars The astronomical object $4 \mathrm{U} 014+61$ has the distinction of creating the most powerful magnetic field ever observed. This object is referred to as a "magnetar" (a subclass of pulsars), and its magnetic field is $1.3 \times 10^{15}$ times greater than the Earth's
magnetic field. (a) Suppose a 2.5 straight wire carrying a current of 1.1 $\mathrm{A}$ is placed in this magnetic field at an angle of $65^{\circ}$ to the field lines. What force does this wire experience? (b) A field this strong can significantly change the behavior of an atom. To see
this, consider an electron moving with a speed of $2.2 \times 10^{6} \mathrm{m} / \mathrm{s}$ . Compare the maximum magnetic force exerted on the electron
to the electric force a proton exerts on an electron in a hydrogen
atom. The radius of the hydrogen atom is $5.29 \times 10^{-11} \mathrm{m} .$

Luis Mendoza

Numerade Educator

Problem 84

Consider a system consisting of two concentric solenoids, as illustrated in FlGuRE $22-62 .$ The current in the outer solenoid is $I_{1}=1.25 \mathrm{A},$ and the current in the inner solenoid is $I_{2}=2.17 \mathrm{A}$ . Given that the number of turns per centimeter is 105 for the outer solenoid and 125 for the inner solenoid, find the magnitude and direction of the magnetic field (a) between the solenoids and (b) inside the inner solenoid.

Luis Mendoza

Numerade Educator

Problem 85

Solenoids produce magnetic fields that are relatively intense for the amount of current they carry. To make a direct comparison, consider a solenoid with 48.0 turns per centimeter, a radius of $1.27 \mathrm{~cm},$ and a current of $0.776 \mathrm{~A}$. (a) Find the magnetic field at the center of the solenoid. (b) What current must a long, straight wire carry to have the same magnetic field as that found in part (a)? Let the distance from the wire be the same as the radius of the solenoid, $1.27 \mathrm{~cm}$.

Luis Mendoza

Numerade Educator

Problem 85

Suppose a neuron in the brain carries a current of $5.0 \times 10^{-8} \mathrm{A}$ . Treating the neuron as a straight wire, what is the magnetic field it produces at a distance of 7.5 $\mathrm{cm} ?$
$$\begin{array}{lll}{\text { A. } 1.3 \times 10^{-13} \mathrm{T}} & {\text { B. } 4.2 \times 10^{-12} \mathrm{T}} \\ {\text { C. } 1.1 \times 10^{-10} \mathrm{T}} & {\text { D. } 3.3 \times 10^{-7} \mathrm{T}}\end{array}$$

Luis Mendoza

Numerade Educator

Problem 86

The current in a solenoid with 28 turns per centimeter is 0.55 $\mathrm{A}$ . The solenoid has a radius of 1.5 $\mathrm{cm} .$ A long, straight wire runs along the axis of the solenoid, carrying a current of 16 $\mathrm{A}$ . Find the magnitude of the net magnetic field a radial distance of 0.75 $\mathrm{cm}$ from the straight wire.

Luis Mendoza

Numerade Educator

Problem 87

BIOPredict//Calculate Transcranial Magnetic Stimulation One way to study brain function is to produce a rapidly changing magnetic field within the brain. When this technique, known as transcranial magnetic stimulation $(\mathrm{TMS}),$ is applied to the prefrontal cortex, for example, it can reduce a person's ability to conjugate verbs, though other thought processes are unaffected. The rapidly varying magnetic field is produced with a circular coil of 21 turns and a radius of 6.0 $\mathrm{cm}$ placed directly on the head. The current in this loop increases at the rate of $1.2 \times 10^{7} \mathrm{A} / \mathrm{s}$ discharging a capacitor).(a) At what rate does the magnetic field at the center of the coil increase? (b) Suppose a second coil with half the area of the first coil is used instead. Would your answer to part (a) increase, decrease, or stay the same? By what factor?

Luis Mendoza

Numerade Educator

Problem 88

Synchrotron Undulator In one portion of a synchrotron undulator, electrons traveling at $2.99 \times 10^{8} \mathrm{m} / \mathrm{s}$ enter a region of uniform magnetic field with a strength of 0.844 $\mathrm{T.}$ (a) What is the acceleration of an electron in this region? (b) The total power of $X$ -rays emitted by these electrons is given by $P=\left(1.07 \times 10^{-45}\right) a^{2} \mathrm{W},$ where $a$ is the acceleration in $\mathrm{m} / \mathrm{s}^{2} .$ What power is emitted by the electrons in this portion of the undulator?

Luis Mendoza

Numerade Educator

Problem 89

Predict/Calculate A single current-carrying circular loop of radius $R$ is placed next to a long, straight wire, as shown in FlGURE $22-63 .$ The current in the wire points to the right and is of magnitude $I .$ (a) In which direction must current flow in the loop to produce zero magnetic field at its center? Explain. (b) Calculate the magnitude of the current in part (a).

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 90

A thin ring of radius $R$ and charge per length $\lambda$ rotates with an angular speed $\omega$ about an axis perpendicular to its plane and passing through its center. Find the magnitude of the magnetic field at the center of the ring.

Luis Mendoza

Numerade Educator

Problem 91

A solenoid is made from a $25-\mathrm{m}$ length of wire of resistivity $2.3 \times 10^{-8} \Omega \cdot \mathrm{m} .$ The wire, whose radius is $2.1 \mathrm{mm},$ is wrapped
uniformly onto a plastic tube 4.5 $\mathrm{cm}$ in diameter and 1.65 $\mathrm{m}$ long.
Find the emf to which the ends of the wire must be connected to
produce a magnetic field of 0.015 T within the solenoid.

Luis Mendoza

Numerade Educator

Problem 92

Magnetic Fields in the Bohr Model In the Bohr model of the hydrogen atom, the electron moves in a circular orbit of radius $5.29 \times 10^{-11} \mathrm{m}$ about the nucleus. Given that the charge on the electron is $-1.60 \times 10^{-19} \mathrm{C},$ and that its speed is $2.2 \times 10^{6} \mathrm{m} / \mathrm{s}$ , find the magnitude of the magnetic field the electron produces at the nucleus of the atom.

Luis Mendoza

Numerade Educator

Problem 93

A single-turn square loop carries a current of 18 A. The loop is 15 $\mathrm{cm}$ on a side and has a mass of 0.035 kg. Initially the loop lies flat on a horizontal tabletop. When a horizontal magnetic field is
turned on, it is found that only one side of the loop experiences an upward force. Find the minimum magnetic field, $B_{\text { min }},$ necessary to start tipping the loop up from the table. the source of brain activity to within millimeters. When the information from MEG is overlaid with the anatomical data from an MRI scan, the result is a richly detailed "map" of the electrical activity within the brain.

Luis Mendoza

Numerade Educator

Problem 94

Approximating a neuron by alstraight wire, what electric current is needed to produce a magnetic field of $1.0 \times 10^{-15} \mathrm{T}$ at a distance of 5.0 $\mathrm{cm}^{2}$
$$\begin{array}{lll}{\text { A. } 4.0 \times 10^{-22} \mathrm{A}} & {\text { B. } 7.9 \times 10^{-11} \mathrm{A}} \\ {\text { C. } 2.5 \times 10^{-10} \mathrm{A}} & {\text { D. } 1.0 \times 10^{-7} \mathrm{A}}\end{array}$$

Luis Mendoza

Numerade Educator

Problem 96

A given neuron in the brain carries a current of $3.1 \times 10^{-8}$ . If the SQUID detects a magnetic field of $2.8 \times 10^{-14} \mathrm{T}$ , how far away is the neuron? Treat the neuron as a straight wire.
$$\begin{array}{ll}{\text { A. } 22 \mathrm{cm}} & {\text { B. } 70 \mathrm{cm}} \\ {\text { C. } 140 \mathrm{cm}} & {\text { D. } 176 \mathrm{cm}}\end{array}$$

Luis Mendoza

Numerade Educator

Problem 97

A SQUID detects a magnetic field of $1.8 \times 10^{-14} \mathrm{T}$ at a distance of 13 $\mathrm{cm} .$ How many electrons flow through the neuron per second? Treat the neuron as a straight wire.
$$\begin{array}{ll}{\text { A. } 1.2 \times 10^{10}} & {\text { B. } 2.3 \times 10^{10}} \\ {\text { C. } 7.3 \times 10^{10}} & {\text { D. } 9.2 \times 10^{10}}\end{array}$$

Luis Mendoza

Numerade Educator

Problem 98

Predict/Calculate REFERRING TO EXAMPLE $22-7$ Suppose the speed of the isotopes is doubled. (a) Does the separation distance, $d$ , increase, decrease, or stay the same? Explain. (b) Find the separation distance for this case.

Luis Mendoza

Numerade Educator

Problem 99

Predict/Calculate REFERRING TO EXAMPLE $22-7$ Suppose we change the initial speed of $^{288} \mathrm{U}$, leaving everything else the same. (a) If we want the separation distance to be zero, should the initial speed of $^{238} U$ be increased or decreased? Explain. (b) Find the required
initial speed.

Luis Mendoza

Numerade Educator

Problem 100

REFFERING TO QUICK EXAMPLE $22-15$ The current $I_{1}$ is adjusted until the magnetic field halfway between the wires has a magnitude of $7.5 \times 10^{-7} \mathrm{T}$ and points into the page. Everything else in the system remains the same as in Quick Example $22-15 .$ Find the
magnitude and direction of $I_{1}$ .

Luis Mendoza

Numerade Educator

Problem 101

REFERRING TO Quick EXAMPLE $22-15$ The current $I_{2}$ is adjusted until the magnetic field 5.5 $\mathrm{cm}$ below wire 2 has a magnitude of $2.5 \times 10^{-6} \mathrm{T}$ and points out of the page. Everything else in the system remains the same as in Quick Example $22-15 .$ Find the
magnitude and direction of $I_{2}$ .

Luis Mendoza

Numerade Educator