Essential University Physics Volume 2 3rd Edition Chapter 26
Problem 1
A charged particle moves through a region containing only a magnetic field. Under what condition will it experience no force?
Aspen F.
Numerade Educator
Problem 2
An electron moving with velocity $\vec{v}$ through a magnetic field $\vec{B}$ experiences a magnetic force $\vec{F} .$ Which of the vectors $\vec{F}, \vec{v}$ and $\vec{B}$ must be at right angles?
Aspen F.
Numerade Educator
Problem 3
A magnetic field points out of this page. Will a positively charged particle moving in the plane of the page circle clockwise or counterclockwise as viewed from above?
Aspen F.
Numerade Educator
Problem 4
Do particles in a cyclotron gain energy from the electric field, the magnetic field, or both? Explain.
Aspen F.
Numerade Educator
Problem 5
An electron and a proton moving at the same speed enter a region containing a uniform magnetic field. Which is deflected more from its original path?
Aspen F.
Numerade Educator
Problem 6
Two identical particles carrying equal charge are moving in opposite directions, perpendicular to a uniform magnetic field, when they collide elastically head-on. Describe their subsequent motion.
Aspen F.
Numerade Educator
Problem 7
The Biot-Savart law shows that the magnetic field of a current element decreases as $1 / r^{2} .$ Could you put together a complete circuit whose field exhibits this decrease? Why or why not?
Donya D.
Numerade Educator
Problem 8
The Biot-Savart law shows that the magnetic field of a current element decreases as $1 / r^{2} .$ Could you put together a complete circuit whose field exhibits this decrease? Why or why not?
Donya D.
Numerade Educator
Problem 9
Do currents in the same direction attract or repel? Explain.
Aspen F.
Numerade Educator
Problem 10
If a current is passed through an unstretched spring, will the spring contract or expand? Explain.
Aspen F.
Numerade Educator
Problem 11
Figure 26.38 shows some magnetic field lines associated with two parallel wires carrying equal currents perpendicular to the page. Are the currents in the same or opposite directions? How can you tell? Note: The only currents in Fig. 26.38 are those in the two wires.
CAN'T COPY THE FIGURE
Aspen F.
Numerade Educator
Problem 12
Why is a piece of iron attracted into a solenoid?
Aspen F.
Numerade Educator
Problem 13
Would there be a magnetic force on a piece of iron deep inside a long solenoid? Explain.
Aspen F.
Numerade Educator
Problem 14
An unmagnetized piece of iron has no net magnetic dipole moment, yet it's attracted to either pole of a bar magnet. Why?
Donya D.
Numerade Educator
Problem 15
Find (a) the minimum magnetic field needed to exert a $5.4-\mathrm{fN}$ force on an electron moving at $21 \mathrm{Mm} / \mathrm{s}$ and (b) the field strength required if the field were at $45^{\circ}$ to the electron's velocity.
Aspen F.
Numerade Educator
Problem 16
An electron moving at right angles to a $0.10-$ T magnetic field experiences an acceleration of $6.0 \times 10^{15} \mathrm{m} / \mathrm{s}^{2} .$ (a) What's its speed?
(b) By how much does its speed change in 1 ns?
Aspen F.
Numerade Educator
Problem 17
Find the magnitude of the magnetic force on a proton moving at $2.5 \times 10^{5} \mathrm{m} / \mathrm{s}$ (a) perpendicular; (b) at $30^{\circ} ;$ (c) parallel to a $0.50-\mathrm{T}$ magnetic field.
Aspen F.
Numerade Educator
Problem 18
The magnitude of Earth's magnetic field is about 0.5 gauss near Earth's surface. What's the maximum possible magnetic force on an electron with kinetic energy of 1 keV? Compare with the gravitational force on the electron.
Aspen F.
Numerade Educator
Problem 19
A velocity selector uses a 60 -mT magnetic field perpendicular to a 24 -kN/C electric field. At what speed will charged particles pass through the selector undeflected?
Aspen F.
Numerade Educator
Problem 20
Find the radius of the path described by a proton moving at $15 \mathrm{km} / \mathrm{s}$ in a plane perpendicular to a $400-\mathrm{G}$ magnetic field.
Aspen F.
Numerade Educator
Problem 21
How long does it take an electron to complete a circular orbit perpendicular to a $1.0-$ G magnetic field?
Donya D.
Numerade Educator
Problem 22
Radio astronomers detect electromagnetic radiation at a frequency of $42 \mathrm{MHz}$ from an interstellar gas cloud. If the radiation results from electrons spiraling in a magnetic field, what's the field strength?
Donya D.
Numerade Educator
Problem 23
In a microwave oven, electrons describe circular motion in a magnetic field within a special tube called a magnetron; as you'll learn in Chapter 29 , the electrons' motion results in the production of micowaves. (a) If the electrons circle at a frequency of $2.45 \mathrm{GHz},$ what's the magnetic field strength? (b) If the magnetron can accommodate electron orbits with maximum diameter $2.72 \mathrm{mm},$ what's the electrons' energy in eV?
Donya D.
Numerade Educator
Problem 24
Two protons, moving in a plane perpendicular to a uniform $500-\mathrm{G}$ magnetic field, undergo an elastic head-on collision. How much time elapses before they collide again?
Aspen F.
Numerade Educator
Problem 25
Find the magnitude of the force on a 65.5 -cm-long wire carrying $12.0 \mathrm{A}$ at right angles to a $475-\mathrm{G}$ magnetic field.
Aspen F.
Numerade Educator
Problem 26
A wire carrying 15 A makes a $25^{\circ}$ angle with a uniform magnetic field. The magnetic force per unit length of wire is $0.31 \mathrm{N} / \mathrm{m}$ Find (a) the magnetic field strength and (b) the maximum force per unit length that could be achieved by reorienting the wire.
Aspen F.
Numerade Educator
Problem 27
You're on a team performing a high-magnetic-field experiment. A conducting bar carrying 4.1 kA will pass through a 1.3-m-long region containing a 12 -T magnetic field, making a $60^{\circ}$ angle with the field. A colleague proposes resting the bar on wooden blocks. You argue that it will have to be clamped in place, and to back up your argument you claim that the magnetic force will exceed 10,000 pounds. Are you right?
Donya D.
Numerade Educator
Problem 28
A wire with mass per unit length $75 \mathrm{g} / \mathrm{m}$ runs horizontally at right angles to a horizontal magnetic field. A 6.2 - A current in the wire results in its being suspended against gravity. What's the magnetic field strength?
Aspen F.
Numerade Educator
Problem 29
A wire carries 6.71 A. You form it into a single-turn circular loop and measure a magnetic field of $42.8 \mu \mathrm{T}$ at the loop center. (a) What's the loop's radius? (b) What's the field strength on the loop axis at $10.0 \mathrm{cm}$ from the loop center?
Aspen F.
Numerade Educator
Problem 30
A single-turn wire loop is $2.0 \mathrm{cm}$ in diameter and carries a 650 -mA current. Find the magnetic field strength (a) at the loop center and (b) on the loop axis, $20 \mathrm{cm}$ from the center.
Aspen F.
Numerade Educator
Problem 31
A 2.2 -m-long wire carrying $3.5 \mathrm{A}$ is wound into a tight coil $5.0 \mathrm{cm}$ in diameter. Find the magnetic field at its center.
Aspen F.
Numerade Educator
Problem 32
What's the current in a long wire if the magnetic field strength
$1.2 \mathrm{cm}$ from the wire's axis is $67 \mu \mathrm{T} ?$
Aspen F.
Numerade Educator
Problem 33
In standard household wiring, parallel wires about $1 \mathrm{cm}$ apart carry currents of about 15 A. What's the force per unit length between these wires?
Aspen F.
Numerade Educator
Problem 34
Earth's magnetic dipole moment is $8.0 \times 10^{22} \mathrm{A} \cdot \mathrm{m}^{2} .$ Find the magnetic field strength at Earth's magnetic poles.
Donya D.
Numerade Educator
Problem 35
A single-turn square wire loop $18.0 \mathrm{cm}$ on a side carries a 1.25-A current. (a) What's the loop's magnetic dipole moment? (b) What's the magnitude of the torque the loop experiences when it's in a 2.12 -T magnetic field with the loop's dipole moment vector at $65.0^{\circ}$ to the field?
Aspen F.
Numerade Educator
Problem 36
An electric motor contains a 250 -turn circular coil $6.2 \mathrm{cm}$ in diameter. If it develops a maximum torque of $1.2 \mathrm{N} \cdot \mathrm{m}$ at a current of $3.3 \mathrm{A},$ what's the magnetic field strength?
Aspen F.
Numerade Educator
Problem 37
The line integral of the magnetic field on a closed path surrounding a wire has the value $8.8 \mu \mathrm{T}$ -m. Find the current in the wire.
Aspen F.
Numerade Educator
Problem 38
The magnetic field shown in Fig. 26.39 has uniform magnitude $75 \mu \mathrm{T},$ but its direction reverses abruptly. Find the current encircled by the rectangular loop shown.
CAN'T COPY THE FIGURE
Ajay S.
Numerade Educator
Problem 39
Number 12 gauge wire, commonly used in household wiring, is $2.053 \mathrm{mm}$ in diameter and can safely carry currents of up to 20.0 A. For a wire carrying this maximum current, find the magnetic field strength (a) $0.150 \mathrm{mm}$ from the wire's axis, (b) at the wire's surface, and (c) 0.375 mm beyond the wire's surface.
Donya D.
Numerade Educator
Problem 40
Show that Equations 26.18 and 26.19 give the same results when evaluated at the wire's surface.
Aspen F.
Numerade Educator
Problem 41
A superconducting solenoid has 3300 turns per meter and carries 4.1 kA. Find the magnetic field strength in the solenoid.
Aspen F.
Numerade Educator
Problem 42
A particle carrying a 50 -\muC charge moves with velocity $\vec{v}=5.0 \hat{\imath}+3.2 \hat{k} \mathrm{m} / \mathrm{s}$ through a magnetic field given by $\vec{B}=9.4 \hat{\imath}+6.7 \hat{\jmath}$ T. (a) Find the magnetic force on the particle. (b) Form the dot products $\vec{F} \cdot \vec{v}$ and $\vec{F} \cdot \vec{B}$ to show explicitly that the force is perpendicular to both $\vec{v}$ and $\vec{B}$.
Donya D.
Numerade Educator
Problem 43
Jupiter has the strongest magnetic field in our solar system, about
$14 \mathrm{G}$ at its poles. Approximating the field as that of a dipole, find Jupiter's magnetic dipole moment. (Hint: Consult Appendix E.)
Donya D.
Numerade Educator
Problem 44
A proton moving with velocity $\vec{v}_{1}=3.6 \times 10^{4} \hat{\jmath} \mathrm{m} / \mathrm{s}$ experiences a magnetic force of $7.4 \times 10^{-16} \hat{\imath} \mathrm{N} .$ A second proton moving on the $x$ -axis experiences a magnetic force of $2.8 \times 10^{-16} \hat{\jmath} \mathrm{N}$. Find the magnitude and direction of the magnetic field (assumed uniform), and the velocity of the second proton.
Donya D.
Numerade Educator
Problem 45
A simplified model of Earth's magnetic field has it originating in a single current loop at the outer edge of the planet's liquid core (radius $3000 \mathrm{km}$ ). What current would give the 62 - $\mu$ T field measured at the north magnetic pole?
Rashmi S.
Numerade Educator
Problem 46
A beam of electrons moving in the $x$ -direction at $8.7 \mathrm{Mm} / \mathrm{s}$ enters a region where a uniform $180-$ G magnetic field points in the $y$ direction. The boundary of the field region is perpendicular to the beam. How far into the field region does the beam penetrate?
Donya D.
Numerade Educator
Problem 47
Show that the orbital radius of a charged particle moving at right angles to a magnetic field $B$ can be written $r=\sqrt{2 K m / q B}$ where $K$ is the kinetic energy in joules, $m$ the particle's mass, and $q$ its charge.
Donya D.
Numerade Educator
Problem 48
A 90 -cm-diameter cyclotron with a 2.0 -T magnetic field is used to accelerate deuterium nuclei (one proton plus one neutron).
(a) At what frequency should the dee voltage be alternated?
(b) What's the maximum kinetic energy of the deuterons?
(c) If the magnitude of the potential difference between the dees is $1500 \mathrm{V}$, how many orbits do the deuterons complete before reaching maximum energy?
Donya D.
Numerade Educator
Problem 49
An electron is moving in a uniform $0.25-$ T magnetic field; its velocity components parallel and perpendicular to the field are both $3.1 \mathrm{Mm} / \mathrm{s}$. (a) What's the radius of the electron's spiral path?
(b) How far does it move along the field direction in the time it takes to complete a full orbit about the field?
Donya D.
Numerade Educator
Problem 50
A wire of negligible resistance is bent into a rectangle as in Fig. $26.40,$ and a battery and resistor are connected as shown. The right-hand side of the circuit extends into a region containing a uniform $38-\mathrm{mT}$ magnetic field pointing into the page. Find the magnitude and direction of the net force on the circuit.
CAN'T COPY THE FIGURE
Donya D.
Numerade Educator
Problem 51
You're designing a prosthetic ankle that includes a miniature electric motor containing a 150 -turn circular coil $15 \mathrm{mm}$ in diameter. The motor needs to develop a maximum torque of
$3.1 \mathrm{mN} \cdot \mathrm{m} .$ The strongest magnets available that will fit in the prosthesis produce a 220 -mT field. What current do you need in your motor's coil?
Donya D.
Numerade Educator
Problem 52
A 20 -cm-long conducting rod with mass $18 \mathrm{g}$ is suspended by wires of negligible mass (Fig. 26.41 ). A uniform magnetic field of 0.15 T points horizontally into the page, as shown. An external circuit supplies current between the supports $A$ and $B$ (a) What's the minimum current necessary to move the bar to the upper position, so it's supported against gravity? (b) What direction should the current flow?
CAN'T COPY THE FIGURE
Aspen F.
Numerade Educator
Problem 53
A rectangular copper strip measures $1.0 \mathrm{mm}$ in the direction of a uniform 2.4 -T magnetic field. When the strip carries a 6.8 -A current perpendicular to the field, a 1.2 - $\mu$ V Hall potential develops across the strip. Find the number density of free electrons in the copper.
Donya D.
Numerade Educator
Problem 54
A single-turn wire loop $10 \mathrm{cm}$ in diameter carries a 12 - A current. It experiences a $0.015 \mathrm{N} \cdot \mathrm{m}$ torque when the normal to the loop plane makes a $25^{\circ}$ angle with a uniform magnetic field. Find the magnetic field strength.
Aspen F.
Numerade Educator
Problem 55
A simple electric motor consists of a 220 -turn coil, $4.2 \mathrm{cm}$ in diameter, mounted between the poles of a magnet that produces a 95 -mT field. When a 15 -A current flows in the coil, what are (a) the coil's magnetic dipole moment and (b) the motor's maximum torque?
Donya D.
Numerade Educator
Problem 56
Nuclear magnetic resonance (NMR) is a technique for analyzing chemical structures and also the basis of magnetic resonance imaging used for medical diagnosis. NMR relies on sensitive measurements of the energy needed to flip atomic nuclei by $180^{\circ}$ in a given magnetic field. In an apparatus with a 9.4 -T magnetic field. what energy is needed to flip a proton $\left(\mu=1.41 \times 10^{-26} \mathrm{A} \cdot \mathrm{m}^{2}\right)$ from parallel to antiparallel to the field?
Donya D.
Numerade Educator
Problem 57
A wire carrying 1.5 A passes through a 48 -mT magnetic field. The wire is perpendicular to the field and makes a quarter-circle turn of radius $21 \mathrm{cm}$ in the field region, as shown in Fig. 26.42 Find the magnitude and direction of the magnetic force on the curved section of wire.
CAN'T COPY THE FIGURE
Donya D.
Numerade Educator
Problem 58
Your company is developing a device incorporating a $20-\mathrm{cm}-$ diameter coil carrying 0.50 A that, when properly oriented, will just cancel Earth's 50 - $\mu$ T magnetic field at the coil's center. How much wire must you requisition for each coil?
Donya D.
Numerade Educator
Problem 59
A single piece of wire carrying current $I$ is bent so it includes a circular loop of radius $a$, as shown in Fig. $26.43 .$ Find an expression for the magnetic field at the loop center.
CAN'T COPY THE FIGURE
Donya D.
Numerade Educator
Problem 60
Part of a long wire carrying current $I$ is bent into a semicircle of radius $a$, as in Fig. $26.44 .$ Use the Biot-Savart law to find the magnetic field at $P$, the center of the semicircle.
Donya D.
Numerade Educator
Problem 61
Part of a long wire carrying current $I$ is bent into a semicircle of radius $a$, as in Fig. $26.44 .$ Use the Biot-Savart law to find the magnetic field at $P$, the center of the semicircle.
CAN'T COPY THE FIGURE
Donya D.
Numerade Educator
Problem 62
Three parallel wires of length $l$ each carry current $I$ in the same direction. They're positioned at the vertices of an equilateral triangle of side $a,$ and oriented perpendicular to the triangle. Find an expression for the magnitude of the force on each wire.
Donya D.
Numerade Educator
Problem 63
A long, straight wire carries a 25 - A current. A 10 -cm by 15 -cm rectangular wire loop carrying $850 \mathrm{mA}$ is $3.0 \mathrm{cm}$ from the wire, as shown in Fig. $26.45 .$ Find the magnitude and direction of the net magnetic force on the loop.
CAN'T COPY THE FIGURE
Donya D.
Numerade Educator
Problem 64
A long conducting rod of radius $R$ carries a nonuniform current density $J=J_{0} r / R,$ where $J_{0}$ is a constant and $r$ is the radial distance from the rod's axis. Find expressions for the magnetic field strength (a) inside and (b) outside the rod.
Donya D.
Numerade Educator
Problem 65
A long, hollow conducting pipe of radius $R$ carries a uniform current $I$ along the pipe, as shown in Fig. $26.46 .$ Use Ampère's law to find the magnetic field strength (a) inside and (b) outside the pipe.
CAN'T COPY THE FIGURE
Donya D.
Numerade Educator
Problem 66
The coaxial cable shown in Fig. 26.47 consists of a solid inner conductor of radius $a$ and a hollow outer conductor of inner radius $b$ and thickness $c .$ The two carry equal but opposite currents $I$ uniformly distributed. Find expressions for the magnetic field as a function of radial position $r$ (a) within the inner conductor,
(b) between the inner and outer conductors, and (c) beyond the outer conductor.
CAN'T COPY THE FIGURE
Donya D.
Numerade Educator
Problem 67
A solenoid used in a plasma physics experiment is $10 \mathrm{cm}$ in diameter, is $1.0 \mathrm{m}$ long, and carries a $35-\mathrm{A}$ current to produce a $100-\mathrm{mT}$ magnetic field. (a) How many turns are in the solenoid?
(b) If the solenoid resistance is $2.7 \Omega,$ how much power does it dissipate?
Donya D.
Numerade Educator
Problem 68
You have $10 \mathrm{m}$ of 0.50 -mm-diameter copper wire and a battery capable of passing 15 A through the wire. What magnetic field strengths could you obtain (a) inside a 2.0 -cm-diameter solenoid wound with the wire as closely spaced as possible and (b) at the center of a single circular loop made from the wire?
Donya D.
Numerade Educator
Problem 69
Derive Equation 26.21 for the solenoid field by considering the solenoid to be made of infinitesimal current loops. Use Equation 26.9 for the loop fields, and integrate over all loops.
Problem 70
The largest lightning strikes have peak currents of around $250 \mathrm{kA}$ flowing in essentially cylindrical channels of ionized air. How far from such a flash would the resulting magnetic field be equal to Earth's magnetic field strength, about $50 \mu \mathrm{T} ?$
Donya D.
Numerade Educator
Problem 71
A coaxial cable (see Fig. 26.47 ) consists of a 1.0 -mm-diameter inner conductor and a $0.20-\mathrm{mm}$ -thick outer conductor with interior diameter $1.0 \mathrm{cm} .$ A 100 -mA current flows down the inner conductor and back along the outer conductor. Find the magnetic field strength (a) $0.10 \mathrm{mm},$ (b) $5.0 \mathrm{mm},$ and (c) $2.0 \mathrm{cm}$ from the cable axis.
Donya D.
Numerade Educator
Problem 72
Indium antimonide (InSb) is a semiconductor commonly used in Hall-effect devices because of its relatively large Hall coefficient. A magnetic-field sensor is made from a $50-\mu \mathrm{m}$ -thick strip of InSb, with Hall coefficient $228 \mathrm{cm}^{3} / \mathrm{C}$. The table below shows the Hall potential as a function of current when the sensor is oriented with its current perpendicular to the unknown magnetic field. Plot the Hall potential against a quantity that should give a straight line, determine a best-fit line, and from it find the magnetic field strength.
$$\begin{array}{|l|l|l|l|l|l|}
\hline I(\mathrm{mA}) & 10.0 & 20.0 & 30.0 & 40.0 & 50.0 \\
\hline V_{\mathrm{H}}(\mathrm{mV}) & 0.393 & 0.750 & 1.24 & 1.56 & 1.97 \\
\hline
\end{array}$$
Donya D.
Numerade Educator
Problem 73
Suppose the current sheet in Example 26.9 is actually a slab with non-negligible thickness $d$ and that the current is distributed uniformly throughout its volume. Find an expression for the magnetic field inside the slab as a function of the perpendicular distance $x$ from the center plane of the slab. Show that your result agrees with that of Example 26.9 at the surface of the slab.
Problem 74
A circular wire loop of radius $15 \mathrm{cm}$ and negligible thickness carries a 2.0 -A current. Use suitable approximations to find the magnetic field of this loop (a) in the loop plane, 1.0 mm outside the loop, and (b) on the loop axis, 3.0 m from the loop center.
Problem 75
A long, flat conducting bar of width $w$ carries a total current $I$ distributed uniformly, as shown in Fig. $26.48 .$ Use approximations to write expressions for the magnetic field strength (a) near the conductor surface $(r \ll w)$ but not near its edges and (b) far from the conductor $(r \gg w)$.
Donya D.
Numerade Educator
Problem 76
A long, hollow conducting pipe of radius $R$ and length $l$ carries a uniform current $I$ flowing around the pipe (Fig. 26.49 ). Find expressions for the magnetic field (a) inside and (b) outside the pipe. (Hint: What configuration does this resemble?)
CAN'T COPY THE FIGURE
Rashmi S.
Numerade Educator
Problem 77
A solid conducting wire of radius $R$ runs parallel to the $z$ -axis and carries a current density given by $\vec{J}=J_{0}(1-r / R) \hat{k},$ where $J_{0}$ is a constant and $r$ is the distance from the wire axis. Find expressions for (a) the total current in the wire and (b) the magnetic field for $r>R$ and $(\mathrm{c}) r<R$.
Problem 78
A disk of radius $a$ carries uniform surface charge density $\sigma$ and rotates with angular speed $\omega$ about the disk axis. Show that the magnetic field at the disk's center is $\frac{1}{2} \mu_{0} \sigma \omega a$.
Donya D.
Numerade Educator
Problem 79
You're developing a system to orient an orbiting telescope. The system uses three perpendicular coils, with torques developed in Earth's magnetic field when current passes through them. Weight limitations restrict you to a length $l$ of wire for each coil. A colleague argues you'll get the greatest dipole moment and therefore the most torque with a multi-turn coil. You say a 1 -turn coil is best. Who's right?
Problem 80
The structure shown in Fig. 26.50 is made from conducting rods. The upper horizontal rod (mass 22 g, length $95 \mathrm{cm}$ ) is free to slide vertically on the uprights while maintaining electrical contact. A battery connected across the insulating gap at the bottom of the left-hand upright drives 66 A through the structure. At what height $h$ will the upper wire be in equilibrium?
CAN'T COPY THE FIGURE
Donya D.
Numerade Educator
Problem 81
A long, flat conducting ribbon of width $w$ is parallel to a long, straight wire; its nearedge is a distance $a$ from the wire (Fig. 26.51 ). Wire and ribbon carry the same current $I$; it's distributed uniformly over the ribbon. Use integration to show that the force per unit length between the two has magnitude $\frac{\mu_{0} I^{2}}{2 \pi w} \ln \left(\frac{a+w}{a}\right)$.
CAN'T COPY THE FIGURE
Problem 82
Find an expression for the magnetic field at the center of a square loop of side $a$ carrying current $I$.
Donya D.
Numerade Educator
Problem 83
Repeat the calculation in Problem 69 for a solenoid of finite length $l$ and cross-sectional radius $a$ to find the magnetic field strength at the center of the solenoid's axis.
Problem 84
A magnetic dipole $\vec{\mu}=\mu \hat{\imath}$ is on the axis of a circular current loop of radius $a$ oriented as shown in Fig. $26.17 a,$ a distance $x$ from the center. Differentiate Equation 26.16 to find the force on the dipole, and evaluate its magnitude for $x=a$. Is the force attractive or repulsive?
Problem 85
You're an engineer at a nuclear power plant, and one of your colleagues has drawn up plans to reroute the conductors carrying current from the plant's electric generator. Your colleague wants to carry this current on two parallel conducting rods $30 \mathrm{cm}$ apart; each rod carries 15 kA with the currents flowing in opposite directions. The proposal calls for clamping the conductors in place every meter, with clamps capable of withstanding a maximum force of $100 \mathrm{N}$. Is the clamp design adequate?
Donya D.
Numerade Educator
Problem 86
Derive Equation 26.20 by considering the current sheet to be made of infinitely many infinitesimal line currents.
Problem 87
Your roommate is sold on "magnet therapy," a sham treatment using small bar magnets attached to the body. You skeptically ask your roommate how this is supposed to work. He mumbles something about the Hall effect speeding blood flow. In reply, you estimate the Hall potential associated with typical blood parameters in the $100-$ G field of a bar magnet: red blood cells carrying 2 -pC charge in a 12 -cm/s flow through a 3.0 -mm-diameter blood vessel containing 5 billion red blood cells per mL. To show that the Hall potential is negligible, you compare your estimate with the tens of $\mathrm{mV}$ typical of bioelectric activity. How do the two values compare?
Problem 88
A toroid is a solenoid-like coil bent into a circle (Fig. $26.52 a$ ). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us with an almost unlimited energy source using deuterium fuel extracted from seawater.
The ITER consortium, an international collaboration, is building a large toroidal fusion experiment in France; it's expected to be the first fusion device to produce energy on a large scale. Figure $26.52 b$ shows a cross section of a toroid, with current emerging from the page at the inner edge and descending at the outer edge. The black circle is an Ampèrian loop.
(a)CAN'T COPY THE FIGURE
(b)CAN'T COPY THE FIGURE
The magnetic field associated with the toroid is nonzero
a. only within the "hole" in the donut-shaped coil.
b. only within the region bounded by the coils.
c. only outside the coils.
d. everywhere.
Donya D.
Numerade Educator
Problem 89
A toroid is a solenoid-like coil bent into a circle (Fig. $26.52 a$ ). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us with an almost unlimited energy source using deuterium fuel extracted from seawater.
The ITER consortium, an international collaboration, is building a large toroidal fusion experiment in France; it's expected to be the first fusion device to produce energy on a large scale. Figure $26.52 b$ shows a cross section of a toroid, with current emerging from the page at the inner edge and descending at the outer edge. The black circle is an Ampèrian loop.
(a)CAN'T COPY THE FIGURE
(b)CAN'T COPY THE FIGURE
In Fig. $26.52 b,$ the magnetic field lines must be
a. straight, and pointing into the page.
b. straight, and pointing out of the page.
c. straight, and pointing radially.
d. circular.
Donya D.
Numerade Educator
Problem 90
A toroid is a solenoid-like coil bent into a circle (Fig. $26.52 a$ ). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us with an almost unlimited energy source using deuterium fuel extracted from seawater.
The ITER consortium, an international collaboration, is building a large toroidal fusion experiment in France; it's expected to be the first fusion device to produce energy on a large scale. Figure $26.52 b$ shows a cross section of a toroid, with current emerging from the page at the inner edge and descending at the outer edge. The black circle is an Ampèrian loop.
(a)CAN'T COPY THE FIGURE
(b)CAN'T COPY THE FIGURE
Doubling the total number of turns $N$ in the toroid, without changing its size or the current, will
a. double the magnetic field.
b. quadruple the magnetic field.
c. halve the magnetic field.
d. not change the magnetic field.
Donya D.
Numerade Educator
Problem 91
A toroid is a solenoid-like coil bent into a circle (Fig. $26.52 a$ ). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us with an almost unlimited energy source using deuterium fuel extracted from seawater.
The ITER consortium, an international collaboration, is building a large toroidal fusion experiment in France; it's expected to be the first fusion device to produce energy on a large scale. Figure $26.52 b$ shows a cross section of a toroid, with current emerging from the page at the inner edge and descending at the outer edge. The black circle is an Ampèrian loop.
(a)CAN'T COPY THE FIGURE
(b)CAN'T COPY THE FIGURE
The toroid has inner radius $R_{\text {in }}$ and outer radius $R_{\text {out }},$ while $r$ is the radial coordinate measured from the center. The toroid is made from wire wound into a total of $N$ turns, and carries current
I. Which of the following is the correct formula for the magnetic field within the coils?
a. $B=\mu_{0} N I$
b. $B=\mu_{0} N I / 2 \pi R_{\text {in }}$
c. $B=\mu_{0} N I / 2 \pi R_{\text {out }}$
d. $B=\mu_{0} N I / 2 \pi r$
Donya D.
Numerade Educator
Essential University Physics Volume 2 3rd Edition Chapter 26
Source: https://www.numerade.com/books/chapter/magnetism-force-and-field-2/
0 Response to "Essential University Physics Volume 2 3rd Edition Chapter 26"
Post a Comment