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physics
university physics
University Physics with Modern Physics 14th edition Hugh D. Young, Roger A. Freedman - Solutions
Calculate the magnitude and direction of the magnetic field at point P due to the current in the semicircular section of wire shown in Fig. E28.34.Figure e28.34 R P
The magnetic field around the head has been measured to be approximately 3.0 × 10-8 G. Although the currents that cause this field are quite complicated, we can get a rough estimate of their size by modeling them as a single circular current loop 16 cm (the width of a typical head) in diameter.
A cylinder of iron is placed so that it is free to rotate around its axis. Initially the cylinder is at rest, and a magnetic field is applied to the cylinder so that it is magnetized in a direction parallel to its axis. If the direction of the external field is suddenly reversed, the direction of
The magnetic susceptibility of paramagnetic materials is quite strongly temperature dependent, but that of diamagnetic materials is nearly independent of temperature. Why the difference?
What features of atomic structure determine whether an element is diamagnetic or paramagnetic? Explain.
If a magnet is suspended over a container of liquid air, it attracts droplets to its poles. The droplets contain only liquid oxygen; even though nitrogen is the primary constituent of air, it is not attracted to the magnet. Explain what this tells you about the magnetic susceptibilities of oxygen
Why should the permeability of a paramagnetic material be expected to decrease with increasing temperature?
Show that the units A ∙ m2 and J/T for the Bohr magneton are equivalent.
A metal ring carries a current that causes a magnetic field B0 at the center of the ring and a field B at point P a distance x from the center along the axis of the ring. If the radius of the ring is doubled, find the magnetic field at the center. Will the field at point P change by the same
A square wire loop 10.0 cm on each side carries a clockwise current of 8.00 A. Find the magnitude and direction of the magnetic field at its center due to the four 1.20-mm wire segments at the midpoint of each side.
In the circuit shown in Fig. Q28.13, when switch S is suddenly closed, the wire L is pulled toward the lower wire carrying currentI. Which (a or b) is the positive terminal of the battery? How do you know?Figure Q28.13 as S.
Two very long, parallel wires carry equal currents in opposite directions.(a) Is there any place that their magnetic fields completely cancel? If so, where? If not, why not?(b) How would the answer to part (a) change if the currents were in the same direction?
Magnetic field lines never have a beginning or an end. Use this to explain why it is reasonable for the field of an ideal toroidal solenoid to be confined entirely to its interior, while a straight solenoid must have some field outside.
What are the relative advantages and disadvantages of Ampere’s law and the law of Biot and Savart for practical calculations of magnetic fields?
A current was sent through a helical coil spring. The spring contracted, as though it had been compressed. Why?
Two concentric, coplanar, circular loops of wire of different diameter carry currents in the same direction. Describe the nature of the force exerted on the inner loop by the outer loop and on the outer loop by the inner loop.
A negative charge q = -3.60 × 10-6 C is located at the origin and has velocity v̅(vector) = (7.50 × 104 m/s)î + (-4.90 × 104 m/s)ĵ. At this instant what are the magnitude and direction of the magnetic field produced by this charge at the point x = 0.200 m, y = -0.300 m, z = 0?
In deriving the force on one of the long, current-carrying conductors in Section 28.4, why did we use the magnetic field due to only one of the conductors? That is, why didn’t we use the total magnetic field due to both conductors?
Suppose you have three long, parallel wires arranged so that in cross section they are at the corners of an equilateral triangle. Is there any way to arrange the currents so that all three wires attract each other? So that all three wires repel each other? Explain.
Pairs of conductors carrying current into or out of the power-supply components of electronic equipment are sometimes twisted together to reduce magnetic-field effects. Why does this help?
Two parallel conductors carrying current in the same direction attract each other. If they are permitted to move toward each other, the forces of attraction do work. From where does the energy come? Does this contradict the assertion in Chapter 27 that magnetic forces on moving charges do no
The text discussed the magnetic field of an infinitely long, straight conductor carrying a current. Of course, there is no such thing as an infinitely long anything. How do you decide whether a particular wire is long enough to be considered infinite?
Streams of charged particles emitted from the sun during periods of solar activity create a disturbance in the earth’s magnetic field. How does this happen?
A topic of current interest in physics research is the search (thus far unsuccessful) for an isolated magnetic pole, or magnetic monopole. If such an entity were found, how could it be recognized? What would its properties be?
The large magnetic fields used in MRI can produce forces on electric currents within the human body. This effect has been proposed as a possible method for imaging €œbiocurrents€ flowing in the body, such as the current that flows in individual nerves. For a magnetic field
Which of following elements is a candidate for MRI?(a) 12C6;(b) 16O8;(c) 40Ca20;(d) 31P15.Magnetic resonance imaging (MRI) is a powerful imaging method that, unlike x-ray imaging, allows sharp images of soft tissue to be made without exposing the patient to potentially damaging radiation. A
The lower end of the thin uniform rod in Fig. P27.74 is attached to the floor by a frictionless hinge at point P. The rod has mass 0.0840 kg and length 18.0 cm and is in a uniform magnetic field B = 0.120 T that is directed into the page. The rod is held at an angle θ = 53.0° above
A uniform bar has mass 0.0120 kg and is 30.0 cm long. It pivots without friction about an axis perpendicular to the bar at point a (Fig. P27.72). The gravitational force on the bar acts in the -y-direction. The bar is in a uniform magnetic field that is directed into the page and has magnitude B =
A uniform bar of length L carries a current I in the direction from point a to point b (Fig. P27.70). The bar is in a uniform magnetic field that is directed into the page. Consider the torque about an axis perpendicular to the bar at point a that is due to the force that the magnetic field exerts
The amount of meat in prehistoric diets can be determined by measuring the ratio of the isotopes 15N to 14N in bone from human remains. Carnivores concentrate 15N, so this ratio tells archaeologists how much meat was consumed. For a mass spectrometer that has a path radius of 12.5 cm for 12C ions
Singly ionized (one electron removed) atoms are accelerated and then passed through a velocity selector consisting of perpendicular electric and magnetic fields. The electric field is 155 V/m and the magnetic field is 0.0315 T. The ions next enter a uniform magnetic field of magnitude 0.0175 T that
In a cyclotron, the orbital radius of protons with energy 300 keV is 16.0 cm. You are redesigning the cyclotron to be used instead for alpha particles with energy 300 keV. An alpha particle has charge q = +2e and mass m = 6.64 × 10-27 kg. If the magnetic field isn’t changed, what will be the
Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. These cyclotrons typically accelerate H- (the hydride ion, which has one proton and two electrons) to an energy of 5 MeV to 20 MeV. This ion has a mass very close to that of a proton because the electron
Hall-effect voltages are much greater for relatively poor conductors (such as germanium) than for good conductors (such as copper), for comparable currents, fields, and dimensions. Why?
In a Hall-effect experiment, is it possible that no transverse potential difference will be observed? Under what circumstances might this happen?
When the polarity of the voltage applied to a dc motor is reversed, the direction of motion does not reverse. Why not? How could the direction of motion be reversed?
The magnetic force acting on a charged particle can never do work because at every instant the force is perpendicular to the velocity. The torque exerted by a magnetic field can do work on a current loop when the loop rotates. Explain how these seemingly contradictory statements can be reconciled.
Could an accelerator be built in which all the forces on the particles, for steering and for increasing speed, are magnetic forces? Why or why not?
A student claims that if lightning strikes a metal flagpole, the force exerted by the earth’s magnetic field on the current in the pole can be large enough to bend it. Typical lightning currents are of the order of 104 to 105 A. Is the student’s opinion justified? Explain your reasoning.
A horizontal rectangular surface has dimensions 2.80 cm by 3.20 cm and is in a uniform magnetic field that is directed at an angle of 30.0° above the horizontal. What must the magnitude of the magnetic field be to produce a flux of 3.10 × 10-4 Wb through the surface?
Each of the lettered points at the corners of the cube in Fig. Q27.12 represents a positive charge q moving with a velocity of magnitude v in the direction indicated. The region in the figure is in a uniform magnetic field BÌ…(vector), parallel to the x-axis and directed toward the right. Which
Several charges enter a uniform magnetic field directed into the page. (a) What path would a positive charge q moving with a velocity of magnitude v follow through the field?(b) What path would a positive charge q moving with a velocity of magnitude 2v follow through the field?(c) What path
A flat, square surface with side length 3.40 cm is in the xy-plane at z = 0. Calculate the magnitude of the flux through this surface produced by a magnetic field B̅(vector) = (0.200 T)î (0.300 T)ĵ - (0.500 T)k̂.
A loose, floppy loop of wire is carrying current I. The loop of wire is placed on a horizontal table in a uniform magnetic field B̅(vector) perpendicular to the plane of the table. This causes the loop of wire to expand into a circular shape while still lying on the table. In a diagram, show all
How could the direction of a magnetic field be determined by making only qualitative observations of the magnetic force on a straight wire carrying a current?
How might a loop of wire carrying a current be used as a compass? Could such a compass distinguish between north and south? Why or why not?
A charged particle moves through a region of space with constant velocity (magnitude and direction). If the external magnetic field is zero in this region, can you conclude that the external electric field in the region is also zero? Explain. (By “external” we mean fields other than those
If the magnetic force does no work on a charged particle, how can it have any effect on the particle’s motion? Are there other examples of forces that do no work but have a significant effect on a particle’s motion?
A charged particle is fired into a cubical region of space where there is a uniform magnetic field. Outside this region, there is no magnetic field. Is it possible that the particle will remain inside the cubical region? Why or why not?
The magnetic force on a moving charged particle is always perpendicular to the magnetic field B̅(vector). Is the trajectory of a moving charged particle always perpendicular to the magnetic field lines? Explain your reasoning.
Section 27.2 describes a procedure for finding the direction of the magnetic force using your right hand. If you use the same procedure, but with your left hand, will you get the correct direction for the force? Explain.
At any point in space, the electric field E̅(vector) is defined to be in the direction of the electric force on a positively charged particle at that point. Why don’t we similarly define the magnetic field B̅(vector) to be in the direction of the magnetic force on a moving, positively charged
Can a charged particle move through a magnetic field without experiencing any force? If so, how? If not, why not?
Cell membranes across a wide variety of organisms have a capacitance per unit area of 1 µF/cm2. For the electrical signal in a nerve to propagate down the axon, the charge on the membrane “capacitor” must change. What time constant is required when the ion channels are open?(a) 1 µs;(b) 10
In a simple model of an axon conducting a nerve signal, ions move across the cell membrane through open ion channels, which act as purely resistive elements. If a typical current density (current per unit cross-sectional area) in the cell membrane is 5 mA/cm2 when the voltage across the membrane
Assume that a typical open ion channel spanning an axon’s membrane has a resistance of 1 × 1011 Ω. We can model this ion channel, with its pore, as a 12-nm-long cylinder of radius 0.3 nm. What is the resistivity of the fluid in the pore?(a) 10 Ω ∙ m;(b) 6 Ω ∙ m;(c) 2 Ω ∙ m;(d) 1 Ω ∙
The electronics supply company where you work has two different resistors, R1 and R2, in its inventory, and you must measure the values of their resistances. Unfortunately, stock is low, and all you have are R1 and R2 in parallel and in series and you can’t separate these two resistor
You set up the circuit shown in Fig. 26.20, where C = 5.00 × 10-6F. At time t = 0, you close the switch and then measure the charge q on the capacitor as a function of the current i in the resistor. Your results are given in the table:(a) Graph q as a function of i. Explain why the
You set up the circuit shown in Fig. 26.22a, where R = 196 Ω. You close the switch at time t = 0 and measure the magnitude i of the current in the resistor R as a function of time t since the switch was closed. Your results are shown in Fig. P26.80, where you have chosen to plot ln i as
A 6.00 µF capacitor that is initially uncharged is connected in series with a 5.00 Ω resistor and an emf source with ε = 50.0 V and negligible internal resistance. At the instant when the resistor is dissipating electrical energy at a rate of 300 W, how much energy has been stored in the
In the circuit shown in Fig. P26.64, ε = 24.0 V, R1= 6.00 Ω, R3= 12.0 Ω, and R2can vary between 3.00 Ω and 24.0 Ω. For what value of R2is the power dissipated by heating element R1 the greatest? Calculate the magnitude of the
In Fig. P26.54, the battery has negligible internal resistance and ε = 48.0 V. R1= R2= 4.00 Ω and R4= 3.00 Ω. What must the resistance R3be for the resistor network to dissipate electrical energy at a rate of 295 W?Figure P26.54 ww R1 R2 R3 R4
You connect a battery, resistor, and capacitor as in Fig. 26.20a, where R = 12.0 Ω and C = 5.00 × 10-6F. The switch S is closed at t = 0. When the current in the circuit has magnitude 3.00 A, the charge on the capacitor is 40.0 × 10-6C.(a) What is the emf of
A galvanometer having a resistance of 25.0 Ω has a 1.00 Ω shunt resistance installed to convert it to an ammeter. It is then used to measure the current in a circuit consisting of a 15.0 Ω resistor connected across the terminals of a 25.0 V battery having no appreciable internal resistance.(a)
When a capacitor, battery, and resistor are connected in series, does the resistor affect the maximum charge stored on the capacitor? Why or why not? What purpose does the resistor serve?
For very large resistances it is easy to construct R-C circuits that have time constants of several seconds or minutes. How might this fact be used to measure very large resistances, those that are too large to measure by more conventional means?
Verify that the time constant RC has units of time.
In the circuit shown in Fig. E26.18, ε = 36.0 V, R1= 4.00 Ω, R2= 6.00 Ω, and R3= 3.00 Ω.(a) What is the potential difference Vab between points a and b when the switch S is open and when S is closed?(b) For each resistor, calculate the current
Will the capacitors in the circuits shown in Fig. Q26.18 charge at the same rate when the switch S is closed? If not, in which circuit will the capacitors charge more rapidly? Explain.Figure Q26.18 (a) C. (b)
The emf of a flashlight battery is roughly constant with time, but its internal resistance increases with age and use. What sort of meter should be used to test the freshness of a battery?
Identical light bulbs A, B, and C are connected as shown in Fig. Q26.16. When the switch S is closed, bulb C goes out. Explain why. What happens to the brightness of bulbs A and B? Explain.Figure Q26.16
In a two-cell flashlight, the batteries are usually connected in series. Why not connect them in parallel? What possible advantage could there be in connecting several identical batteries in parallel?
The battery in the circuit shown in Fig. Q26.14 has no internal resistance. After you close the switch S, will the brightness of bulb B1increase, decrease, or stay the same? Figure Q26.14 B1 B2
Is it possible to connect resistors together in a way that cannot be reduced to some combination of series and parallel combinations? If so, give examples. If not, state why not.
In Fig. E26.11 the battery has emf 35.0 V and negligible internal resistance. R1= 5.00 Ω. The current through R1is 1.50 A, and the current through R3= 4.50 A. What are the resistances R2and R3?Figure E26.11 R2 ww- R3
Consider the circuit shown in Fig. Q26.12. What happens to the brightnesses of the bulbs when the switch S is closed if the battery(a) Has no internal resistance and(b) Has nonnegligible internal resistance? Explain why.Figure Q26.12
In Fig. E26.11, R1= 3.00 Ω, R2= 6.00 Ω, and R3= 5.00 Ω. The battery has negligible internal resistance. The current I2through R2is 4.00 A.(a) What are the currents I1 and I3?(b) What is the emf of the battery?Figure E26.11 R2 R3
A real battery, having nonnegligible internal resistance, is connected across a light bulb as shown in Fig. Q26.10. When the switch S is closed, what happens to the brightness of the bulb? Why?Figure Q26.10 ww
A light bulb is connected in the circuit shown in Fig. Q26.9. If we close the switch S, does the bulb€™s brightness increase, decrease, or remain the same? Explain why.Figure Q26.9 ww
A resistor consists of three identical metal strips connected as shown in Fig. Q26.8. If one of the strips is cut out, does the ammeter reading increase, decrease, or stay the same? Why?Figure Q26.8 (A)
For the circuit shown in Fig. E26.7 find the reading of the idealized ammeter if the battery has an internal resistance of 3.26 Ω.Figure E26.7 45.0 0 25.0 V 18.0 N -w 15.0 N
A battery with no internal resistance is connected across identical light bulbs as shown in Fig. Q26.7. When you close the switch S, will the brightness of bulbs B1 and B2change? If so, how will it change? Explain.Figure Q26.7 B1 B2
If two resistors R1and R2(R2> R1) are connected in parallel as shown in Fig. Q26.6, which of the following must be true? In each case justify your answer.(a) I1 = I2.(b) I3 = I4.(c) The current is greater in R1 than in R2.(d) The rate of electrical energy consumption is the same for both
If two resistors R1and R2(R2> R1) are connected in series as shown in Fig. Q26.5, which of the following must be true? In each case justify your answer.(a) I1 = I2 = I3.(b) The current is greater in R1 than in R2(c) The electrical power consumption is the same for both resistors.(d) The
In the circuit shown in Fig. Q26.4, three identical light bulbs are connected to a flashlight battery. How do the brightnesses of the bulbs compare? Which light bulb has the greatest current passing through it? Which light bulb has the greatest potential difference between its terminals? What
You connect a number of identical light bulbs to a flashlight battery.(a) What happens to the brightness of each bulb as more and more bulbs are added to the circuit if you connect them(i) In series and(ii) In parallel?(b) Will the battery last longer if the bulbs are in series or in parallel?
Two 120-V light bulbs, one 25-W and one 200-W, were connected in series across a 240-V line. It seemed like a good idea at the time, but one bulb burned out almost immediately. Which one burned out, and why?
The text states that good thermal conductors are also good electrical conductors. If so, why don’t the cords used to connect toasters, irons, and similar heat producing appliances get hot by conduction of heat from the heating element?
High-voltage power supplies are sometimes designed intentionally to have rather large internal resistance as a safety precaution. Why is such a power supply with a large internal resistance safer than a supply with the same voltage but lower internal resistance?
A fuse is a device designed to break a circuit, usually by melting when the current exceeds a certain value. What characteristics should the material of the fuse have?
Ordinary household electric lines in North America usually operate at 120 V. Why is this a desirable voltage, rather than a value considerably larger or smaller? On the other hand, automobiles usually have 12-V electrical systems. Why is this a desirable voltage?
Long-distance, electric-power, transmission lines always operate at very high voltage, sometimes as much as 750 kV. What are the advantages of such high voltages? What are the disadvantages?
Small aircraft often have 24-V electrical systems rather than the 12-V systems in automobiles, even though the electrical power requirements are roughly the same in both applications. The explanation given by aircraft designers is that a 24-V system weighs less than a 12-V system because thinner
Eight flashlight batteries in series have an emf of about 12 V, similar to that of a car battery. Could they be used to start a car with a dead battery? Why or why not?
The energy that can be extracted from a storage battery is always less than the energy that goes into it while it is being charged. Why?
A ductile metal wire has resistance R. What will be the resistance of this wire in terms of R if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? The amount of metal does not change, so stretching
(See Discussion Question Q25.14.) An ideal ammeter A is placed in a circuit with a battery and a light bulb as shown in Fig. Q25.15a, and the ammeter reading is noted. The circuit is then reconnected as in Fig. Q25.15b, so that the positions of the ammeter and light bulb are reversed.(a) How does
A light bulb glows because it has resistance. The brightness of a light bulb increases with the electrical power dissipated in the bulb.(a) In the circuit shown in Fig. Q25.14a, the two bulbs A and B are identical. Compared to bulb A, does bulb B glow more brightly, just as brightly, or less
A 14-gauge copper wire of diameter 1.628 mm carries a current of 12.5 mA.(a) What is the potential difference across a 2.00-m length of the wire?(b) What would the potential difference in part (a) be if the wire were silver instead of copper, but all else were the same?
Why does an electric light bulb nearly always burn out just as you turn on the light, almost never while the light is shining?
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