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physics
mechanics
Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions
A vertical magnetic field is perpendicular to the horizontal plane of a wire loop. When the loop is rotated about a horizontal axis in the plane, the current induced in the loop reverses direction twice per rotation. Explain why there are two reversals for one rotation.
Would a ground fault interrupter work if the circuit used dc current instead of ac? Explain.
In the study of thermodynamics, we thought of a refrigerator as a reversed heat engine. (a) Explain how a generator is a reversed electric motor. (b) What kind of device is a reversed loudspeaker?
Two identical circular coils of wire are separated by a fixed center-to-center distance. Describe the orientation of the coils that would (a) maximize or (b) minimize their mutual inductance.
(a) Explain why a transformer works for ac but not for dc. (b) Explain why a transformer designed to be connected to an emf of amplitude 170 V would be damaged if connected to a dc emf of 170 V.
Credit cards have a magnetic strip that encodes information about the credit card account. Why do devices that read the magnetic strip often include the instruction to swipe the card rapidly? Why can't the magnetic strip be read if the card is swiped too slowly?
Think of an example that illustrates why an "anti-Lenz" law would violate the conservation of energy. (The "anti- Lenz" law is: The direction of induced emfs and currents always reinforces the change that produces them.)
A 2-m-long copper pipe is held vertically. When a marble is dropped down the pipe, it falls through in about 0.7 s. A magnet of similar size and shape dropped down the pipe takes much longer. Why?
An electric mixer is being used to mix up some cake batter. What happens to the motor if the batter is too thick, so the beaters are turning slowly?
A circular loop of wire can be used as an antenna to sense the changing magnetic fields in an electromagnetic wave (such as a radio transmission). What is the advantage of using a coil with many turns rather than a single loop?
Some low-cost tape recorders do not have a separate microphone. Instead, the speaker is used as a microphone when recording. Explain how this works.
A transformer is essentially a mutual inductance device. Two coils are wound around an iron core; an alternating current in one coil induces an emf in the second. The core is normally made of either laminated iron-thin sheets of iron with an insulating material between them-or of a bundle of
High-voltage power lines run along the edge of a farmer's field. Describe how the farmer might be able to steal electric power without making any electrical connection to the power line. (Yes, it works. Yes, it has been done. Yes, it is illegal.)
A certain amount of energy must be supplied to increase the current through an inductor from 0 mA to 10 mA. Does it take the same amount of energy, more, or less to increase the current from 10 mA to 20 mA?
The primary coil of a transformer is connected to a dc battery. Is there an emf induced in the secondary coil? If so, why do we not use transformers with dc sources?
A metal plate is attached to the end of a rod and positioned so that it can swing into and out of a perpendicular magnetic field pointing out of the plane of the paper as shown. In position 1, the plate is just swinging into the field; in position 2, the plate is swinging out of the field. Does an
Magnetic induction is the principle behind the operation of me chanical speedometers used in automobiles and bicycles. In the drawing, a simplified version of the speedometer, a metal disk is free to spin about the vertical axis passing through its center. Suspended above the disk is a horseshoe
Wires that carry telephone signals are twisted. The twisting reduces the noise on the line from nearby electric devices that produce changing currents. How does the twisting reduce noise pickup?
The magnetic flux through a flat surface is known. The area of the surface is also known. Is that information enough to calculate the average magnetic field on the surface? Explain.
In Fig. 20.2, a metal rod of length L moves to the right at speed v. (a) What is the current in the rod, in terms of v, B, L, and R? (b) In what direction does the current flow? (c) What is the direction of the magnetic force on the rod? (d) What is the magnitude of the magnetic force on the rod
A solid copper disk of radius R rotates at angular velocity w in a perpendicular magnetic field B. The figure shows the disk rotating clockwise and the magnetic field into the page.(a) Is the charge that accumulates on the edge of the disk positive or negative? Explain.(b) What is the potential
A square loop of wire of side 2.3 cm and electrical resistance 79 Ω is near a long straight wire that carries a current of 6.8 A in the direction indicated. The long wire and loop both lie in the plane of the page. The left side of the loop is 9.0 cm from the wire.(a) If the loop is at rest,
A solid metal cylinder of mass m rolls down parallel metal rails spaced a distance L apart with a constant acceleration of magnitude a0 [part (a) of figure]. The rails are inclined at an angle q to the horizontal. Now the rails are connected electrically at the top and immersed in a magnetic field
A horizontal desk surface measures 1.3 m × 1.0 m. If Earth's magnetic field has magnitude 0.44 mT and is directed 65° below the horizontal, what is the magnetic flux through the desk surface?
A square loop of wire, 0.75 m on each side, has one edge along the positive z-axis and is tilted toward the yz-plane at an angle of 30.0° with respect to the horizontal (xzplane). There is a uniform magnetic field of 0.32 T pointing in the positive x-axis direction.(a) What is the flux through the
A long straight wire carrying a steady current is in the plane of a circular loop of wire. See the figure with Multiple-Choice Question 4. (a) If the loop is moved closer to the wire, what direction does the induced current in the loop flow? (b) At one instant, the induced emf in the loop is 3.5
A long straight wire carrying a current I is in the plane of a circular loop of wire. See the figure with Multiple- Choice Question 4. The current I is decreasing. Both the loop and the wire are held in place by external forces. The loop has resistance 24 Ω. (a) In what direction does the induced
While I1 is increasing, does current flow in loop 2? If so, does it flow clockwise or counterclockwise as viewed from the right? Explain.Two wire loops are side by side, as shown. The current I1 in loop 1 is supplied by an external source (not shown) and is clockwise as viewed from the right.
While I1 is increasing, what is the direction of the magnetic force exerted on loop 2, if any? Explain.Two wire loops are side by side, as shown. The current I1 in loop 1 is supplied by an external source (not shown) and is clockwise as viewed from the right.
While I1 is constant, does current flow in loop 2? If so, does it flow clockwise or counterclockwise as viewed from the right? Explain.Two wire loops are side by side, as shown. The current I1 in loop 1 is supplied by an external source (not shown) and is clockwise as viewed from the right.
Suppose that the current were to flow in the direction opposite to that found in Problem 1. (a) In what direction would the magnetic force on the rod be? (b) In the absence of an external force, what would happen to the rod's kinetic energy? (c) Why is this not possible? Returning to the correct
Refer to Fig. 20.2. The rod has length L and its position is x at some instant, as shown in the figure. Express your answers in terms of x, L, v, B (the magnetic field strength), and R, as needed.(a) What is the area enclosed by the conducting loop at this instant?(b) What is the magnetic flux
A circular conducting coil with radius 3.40 cm is placed in a uniform magnetic field of 0.880 T with the plane of the coil perpendicular to the magnetic field. The coil is rotated 180° about the axis in 0.222 s.(a) What is the average induced emf in the coil during this rotation? (b) If the
Verify that, in SI units, ΔΦB/Δt can be measured in volts-in other words, that 1 Wb/s = 1 V.
The component of the external magnetic field along the central axis of a 50-turn coil of radius 5.0 cm increases from 0 to 1.8 T in 3.6 s. (a) If the resistance of the coil is 2.8 Ω, what is the magnitude of the induced current in the coil? (b) What is the direction of the current if the axial
In the figure, switch S is initially open. It is closed, and then opened again a few seconds later.(a) In what direction does current flow through the ammeter when switch S is closed? (b) In what direction does current flow when switch S is then opened? (c) Sketch a qualitative graph of the current
Another example of motional emf is a rod attached at one end and rotating in a plane perpendicular to a uniform magnetic field. We can analyze this motional emf using Faraday's law.(a) Consider the area that the rod sweeps out in each revolution and find the magnitude of the emf in terms of the
(a) For a particle moving in simple harmonic motion, the position can be written x(t) = xm cos wt. What is the velocity vx(t) as a function of time for this particle? (b) Using the small-angle approximation for the sine function, find the slope of the graph of Φ(t) = Φ0 sin wt at t = 0. Does your
Two loops of wire are next to one another in the same plane.(a) If the switch S is closed, does current flow in loop 2? If so, in what direction?(b) Does the current in loop 2 flow for only a brief moment, or does it continue?(c) Is there a magnetic force on loop 2? If so, in what direction?(d) Is
A dc motor has coils with a resistance of 16 Ω and is connected to an emf of 120.0 V. When the motor operates at full speed, the back emf is 72 V. (a) What is the current in the motor when it first starts up? (b) What is the current when the motor is at full speed? (c) If the current is 4.0 A with
Tim is using a cordless electric weed trimmer with a dc motor to cut the long weeds in his back yard. The trimmer generates a back emf of 18.00 V when it is connected to an emf of 24.0 V dc. The total electrical resistance of the electric motor is 8.00 Ω.(a) How much current flows through the
To maintain a constant emf, the moving rod of Fig. 20.2 must maintain a constant velocity. In order to maintain a constant velocity, some external force must pull it to the right. (a) What is the magnitude of the external force required, in terms of v, B, L, and R? (See Problem 1.) (b) At what
A dc motor is connected to a constant emf of 12.0 V. The resistance of its windings is 2.0 Ω. At normal operating speed, the motor delivers 6.0 W of mechanical power. (a) What is the initial current drawn by the motor when it is first started up? (b) What current does it draw at normal operating
A step-down transformer has 4000 turns on the primary and 200 turns on the secondary. If the primary voltage amplitude is 2.2 kV, what is the secondary voltage amplitude?
A step-down transformer has a turns ratio of 1/100. An ac voltage of amplitude 170 V is applied to the primary. If the primary current amplitude is 1.0 mA, what is the secondary current amplitude?
A doorbell uses a transformer to deliver an amplitude of 8.5 V when it is connected to a 170-V amplitude line. If there are 50 turns on the secondary, (a) What is the turns ratio? (b) How many turns does the primary have?
The primary coil of a transformer has 250 turns; the secondary coil has 1000 turns. An alternating current is sent through the primary coil. The emf in the primary is of amplitude 16 V. What is the emf amplitude in the secondary?
A transformer with a primary coil of 1000 turns is used to step up the standard 170-V amplitude line voltage to a 220-V amplitude. How many turns are required in the secondary coil?
A transformer with 1800 turns on the primary and 300 turns on the secondary is used in an electric slot car racing set to reduce the input voltage amplitude of 170 V from the wall output. The current in the secondary coil is of amplitude 3.2 A. What is the voltage amplitude across the secondary
A transformer for an answering machine takes an ac voltage of amplitude 170 V as its input and supplies a 7.8-V amplitude to the answering machine. The primary has 300 turns. (a) How many turns does the secondary have? (b) When idle, the answering machine uses a maximum power of 5.0 W. What is the
A 2-m-long copper pipe is held vertically. When a marble is dropped down the pipe, it falls through in about 0.7 s. A magnet of similar size and shape takes much longer to fall through the pipe.(a) As the magnet is falling through the pipe with its north pole below its south pole, what direction do
In Fig. 20.2, what would the magnitude (in terms of v, L, R, and B) and direction (CW or CCW) of the current be if the direction of the magnetic field were: (a) Into the page; (b) To the right (in the plane of the page); (c) Up (in the plane of the page); (d) Such that it has components both out of
In Problem 39, the pipe is suspended from a spring scale. The weight of the pipe is 12.0 N; the weight of the marble and magnet are each 0.3 N. Sketch graphs to show the reading of the spring scale as a function of time for the fall of the marble and again for the fall of the magnet. Label the
When the current in loop 1 is I1 = 0.75 A, the magnetic flux through loop 2 is 2.35 × 10−8 T·m2. What is the mutual inductance of the two loops? The current I1 in loop 1 is supplied by an external source (not shown) and is clockwise as viewed from the right.
When the current in loop 1 decreases at a steady rate of 28 A/s, the induced emf in loop 2 is 1.40 mV. (a) What is the direction of the current in loop 2 as viewed from the right? (b) What is the mutual inductance of the two loops? The current I1 in loop 1 is supplied by an external source (not
When the current in loop 1 increases at a steady rate of 9.0 A/s, the current in loop 2 is 0.185 mA. The resistance of loop 2 is 0.66 Ω. (a) What is the direction of the current in loop 2 as viewed from the right? (b) What is the mutual inductance of the two loops?
Two solenoids, of N1 and N2 turns respectively, are wound on the same form. They have the same length L and radius r. (a) What is the mutual inductance of these two solenoids? (b) If an ac current I1 (t) = Im sin w t flows in solenoid 1 (N1 turns), write an expression for the total flux through
A solenoid is made of 300.0 turns of wire, wrapped around a hollow cylinder of radius 1.2 cm and length 6.0 cm. What is the self-inductance of the solenoid?
A solenoid of length 2.8 cm and diameter 0.75 cm is wound with 160 turns per cm. When the current through the solenoid is 0.20 A, what is the magnetic flux through one of the windings of the solenoid?
If the current in the solenoid in Problem 46 is decreasing at a rate of 35.0 A/s, what is the induced emf (a) In one of the windings? (b) In the entire solenoid?
An ideal solenoid has length ℓ. If the windings are compressed so that the length of the solenoid is reduced to 0.50ℓ, what happens to the inductance of the solenoid?
In this problem, you derive the expression for the selfinductance of a long solenoid [Eq. (20-15a)]. The solenoid has n turns per unit length, length ℓ, and radius r. Assume that the current flowing in the solenoid is I. (a) Write an expression for the magnetic field inside the solenoid in terms
A 15.0-g conducting rod of length 1.30 m is free to slide downward between two vertical rails without friction. The rails are connected to an 8.00-Ω resistor, and the entire apparatus is placed in a 0.450-T uniform magnetic field. Ignore the resistance of the rod and rails.(a) What is the
Compare the electric energy that can be stored in a capacitor to the magnetic energy that can be stored in an inductor of the same size (that is, the same volume). For the capacitor, assume that air is between the plates; the maximum electric field is then the breakdown strength of air, about 3
Calculate the equivalent inductance Leq of two ideal inductors, L1 and L2, connected in series in a circuit. Assume that their mutual inductance is negligible.
Calculate the equivalent inductance Leq of two ideal inductors, L1 and L2, connected in parallel in a circuit. Assume that their mutual inductance is negligible.
In Section 20.9, in order to find the energy stored in an inductor, we assumed that the current was increased from zero at a constant rate. In this problem, you will prove that the energy stored in an inductor is UL = 1/2LI2 - that is, it only depends on the current I and not on the previous time
A 5.0-mH inductor and a 10.0-Ω resistor are connected in series with a 6.0-V dc battery.(a) What is the voltage across the resistor immediately after the switch is closed? (b) What is the voltage across the resistor after the switch has been closed for a long time? (c) What is the
In a circuit, a parallel combination of a 10.0- Ω resistor and a 7.0-mH inductor is connected in series with a 5.0-Ω resistor, a 6.0-V dc battery, and a switch.(a) What are the voltages across the 5.0-Ω resistor and the 10.0-Ω resistor, respectively,
Refer to Problem 56. After the switch has been closed for a very long time, it is opened. What are the voltages across(a) The 5.0-Ω resistor(b) The 10.0-Ω resistor immediately after the switch is opened?In problem
No currents flow in the circuit before the switch is closed. Consider all circuit elements to be ideal.(a) At the instant the switch is closed, what are the values of the currents I1 and I2, the potential differences across the resistors, the power supplied by the battery, and the induced emf in
A coil of wire is connected to an ideal 6.00-V battery at t = 0. At t = 10.0 ms, the current in the coil is 204 mA. One minute later, the current is 273 mA. Find the resistance and inductance of the coil.
When the armature of an ac generator rotates at 15.0 rad/s, the amplitude of the induced emf is 27.0 V. What is the amplitude of the induced emf when the armature rotates at 10.0 rad/s?
A 0.67-mH inductor and a 130-Ω resistor are placed in series with a 24-V battery. (a) How long will it take for the current to reach 67% of its maximum value? (b) What is the maximum energy stored in the inductor? (c) How long will it take for the energy stored in the inductor to reach 67% of its
The windings of an electromagnet have inductance L = 8.0 H and resistance R = 2.0 Ω. A 100.0-V dc power supply is connected to the windings by closing switch S2.(a) What is the current in the windings?(b) The electromagnet is to be shut off. Before disconnecting the power supply by opening
A coil has an inductance of 0.15 H and a resistance of 33 Ω. The coil is connected to a 6.0-V ideal battery. When the current reaches half its maximum value: (a) At what rate is magnetic energy being stored in the inductor? (b) At what rate is energy being dissipated? (c) What is the total power
The time constant t for an LR circuit must be some combination of L, R, and ℰ. (a) Write the units of each of these three quantities in terms of V, A, and s. (b) Show that the only combination that has units of seconds is L/R.
In the circuit, switch S is opened at t = 0 after having been closed for a long time.(a) How much energy is stored in the inductor at t = 0?(b) What is the instantaneous rate of change of the inductor's energy at t = 0?(c) What is the average rate of change of the inductor's energy between t = 0.0
In the circuit for Problem 56, after the switch has been closed for a long time, it is opened. How long does it take for the energy stored in the inductor to decrease to 0.10 times its initial value?In problem
A 0.30-H inductor and a 200.0-Ω resistor are connected in series to a 9.0-V battery. (a) What is the maximum current that flows in the circuit? (b) How long after connecting the battery does the current reach half its maximum value? (c) When the current is half its maximum value, find the energy
A coil has an inductance of 0.15 H and a resistance of 33 Ω. The coil is connected to a 6.0-V battery. After a long time elapses, the current in the coil is no longer changing. (a) What is the current in the coil? (b) What is the energy stored in the coil? (c) What is the rate of energy
Switch S2 has been closed for a long time.(a) If switch S1 is closed, will a current flow in the left-hand coil? If so, what direction will it flow across the ammeter?(b) After some time, switch S1 is opened again while switch S2 remains closed. Will a current flow in the left coil? If so, what
In the ac generator of Fig. 20.6, the emf produced is ℰ(t) = w BA sin w t. If the generator is connected to a load of resistance R, then the current that flows isI(t) = ωBA/R sin ωt(a) Find the magnetic forces on sides 2 and 4 at the instant shown in Fig. 20.7. (Remember that q = wt.)(b) Why do
The armature of an ac generator is a circular coil with 50 turns and radius 3.0 cm. When the armature rotates at 350 rpm, the amplitude of the emf in the coil is 17.0 V. What is the strength of the magnetic field (assumed to be uniform)?
A circular metal ring is suspended above a solenoid. The magnetic field due to the solenoid is shown. The current in the solenoid is increasing.(a) What is the direction of the current in the ring? (b) The flux through the ring is proportional to the current in the solenoid. When the current in the
The strings of an electric guitar are made of ferromagnetic metal. The pickup consists of two components. A magnet causes the part of the string near it to be magnetized. The vibrations of the string near the pickup coil produce an induced emf in the coil. The electrical signal in the coil is then
A toroid has a square cross section of side a. The toroid has N turns and radius R. The toroid is narrow (a
An ideal toroid has N turns and self-inductance L. A single turn of wire is wrapped around the toroid [see part (a) of the figure].(a) What is the mutual inductance between the toroid and the single turn of wire? (b) What would the mutual inductance be if the turn of wire had an area twice as large
Suppose you wanted to use Earth's magnetic field to make an ac generator at a location where the magnitude of the field is 0.50 mT. Your coil has 1000.0 turns and a radius of 5.0 cm. At what angular velocity would you have to rotate it in order to generate an emf of amplitude 1.0 V?
A uniform magnetic field of magnitude 0.29 T makes an angle of 13° with the plane of a circular loop of wire. The loop has radius 1.85 cm. What is the magnetic flux through the loop?
A solenoid is 8.5 cm long, 1.6 cm in diameter, and has 350 turns. When the current through the solenoid is 65 mA, what is the magnetic flux through one turn of the solenoid?
How much energy due to Earth's magnetic field is present in 1.0 m3 of space near Earth's surface, at a place where the field has magnitude 0.45 mT?
The largest constant magnetic field achieved in the laboratory is about 40 T. (a) What is the magnetic energy density due to this field? (b) What magnitude electric field would have an equal energy density?
A TV tube requires a 20.0-kV-amplitude power supply. (a) What is the turns ratio of the transformer that raises the 170-V-amplitude household voltage to 20.0 kV? (b) If the tube draws 82 W of power, find the currents in the primary and secondary windings. Assume an ideal transformer.
The armature of an ac generator is a rectangular coil 2.0 cm by 6.0 cm with 80 turns. It is immersed in a uniform magnetic field of magnitude 0.45 T. If the amplitude of the emf in the coil is 17.0 V, at what angular speed is the armature rotating?
The alternator in an automobile generates an emf of amplitude 12.6 V when the engine idles at 1200 rpm. What is the amplitude of the emf when the car is being driven on the highway with the engine at 2800 rpm?
The outside of an ideal solenoid (N1 turns, length L, radius r) is wound with a coil of wire with N2 turns. (a) What is the mutual inductance? (b) If the current in the solenoid is changing at a rate ΔI1/Δt, what is the magnitude of the induced emf in the coil?
A standard ammeter must be inserted in series into the circuit (Section 18.9). An induction ammeter has the great advantage of being able to measure currents without making any electrical connection to the circuit. An iron ring is hinged so that it can be snapped around a wire. A coil is wrapped
A flip coil is a device used to measure a magnetic field. A coil of radius r, N turns, and electrical resistance R is initially perpendicular to a magnetic field of magnitude B. The coil is connected to a special kind of galvanometer that measures the total charge Q that flows through it. To
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