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physics
electricity and magnetism

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

A straight, horizontal segment of wire carries a current in the + x-direction in a magnetic field that is directed in the –z-direction. (a) Is the magnetic force on the wire directed in the (1) – x-, (2) +z-, (3) +y-, or (4) –y-direction? Explain. (b) If the wire is 1.0 m long and carries a
A 2.0-m length of straight wire carries a current of 20 A in a uniform magnetic field of 50 mT whose direction is at an angle of 37o from the direction of the current. Find the force on the wire.
A horizontal magnetic field of 1.0 x 10-4T is at an angle of 30o to the direction of the current in a straight, horizontal wire 75 cm long. If the wire carries a current of 15 A, (a) What is the magnitude of the force on the wire? (b) What angle(s) would be required for the force to be half the
A wire carries a current of 10 A in the in a uniform magnetic field of 0.40 T. Find the magnitude of the force per unit length and the direction of the force on the wire if the magnetic field is (a) In the + x-direction, (b) In the + y-direction, (c) In the +z-direction, (d) In the
A straight current-carrying wire 25 cm long is oriented at right angles to a uniform horizontal magnetic field of 0.30 T pointing in the -x-direction. (a) Along which of the x-y-z axes would the current direction have to be to cause the wire to be subject to a force of (a) 0.050 N in the
A wire carries a current of 10 A in the +x-direction. (a) Find the force per unit length on the wire if it is in a magnetic field that has components of Bx = 0.020 T, By = 0.040 T, and Bz = 0 T. (b) Find the force per unit length on the wire if only the field’s x-component is changed to Bx =
A nearly horizontal dc power line in the midlatitudes of North America carries a current of 1000 A directly eastward. If the Earth’s magnetic field at the location of the power line is northward with a magnitude of 5.0 x 10-5 T at an angle 45o of below the horizontal, what are the magnitude and
A wire is bent as shown in Fig. 19.37 and placed in a magnetic field with a magnitude of 1.0 T in the indicated direction. Find the net force on the whole wire if x = 50 cm and it carries a current of 5.0 A in the direction shown.
A loop of current-carrying wire is in a 1.6-T magnetic field. (a) For the magnetic torque on the loop to be at a maximum, should the plane of the coil be (1) parallel, (2) perpendicular, or (3) at a 45o angle to the magnetic field? Explain. (b) If the loop is rectangular with dimensions 20 cm by
A rectangular wire loop with a cross-sectional area of 0.20 m2 carries a current of 0.25 A. The loop is free to rotate about an axis that is perpendicular to a uniform magnetic field with strength 0.30 T. The plane of the loop is at an angle of to the direction of the magnetic field. (a) What is
Two bar very narrow magnets are located in the x-y plane. Magnet # 1 lies on the x-axis and its north end is at x = +1.0cm, while its south end is at x = + 5.0cm. Magnet # 2 lies on the y-axis and its north end is at y = + 1.0cm, while its south end is at y = + 5.0cm, Magnet # 2 produces a magnetic
The magnetic field at the center of a 50-turn coil of radius 15 cm is 0.80 mT. Find the current in the coil.
In Exercise 30, if you wanted to double the field strength while keeping the current and turn count the same, what would the coil area have to be?
(a) Show that the right-hand side of Eq. 19.13b gives the correct SI units for magnetic field. (b) Show that Eq. 19.13 b reduces to Eq. 19.13a when the central axis location is at the center of the loop.
The magnetic field 7.5 cm directly above the center of a 25-turn coil of radius 15 cm is 0.80 mT. Find the current in the coil.
Along, straight wire carries a current of 2.5 A. Find the magnitude of the magnetic field 25 cm from the wire.
In a physics lab, a student discovers that the magnitude of the magnetic field at a certain distance from a long wire is 4.0μT. If the wire carries a current of 5.0 A, what is the distance of the magnetic field from the wire?
A solenoid is 0.20 m long and consists of 100 turns of wire. At its center, the solenoid produces a magnetic field with a strength of 1.5 mT. Find the current in the coil.
Two long, parallel wires carry currents of 8.0 A and 2.0 A (Fig. 19.38).(a) What is the magnitude of the magnetic field midway between the wires? (b) Where on a line perpendicular to and joining the wires is the magnetic field zero?
Two long, parallel wires separated by 50 cm each carry currents of 4.0 A in a horizontal direction. Find the magnetic field midway between the wires if the currents are (a) In the same direction and (b) In opposite directions.
Two long, parallel wires separated by 0.20 m carry equal currents of 1.5 A in the same direction. Find the magnitude and direction of the magnetic field 0.15 m away from each wire on the side opposite the other wire (Fig. 19.39).
A positive charge moves horizontally to the right across this page and enters a magnetic field directed vertically downward in the plane of the page. (a) What is the direction of the magnetic force on the charge: (1) into the page, (2) out of the page, (3) downward in the plane of the page, or (4)
In Fig. 19.38, find the magnetic field (magnitude and direction) at point A, which is located 9.0 cm away from wire 2 on a line perpendicular to the line joining the wires.
A coil of four circular loops of radius 5.0 cm carries a current of 2.0 A clockwise, as viewed from above the coil’s plane. What is the magnetic field at the center of the coil?
A circular loop of wire in the horizontal plane carries a counterclockwise current, as viewed from above. (a) Use the right-hand source rule to determine whether the direction of the magnetic field at the center of the loop is (1) toward or (2) away from the observer. (b) If the diameter of the
A circular loop of wire with a radius of 5.0 cm carries a current of 1.0 A. Another circular loop of wire is con-centric with (that is, has a common center with) the first and has a radius of 10 cm. The magnetic field at the center of the loops is double what the field would be from the first one
A current-carrying solenoid is 10 cm long and is wound with 1000 turns of wire. It produces a magnetic field of 4.0 x 10-4 T at the solenoid’s center. (a) How long would you make the solenoid in order to produce a field of 6.0 x 10-4 T at its center? (b) Adjusting only the windings, what number
A solenoid is wound with 200 turns per centimeter. An outer layer of insulated wire with 180 turns per centimeter is wound over the solenoid€™s first layer of wire. When the solenoid is operating, the inner coil carries a current of 10 A and the outer coil carries a current of 15 A in the
A set of jumper cables used to start a car from another car’s battery is connected to the terminals of both batteries. If 15 A of current exists in the cables during the starting procedure and the cables are parallel and 15 cm apart, (a) Do the wires repel or attract? Explain. (b) What is the
Two long, straight, parallel wires carry the same current in the same direction. (a) Use both the right-hand source and force rules to determine whether the forces on the wires are (1) attractive or (2) repulsive. (b) If the wires are 24 cm apart and experience a force per unit length of 24 mN/m,
Four wires running through the corners of a square with sides of length a, as shown in Fig. 19.41, carry equal currents I. Calculate the magnetic field at the center of the square in terms of I and a.
A 50-cm-long solenoid has 100 turns of wire and carries a current of 0.95 A. It has a ferromagnetic core completely filling its interior where the field is 0.71 T. Determine the (a) Magnetic permeability and (b) Relative magnetic permeability of the material.
A charge of 0.050 C moves vertically in a field of 0.080 T that is oriented 45o from the vertical. What speed must the charge have such that the force acting on it is 10 N?
A circular wire coil consists of 100 turns and is wound tightly around a very long iron cylinder with a radius of 2.5 cm and a relative permeability of 2200. The loop has a current of 7.5 A in it. Determine the magnetic field strength produced by the coil (a) At the center of the coil and (b) At
(a) Exiting from a small linear accelerator near Washington D. C., a proton is moving parallel to the ground. What should the direction(s) of its velocity be in order to maximize the upward component of the Earth’s magnetic force on it? (b) Using a value of 0.05 mT for the value of the
A crude model of the Earth’s magnetic field consists of a circular loop of current with a radius of 500 km with its center coincident with that of the Earth’s. Assuming the plane of the loop to be approximately in the equatorial plane, and using a value of 0.10 mT for the magnitude of the
A particle with charge q and mass m moves in a horizontal plane at right angles to a uniform vertical magnetic field B. (a) What are the period T and frequency f of the particle’s circular motion in terms of q, B, and m? (This frequency is called the cyclotron frequency.) You result should
What is the (a) “Current” due to the electron orbiting in a circular path about the proton in a hydrogen atom? (b) What magnetic field strength does this “electron cur-rent” create at the proton location? (c) If the electron is orbiting clockwise, as viewed from above its orbital plane,
Two long, straight, parallel wires 10 cm apart carry cur-rents in opposite directions. (a) Use the right-hand source and force rules to determine whether the forces on the wires are (1) attractive or (2) repulsive. Show your reasoning. (b) If the wires carry equal currents of 3.0 A, what is the
In Figure 19.38,(a) What is the direction of the magnetic field produced by wire 1 at the location of wire 2? (b) What about midway between the wires? (c) What is the force (including direction) per unit length on wire 1?
A bar magnet is dropped through a coil of wire as shown in Fig. 20.29.(a) Describe what is observed on the galvanometer by sketching a graph of induced emf versus t. (b) Does the magnet fall freely? Explain.
A student has a bright idea for a generator that apparently generates electric energy without a corresponding loss of energy somewhere else. His suggested arrangement is shown in Fig. 20.31. The magnet is initially pulled down and released. When the magnet is attached to a spring, the student
If you wanted to make a more compact ac generator (operating at the same frequency) by reducing the area of the coils, how would could you compensate by changing its other physical characteristics in order to maintain the same emf output? Explain how each characteristic would change (larger,
A metallic plate is in the plane of this paper. A uniform magnetic field is perpendicular to the plane of the paper and creates a magnetic flux in the plate. Give the direction of the eddy currents in the plate (clockwise, counter-clockwise, or zero) for each of the following cases. Assume you are
(a) An antenna has been connected to a car battery. Under these conditions, will the antenna emit electro-magnetic radiation? Why or why not? Explain. (b) Repeat part (a) for the time when the battery is disconnected and the current in the antenna drops to zero.
On a cloudy summer day, you work outside and feel cool, yet that evening you find that you are sunburned. Explain how this is possible.
Radiation exerts pressure on surfaces on which it falls (radiation pressure). (a) Will this pressure be greater on a shiny surface or a dark surface? (b) For a given type of surface, will the pressure be greater using a bright source compared to a source emitting the same color but fainter? (c)
(a) When police radar waves bounce off an oncoming car and are received by the transmitting radar “gun,” they have a different frequency than the emitted waves. Explain. (b) Is the frequency in part (b) higher or lower than the original frequency? What about wavelength? What about wave speed?
Two identical strong magnets are dropped simultaneously by two students into two vertical tubes of the same dimensions (Fig. 20.30). One tube is made of copper, and the other is made of plastic. From which tube will the magnet emerge first? Why?
By using the appropriate SI units, show that the units on both sides of Eq. 20.2 (Faraday’s law) are the same.
(a) In Fig. 20.10, what would happen to the direction of the induced current if the metal rod were moving down-ward instead? (b) What would happen to the direction of the induced magnetic field? Is the induced magnetic field necessarily opposite to the external field direction?
(a) Explain why the maximum emf produced by an ac generator occurs when the flux through its armature coil is zero. (b) Explain why the emf produced by an ac gennrator is zero when the flux through its armature coil is at its maximum.
What should be the diameter of a circular wire loop if it is to have a magnetic field of 0.15 T oriented perpendicular to its area which produces a magnetic flux of 1.2 x 10-2 T ∙ m2?
In 0.20 s, a coil of wire with 50 loops experiences an average induced emf of 9.0 V due to a changing magnetic field perpendicular to the plane of the coil. The radius of the coil is 10 cm, and the initial strength of the magnetic field is 1.5 T. Assuming that the strength of the field decreased
A boy is traveling due north at a constant speed while carrying a metal rod. The rod’s length is oriented in the east– west direction and is parallel to the ground. (a) There will be no induced emf when the rod is (1) at the equator, (2) near the Earth’s magnetic poles, (3) somewhere between
A metal airplane with a wingspan of 30 m flies horizontally along a north– south route in the northern hemi-sphere at a constant speed of in a region where the vertical component of the Earth’s magnetic field is 5.0 x 10-5 T. (a) What is the magnitude of the induced emf between the tips of its
Suppose that the metal rod in Fig. 20.11 is 20 cm long and is moving at a speed of10 m/s in a magnetic field of 0.30 T and that the metal frame is covered with an insulating material. Find (a) The magnitude of the induced emf across the rod and (b) The current in the rod. (c) Repeat these
The flux through a loop of wire changes uniformly from + 40Wb to – 20Wb in 1.5ms. (a) What is the significance of the negative number attached to the final flux value? (b) What is the average induced emf in the loop? (c) If you wanted to double the average induced emf by changing only the
A fixed coil of wire with 10 turns and an area of 0.055m2 is placed in a perpendicular magnetic field. This field oscillates in direction and magnitude at a frequency of 10 Hz and has a maximum value of 0.12 T, (a) What is the average emf induced in the coil during the time it takes for the field
A hospital emergency room ac generator operates at a frequency of 60 Hz. If the output voltage is at a maximum value (magnitude) at t = 0, when is it next (a) A maximum (magnitude), (b) Zero, (c) At its initial value (direction and magnitude)?
A student makes a simple ac generator by using a single square wire loop 10 cm on a side. The loop is then rotated at a frequency of 60 Hz in a magnetic field of 0.015 T. (a) What is the maximum emf output? (b) If she wanted to make the maximum emf output ten times larger by adding loops, how
A simple ac generator consists of a coil with 10 turns (each turn has an area of 50 cm2). The coil rotates in a uniform magnetic field of 350 mT with a frequency of 60 Hz. (a) Write an expression in the form of Eq. 20.5 for the generator’s emf variation with time. (b) Compute the maximum emf.
An ac generator operates at a rotational frequency of 60 Hz and produces a maximum emf of 100 V. Assume that its output at is zero. What is the instantaneous emf (a) At t = 1/240 s? (b) At t = 1/120 s? (c) At t? (d) How much time elapses between successive 0-volt outputs? (e) What maximum emf
A circular loop with an area of 0.015 m2 is in a uniform magnetic field of 0.30 T. What is the flux through the loop’s plane if it is (a) Parallel to the field, (b) At an angle of to the field, and (c) Perpendicular to the field?
The armature of a simple ac generator has 20 circular loops of wire, each with a radius of 10 cm. It is rotated with a frequency of 60 Hz in a uniform magnetic field of 800 mT. (a) What is the maximum emf induced in the loops? (b) How often is this value attained? (c) If the time period in part
The armature of an ac generator has 100 turns. Each turn is a rectangular loop measuring 8.0 cm by 12 cm. The generator has a sinusoidal voltage output with an amplitude of 24 V. (a) If the magnetic field of the generator is 250 mT, with what frequency does the armature turn? (b) If the magnetic
(a) To increase the output of an ac generator, a student has the choice of doubling either the generator’s magnetic field or its frequency. To maximize the increase in emf output, (1) he should double the magnetic field, (2) he should double the frequency, (3) it does not matter which one he
A motor has a resistance of and is connected to a 110-V line. (a) Is the operating current of the motor (1) higher than 44 A, (2) 44 A, or (3) lower than 44 A? Why? (b) If the back emf of the motor at operating speed is 100 V, what is its operating current?
The starter motor in an automobile has a resistance of 0.40 Ω in its armature windings. The motor operates on 12 V and has a back emf of 10 V when running at normal operating speed. How much current does the motor draw (a) When running at its operating speed, (b) When running at half its final
A 240-V dc motor has an armature whose resistance is 1.50Ω. When running at its operating speed, it draws a current of 16.0 A. (a) What is the back emf of the motor when it is operating normally? (b) What is the starting current? (Assume that there is no additional resistance in the circuit.)
The secondary coil of an ideal transformer has 450 turns, and the primary coil has 75 turns. (a) Is this transformer a (1) step-up or (2) step-down transformer? Explain your choice. (b) What is the ratio of the current in the primary coil to the current in the secondary coil? (c) What is the
An ideal transformer steps 8.0 V up to 2000 V, and the 4000-turn secondary coil carries 2.0 A. (a) Find the number of turns in the primary coil. (b) Find the current in the primary coil.
The primary coil of an ideal transformer has 720 turns, and the secondary coil has 180 turns. If the primary coil carries 15 A at a voltage of 120 V, what are (a) The voltage and (b) The output current of the secondary coil?
The transformer in the power supply for a computer’s 500-GB external hard drive changes a 120-V input voltage (from a regular house line) to the 5.0-V output voltage that is required to power the drive. (a) Find the ratio of the number of turns in the primary coil to the number of turns in the
A circular loop (radius of 20 cm) is in a uniform magnetic field of 0.15 T. What angle(s) between the normal to the plane of the loop and the field would result in a flux with a magnitude of 1.4 x 10-2 T ∙ m2?
The primary coil of an ideal transformer is connected to a 120-V source and draws 1.0 A. The secondary coil has 800 turns and supplies an output current of 10 A to run an electrical device. (a) What is the voltage across the secondary coil? (b) How many turns are in the primary coil? (c) If the
An ideal transformer has 840 turns in its primary coil and 120 turns in its secondary coil. If the primary coil draws 2.50 A at 110 V, what are (a) The current and (b) The output voltage of the secondary coil?
The efficiency e of a transformer is defined as the ratio of the power output to the power input, or e = Ps/PP. (a) Show that for an ideal transformer, this expression gives an efficiency of 100%(e = 1.00). (b) Suppose a step-up transformer increased the line voltage from 120 to 240 V, while at
The specifications of a transformer used with a small appliance read as follows: input, 120 V, 6.0 W; output, 9.0 V, 600 mA. (a) Is this transformer (1) an ideal or (2) a nonideal transformer? Why? (b) What is its efficiency?
An ac generator supplies 20 A at 440 V to a 10 000-V power line through a step-up transformer that has 150 turns in its primary coil. (a) If the transformer is efficient (see Exercise 32), how many turns are in the secondary coil? (b) What is the current in the power line?
The electricity supplied in Exercise 34 is transmitted over a line 80.0 km long with a resistance of 0.80 Ω /km. (a) How many kilowatt-hours are saved in 5.00 h by stepping up the voltage? (b) At $0.15/kWh, how much of a savings (to the nearest $ 10) is this to all the consumers the line
A small plant produces electric energy and, through a transformer, sends it out over the transmission lines at 50 A and 20 kV. The line reaches a small town over 25-km-long transmission lines whose resistance is 1.2 Ω /km. (a) What is the power loss in the lines if the energy is transmitted at
Electrical power from a generator is transmitted through a power line 175 km long with a resistance of 1.2 Ω /km. The generator’s output is 50 A at its operating voltage of 440 V. This output is increased by a single step-up for transmission at 44 kV. (a) How much power is lost as joule heat
Find the frequencies of electromagnetic waves with wavelengths of (a) 3.0 cm, (b) 650 nm, and (c) 1.2 fm. (d) Classify the type of light in each case.
In a small town there are only two AM radio stations, one at 920 kHz and one at 1280 kHz. What are the wave-lengths of the radio waves transmitted by each station?
The plane of a conductive loop with an area of 0.020 m2 is perpendicular to a uniform magnetic field of 0.30 T. If the field drops to zero in 0.0045 s, what is the magnitude of the average emf induced in the loop?
A meteorologist for a TV station is using radar to determine the distance to a cloud. He notes that a time of 0.24 ms elapses between the sending and the return of a radar pulse. How far away is the cloud?
How long does a laser beam take to travel from the Earth to a reflector on the Moon and back? Take the distance from the Earth to the Moon to be 2.4 x 105mi. (This experiment was done when the Apollo flights of the early 1970s left laser reflectors on the lunar surface.)
Orange light has a wavelength of 600 nm, and green light has a wavelength of 510 nm. (a) What is the difference in frequency between the two types of light? (b) If you doubled the wavelength of both, what type of light would they become?
A certain type of radio antenna is called a quarter-wavelength antenna, because its length is equal to one-quarter of the wavelength to be received. If you were going to make such antennae for the AM and FM radio bands by using the middle frequencies of each band, what lengths of wire would you use?
Microwave ovens can have cold spots and hot spots due to standing electromagnetic waves, analogous to standing wave nodes and antinodes in strings (Fig. 20.32).(a) The longer the distance between the cold spots, (1) the higher the frequency of the waves, (2) the lower the frequency of the waves,
A basic telephone has both a speaker€“ transmitter and a receiver (Fig. 20.33). Until the advent of digital phones in the 1990s, the transmitter had a diaphragm coupled to a carbon chamber (called the button), which contained loosely packed granules of carbon. As the diaphragm vibrated
In Fig. 20.34, a metal bar moves at constant velocity in a constant magnetic field. That field is directed into the page.(a) The direction of the induced current through the bar is (1) up, (2) down, (3) there is no current. Why? (b) If the magnitude of the magnetic field is 0.55 T, what is the
A transformer is used by a European traveler while she is visiting the United States. She primarily uses it to run a 1200-watt hair dryer she brought with her. When the hair dryer is plugged in to her hotel room outlet in Los Angeles, she notices that it runs exactly as it does at home. The input
A solenoid of length 40.0 cm is made of 10,000 circular coils. It carries a steady current of 12.0 A. Near its center is placed a small, flat, circular metallic coil of 200 circular loops, each with a radius of 2.00 mm. This small coil is oriented so that it receives half of the maximum magnetic
A flat coil of copper wire consists of 100 loops and has a total resistance of . The coil diameter is 4.00 cm and it is in a uniform magnetic field pointing toward you (out the page). The coil orientation is in the plane of the page. It is then pulled to the right (without rotating) until it is
An ideal solenoid with a current of 1.5 A has a radius of 3.0 cm and a turn density of 250 turns/m. (a) What is the magnetic flux (due to its own field) through only one of its loops at its center? (b) What current would be required to double the flux value in part (a)?
The transformer on a utility pole steps the voltage down from 10 000 V to 220 V for use in a college science building. During the day, the transformer delivers electric energy at the rate of 10.0 kW. (a) Assuming the transformer to be ideal, during that time, what are the primary and secondary
Suppose you wanted to build an electric generator using the Earth’s magnetic field. Assume it has a strength of 0.040 mT at your location. Your generator design calls for a coil of 1000 windings rotated at exactly 60 Hz. The coil is oriented so that the normal to the area lines up with the
(a) In May 2008, the United States successfully landed a spacecraft named Phoenix near the northern polar regions of Mars. Immediately upon landing, the craft sent a message indicating that all had gone well. Using the astronomical data in the appendix of this book, determine the shortest amount of

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