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physics
electricity and magnetism

College Physics 7th Edition Raymond A. Serway, Jerry S. Faughn, Chris Vuille, Charles A. Bennett - Solutions

A 0.200-kg metal rod carrying a current of 10.0 A glides on two horizontal rails 0.500 m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient of kinetic friction between the rod and rails is 0.100?
Two species of singly charged positive ions of masses 20.0 x 10–27 kg and 23.4 x 10–27 kg enter a magnetic field at the same location with a speed of 1.00 x 105 m/s. If the strength of the field is 0.200 T, and the ions move perpendicularly to the field, find their distance of separation after
Two parallel conductors carry currents in opposite directions, as shown in Figure. One conductor carries a current of 10.0 A. Point A is the midpoint between the wires, and point C is 5.00 cm to the right of the 10.0-A current. I is adjusted so that the magnetic field at C is zero. Find(a) The
Using an electromagnetic flow meter (Figure), a heart surgeon monitors the flow rate of blood through an artery. Electrodes A and B make contact with the outer surface of the blood vessel, which has interior diameter 3.00 mm.(a) For a magnetic field magnitude of 0.040 0 T, a potential difference of
Two circular loops are parallel, coaxial, and almost in contact 1.00 mm apart (Figure). Each loop is 10.0 cm in radius. The top loop carries a clockwise current of 140 A. The bottom loop carries a counterclockwise current of 140 A.(a) Calculate the magnetic force that the bottom loop exerts on the
A 1.00-kg ball having net charge Q = 5.00 µC is thrown out of a window horizontally at a speed v = 20.0 m/s. The window is at a height h = 20.0 m above the ground. A uniform horizontal magnetic field of magnitude B = 0.010 0 T is perpendicular to the plane of the ball’s trajectory. Find the
The idea that static magnetic fields might have a therapeutic value has been around for centuries. A currently available rare-Earth magnet that is advertised to relieve joint pain is shown in figure. It is 1.0 mm thick and has a field strength of 5.0 x 10?2 T at the center of the flat surface. The
Two long parallel conductors carry currents I1 = 3.00 A and I2 = 3.00 A, both directed into the page in Figure. Determine the magnitude and direction of the resultant magnetic field atP.
A uniform horizontal wire with a linear mass density of 0.50 g/m carries a 2.0-A current. It is placed in a constant magnetic field with a strength of 4.0 x 10–3 T. The field is horizontal and perpendicular to the wire. As the wire moves upward starting from rest, (a) What is its acceleration and
Three long parallel conductors carry currents of I = 2.0 A. Figure is an end view of the conductors, with each current coming out of the page. Given that α = 1.0 cm, determine the magnitude and direction of the magnetic field at points A, B, andC.
Two long parallel wires, each with a mass per unit length of 40 g/m, are supported in a horizontal plane by 6.0-cm-long strings, as shown in figure. Each wire carries the same current I, causing the wires to repel each other so that the angle θ between the supporting strings is 16?.(a) Are the
Protons having a kinetic energy of 5.00MeV are moving in the positive x-direction and enter a magnetic field of 0.050 0 T in the z-direction, out of the plane of the page, and extending from x = 0 to x = 1.00 m as in Figure. (a) Calculate the y -component of the protons? momentum as they leave the
A straight wire of mass 10.0 g and length 5.0 cm is suspended from two identical springs that, in turn, form a closed circuit (Figure). The springs stretch a distance of 0.50 cm under the weight of the wire. The circuit has a total resistance of 12?. When a magnetic field directed out of the page
A solenoid 10.0 cm in diameter and 75.0 cm long is made from copper wire of diameter 0.100 cm with very thin insulation. The wire is wound onto a cardboard tube in a single layer, with adjacent turns touching each other. To produce a field of magnitude 20.0mT at the center of the solenoid, what
Assume that the region to the right of a certain vertical plane contains a vertical magnetic field of magnitude 1.00mT and that the field is zero in the region to the left of the plane. An electron, originally traveling perpendicular to the boundary plane, passes into the region of the field.(a)
Three long wires (wire 1, wire 2, and wire 3) are coplanar and hang vertically. The distance between wire 1 and wire 2 is 20.0 cm. On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 4.00 A. Wire 3 is located such that when it carries a
Two long parallel conductors separated by 10.0 cm carry currents in the same direction. The first wire carries a current I1 = 5.00 A and the second carries I2 = 8.00 A.(a) What is the magnitude of the magnetic field created by I1 at the location of I2? (b) What is the force per unit length exerted
Can a constant magnetic field set a proton at rest into motion? Explain your answer.
No magnetic force acts upon a current-carrying conductor when it is placed in a certain manner in a uniform magnetic field. Explain.
1. Which way would a compass point if you were at Earth’s north magnetic pole?2. A magnet attracts a piece of iron. The iron can then attract another piece of iron. On the basis of domain alignment, explain what happens in each piece of iron.
Describe the change in the magnetic field in the space enclosed by a solenoid carrying a steady current I if(a) The length of the solenoid is doubled, but the number of turns remains the same, and(b) The number of turns is doubled, but the length remains the same.
Why do charged particles from outer space, called cosmic rays, strike Earth more frequently at the poles than at the equator?
How can a current loop be used to determine the presence of a magnetic field in a given region of space?
1. Is it possible to orient a current loop in a uniform magnetic field such that the loop will not tend to rotate?2. Will a nail be attracted to either pole of a magnet? Explain what is happening inside the nail when it is placed near the magnet.3. A wire carries a current of 10.0 A in a direction
Is the magnetic field created by a current loop uniform? Explain.
Is it possible to induce a constant emf for an infinite amount of time?
Find the flux of the Earth’s magnetic field of magnitude 5.00 x 10–5 T through a square loop of area 20.0 cm2(a) When the field is perpendicular to the plane of the loop, (b) When the field makes a 30.0° angle with the normal to the plane of the loop, and (c) When the field makes a 90.0°
A square loop 2.00 m on a side is placed in a magnetic field of magnitude 0.300 T. If the field makes an angle of 50.0° with the normal to the plane of the loop, find the magnetic flux through the loop.
A bar magnet is held above the center of a wire loop in a horizontal plane, as shown in Figure. The south end of the magnet is toward the loop. The magnet is dropped. Find the direction of the current in the resistor as viewed from above(a) While the magnet is falling toward the loop and(b) After
A long, straight wire lies in the plane of a circular coil with a radius of 0.010 m. The wire carries a current of 2.0 A and is placed along a diameter of the coil. (a) What is the net flux through the coil? (b) If the wire passes through the center of the coil and is perpendicular to the plane of
A solenoid 4.00 cm in diameter and 20.0 cm long has 250 turns and carries a current of 15.0 A. Calculate the magnetic flux through the circular cross-sectional area of the solenoid.
A cube of edge length ?? = 2.5 cm is positioned as shown in figure. There is a uniform magnetic field throughout the region with components Bx = + 5.0 T, By = + 4.0 T, and Bz = + 3.0 T.(a) Calculate the flux through the shaded face of the cube.(b) What is the total flux emerging from the volume
A magneto is used to cause the spark in a spark plug in many lawn mowers today. A magneto consists of a permanent magnet mounted on a flywheel so that it spins past a fixed coil. Explain how this arrangement generates a large enough potential difference to cause the spark.
A square, single-turn coil 0.20 m on a side is placed with its plane perpendicular to a constant magnetic field. An emf of 18 mV is induced in the coil winding when the area of the coil decreases at the rate of 0.10 m2/s. What is the magnitude of the magnetic field?
The flexible loop in figure has a radius of 12 cm and is in a magnetic field of strength 0.15 T. The loop is grasped at points A and B and stretched until its area is nearly zero. If it takes 0.20 s to close the loop, find the magnitude of the average induced emf in it during thistime.
A wire loop of radius 0.30 m lies so that an external magnetic field of magnitude 0.30 T is perpendicular to the loop. The field reverses its direction, and its magnitude changes to 0.20 T in 1.5 s. Find the magnitude of the average induced emf in the loop during this time.
A 500-turn circular-loop coil 15.0 cm in diameter is initially aligned so that its axis is parallel to the Earth’s magnetic field. In 2.77 ms, the coil is flipped so that its axis is perpendicular to the Earth’s magnetic field. If an average voltage of 0.166 V is thereby induced in the coil,
The plane of a rectangular coil, 5.0 cm by 8.0 cm, is perpendicular to the direction of a magnetic field B. If the coil has 75 turns and a total resistance of 8.0 Ω, at what rate must the magnitude of B change to induce a current of 0.10 A in the windings of the coil?
A square, single-turn wire loop 1.00 cm on a side is placed inside a solenoid that has a circular cross section of radius 3.00 cm, as shown in figure. The solenoid is 20.0 cm long and wound with 100 turns of wire.(a) If the current in the solenoid is 3.00 A, find the flux through the loop.(b) If
A 300-turn solenoid with a length of 20 cm and a radius of 1.5 cm carries a current of 2.0 A. A second coil of four turns is wrapped tightly about this solenoid so that it can be considered to have the same radius as the solenoid. Find (a) The change in the magnetic flux through the coil and (b)
A circular coil enclosing an area of 100 cm2 is made of 200 turns of copper wire. The wire making up the coil has resistance of 5.0 Ω, and the ends of the wire are connected to form a closed circuit. Initially, a 1.1-T uniform magnetic field points perpendicularly upward through the plane of the
To monitor the breathing of a hospital patient, a thin belt is girded around the patient?s chest as in figure. The belt is a 200-turn coil. When the patient inhales, the area encircled by the coil increases by 39.0 cm2. The magnitude of the Earth?s magnetic field is 50.0 ?T and makes an angle of
Consider the arrangement shown in figure. Assume that R = 6.00 Ω and ℓ = 1.20 m, and that a uniform 2.50-T magnetic field is directed into the page. At what speed should the bar be moved to produce a current of 0.500 A in the resistor?
A Boeing 747 jet with a wingspan of 60.0 m is flying horizontally at a speed of 300 m/s over Phoenix, Arizona, at a location where the Earth?s magnetic field is 50.0 ?T at 58.0? below the horizontal. What voltage is generated between the wingtips?
A 12.0-m-long steel beam is accidentally dropped by a construction crane from a height of 9.00 m. The horizontal component of the Earth’s magnetic field over the region is 18.0 µT. What is the induced emf in the beam just before impact with the Earth? Assume the long dimension of the beam
An automobile has a vertical radio antenna 1.20 m long. The automobile travels at 65.0 km/h on a horizontal road where the Earth’s magnetic field is 50.0 µT, directed toward the north and downwards at an angle of 65.0° below the horizontal. (a) Specify the direction the automobile should move
A helicopter has blades of length 3.0 m, rotating at 2.0 rev/s about a central hub. If the vertical component of Earth’s magnetic field is 5.0 x 10–5 T, what is the emf induced between the blade tip and the central hub?
A bar magnet is positioned near a coil of wire as shown in figure. What is the direction of the current in the resistor when the magnet is moved?(a) To the left?(b) To theright?
A conducting rectangular loop of mass M, resistance R, and dimensions w by ? falls from rest into a magnetic field B as shown in figure. During the time interval before the top edge of the loop reaches the field, the loop approaches a terminal speed vT. (a) Show that vT = MgR/B2w2 (b) Why is vT
A rectangular coil with resistance R has N turns, each of length ? and width w as shown in figure. The coil moves into a uniform magnetic field with constant velocity v. What are the magnitude and direction of the total magnetic force on the coil (a) As it enters the magnetic field, (b) As it moves
In figure what is the direction of the current induced in the resistor at the instant the switch isclosed?
A copper bar is moved to the right while its axis is maintained in a direction perpendicular to a magnetic field, as shown in figure. If the top of the bar becomes positive relative to the bottom, what is the direction of the magneticfield?
Find the direction of the current in the resistor shown in figure(a) At the instant the switch is closed,(b) After the switch has been closed for several minutes, and(c) At the instant the switch isopened.
Find the direction of the current in the resistor R shown in figure after each of the following steps (taken in the order given):(a) The switch is closed.(b) The variable resistance in series with the battery is decreased.(c) The circuit containing resistor R is moved to the left.(d) The switch
A 100-turn square wire coil of area 0.040 m2 rotates about a vertical axis at 1500 rev/min, as indicated in figure. The horizontal component of the Earth's magnetic field at the location of the loop is 2.0 x 10'5 T. Calculate the maximum emf induced in the coil by the Earth's field.
Considerable scientific work is currently underway to determine whether weak oscillating magnetic fields such as those found near outdoor electric power lines can effect human health. One study indicated that a magnetic field of magnitude 1.0 x 10–3 T, oscillating at 60 Hz, might stimulate red
A motor has coils with a resistance of 30 Ω and operates from a voltage of 240 V. When the motor is operating at its maximum speed, the back emf is 145 V. Find the current in the coils (a) When the motor is first turned on and (b) When the motor has reached maximum speed.(c) If the current in the
A coil of 10.0 turns is in the shape of an ellipse having a major axis of 10.0 cm and a minor axis of 4.00 cm. The coil rotates at 100 rpm in a region in which the magnitude of the Earth’s magnetic field is 55 µT. What is the maximum voltage induced in the coil if the axis of rotation of the
A flat coil enclosing an area of 0.10 m2 is rotating at 60 rev/s, with its axis of rotation perpendicular to a 0.20-T magnetic field.(a) If there are 1 000 turns on the coil, what is the maximum voltage induced in the coil?(b) When the maximum induced voltage occurs, what is the orientation of the
In a model AC generator, a 500-turn rectangular coil 8.0 cm by 20 cm rotates at 120 rev/min in a uniform magnetic field of 0.60 T. (a) What is the maximum emf induced in the coil? (b) What is the instantaneous value of the emf in the coil at t = (π/32) s? Assume that the emf is zero at t = 0. (c)
A coiled telephone cord forms a spiral with 70.0 turns, a diameter of 1.30 cm, and an unstretched length of 60.0 cm. Determine the self-inductance of one conductor in the unstretched cord.
A coil has an inductance of 3.0 mH, and the current in it changes from 0.20 A to 1.5 A in 0.20 s. Find the magnitude of the average induced emf in the coil during this period.
Show that the two expressions for inductance given by have the sameunits.
A solenoid of radius 2.5 cm has 400 turns and a length of 20 cm. Find (a) Its inductance and (b) The rate at which current must change through it to produce an emf of 75 mV.
An emf of 24.0 mV is induced in a 500-turn coil when the current is changing at a rate of 10.0 A/s. What is the magnetic flux through each turn of the coil at an instant when the current is 4.00 A?
Show that the SI units for the inductive time constant τ = L/R are seconds.
An RL circuit with L = 3.00 H and an RC circuit with C = 3.00 F have the same time constant. If the two circuits have the same resistance R, (a) What is the value of R and (b) What is this common time constant?
A 6.0-V battery is connected in series with a resistor and an inductor. The series circuit has a time constant of 600 µs, and the maximum current is 300 mA. What is the value of the inductance?
A 25-mH inductor, an 8.0-Ω resistor, and a 6.0-V battery are connected in series. The switch is closed at t = 0. Find the voltage drop across the resistor (a) At t = 0 and (b) After one time constant has passed. Also, find the voltage drop across the inductor (c) At t = 0 and (d) After one time
Calculate the resistance in an RL circuit in which L = 2.50 H and the current increases to 90.0% of its final value in 3.00 s.
Consider the circuit shown in figure. Take ? = 6.00 V, L = 8.00 mH, and R = 4.00 ?. (a) What is the inductive time constant of the circuit? (b) Calculate the current in the circuit 250 ?s after the switch is closed. (c) What is the value of the final steady-state current? (d) How long does it take
How much energy is stored in a 70.0-mH inductor at an instant when the current is 2.00 A?
A 300-turn solenoid has a radius of 5.00 cm and a length of 20.0 cm. Find (a) The inductance of the solenoid and(b) The energy stored in the solenoid when the current in its windings is 0.500 A.
A 24-V battery is connected in series with a resistor and an inductor, with R = 8.0 Ω andL = 4.0 H, respectively. Find the energy stored in the inductor (a) When the current reaches its maximum value and (b) One time constant after the switch is closed.
What is the time constant for?(a) The circuit shown in Figure a and(b) The circuit shown in Figureb?
In figure the bar magnet is being moved toward the loop. Is (V? ? Vb) positive, negative, or zero during this motion? Explain.
Your physics teacher asks you to help her set up a demonstration of Faraday's law for the class. The apparatus consists of a strong permanent magnet that has a field of 0.10 T, a small 10-turn coil of radius 2.0 cm cemented on a wood frame with a handle, some flexible connecting wires, and an
An 820-turn wire coil of resistance 24.0 ? is placed on top of a 12 500-turn, 7.00-cm-long solenoid, as in figure. Both coil and solenoid have cross-sectional areas of 1.00 x 10?4 m2. (a) How long does it take the solenoid current to reach 0.632 times its maximum value? (b) Determine the average
Figure is a graph of induced emf versus time for a coil of N turns rotating with angular speed w in a uniform magnetic field directed perpendicular to the axis of rotation of the coil. Copy this sketch (increasing the scale), and, on the same set of axes, show the graph of emf versus t when(a) The
The plane of a square loop of wire with edge length ? = 0.200 m is perpendicular to the Earth?s magnetic field at a point where B = 15.0 ?T, as in figure. The total resistance of the loop and the wires connecting it to the ammeter is 0.500 ?. If the loop is suddenly collapsed by horizontal forces
A novel method of storing electrical energy has been proposed. A huge underground superconducting coil 1.00 km in diameter would be fabricated. It would carry a maximum current of 50.0 kA through each winding of a 150-turn Nb3Sn solenoid.(a) If the inductance of this huge coil were 50.0 H, what is
A conducting rod of length ℓ moves on two horizontal frictionless rails, as in figure. A constant force of magnitude 1.00 N moves the bar at a uniform speed of 2.00 m/s through a magnetic field that is directed into the page. (a) What is the current in an 8.00-Ω resistor R?(b) What is the rate
The square loop in figure is made of wires with a total series resistance of 10.0 ?. It is placed in a uniform 0.100-T magnetic field directed perpendicular into the plane of the paper. The loop, which is hinged at each corner, is pulled as shown until the separation between points A and B is 3.00
The bolt of lightning depicted in figure passes 200 m from a 100-turn coil oriented as shown. If the current in the lightning bolt falls from 6.02 x 106 A to zero in 10.5 ?s, what is the average voltage induced in the coil? Assume that the distance to the center of the coil determines the average
The wire shown in figure is bent in the shape of a ?tent? with ? = 60? and L = 1.5 m, and is placed in a uniform magnetic field of 0.30 T directed perpendicular to the tabletop. The wire is ?hinged? at points a and b. If the tent is flattened out on the table in 0.10 s, what is the average induced
The magnetic field shown in figure has a uniform magnitude of 25.0 mT directed into the paper. The initial diameter of the kink is 2.00 cm. (a) The wire is quickly pulled taut, and the kink shrinks to a diameter of zero in 50.0 ms. Determine the average voltage induced between endpoints A and B.
An aluminum ring of radius 5.00 cm and resistance 3.00 x 10?4?? is placed around the top of a long air-core solenoid with 1 000 turns per meter and a smaller radius of 3.00 cm, as in figure. If the current in the solenoid is increasing at a constant rate of 270 A/s, what is the induced current in
In figure the rolling axle, 1.50 m long, is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resistor R = 0.400 ? is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, so the axle, rails, and R form a
In 1832, Faraday proposed that the apparatus shown in figure could be used to generate electric current from the water flowing in the Thames River.2 Two conducting plates of length a and width b are placed facing one another on opposite sides of the river, a distance w apart and immersed entirely.
A horizontal wire is free to slide on the vertical rails of a conducting frame, as in figure. The wire has mass m and length ?, and the resistance of the circuit is R. If a uniform magnetic field is directed perpendicular to the frame, what is the terminal speed of the wire as it falls under the
A one-turn coil of wire of area 0.20 m2 and resistance 0.25 ? is in a magnetic field that varies with time as shown in Figure a. The magnetic flux through the coil at t = 0 is as shown in Figure b. (a) When is the induced current the largest? (b) When is it zero? (c) Is the induced current always
A loop of wire is placed in a uniform magnetic field. For what orientation of the loop is the magnetic flux a maximum? For what orientation is the flux zero?
1. As the bar in Figure moves perpendicular to the field, is an external force required to keep it moving with constant speed?2. Does dropping a magnet down a copper tube produce a current in the tube?Explain.
How is electrical energy produced in dams? (That is, how is the energy of motion of the water converted to AC electricity?)
Suppose you would like to steal power for your home from the electric company by placing a loop of wire near a transmission cable in order to induce an emf in the loop (Don’t do this; it’s illegal.) Should you locate the loop so that the transmission cable passes through your loop or simply
A bar magnet is dropped toward a conducting ring lying on the floor. As the magnet falls toward the ring, does it move as a freely falling object?
1. A long, straight wire carrying a current of 2.00 A is placed along the axis of a cylinder of radius 0.500 m and a length of 3.00 m. Determine the total magnetic flux through the cylinder.2. Transcranial magnetic stimulation (TMS) is a noninvasive technique used to stimulate regions of the human
An rms voltage of 100 V is applied to a purely resistive load of 5.00 Ω. Find (a) The maximum voltage applied, (b) The rms current supplied, (c) The maximum current supplied, and (d) The power dissipated.
(a) What is the resistance of a lightbulb that uses an average power of 75.0 W when connected to a 60-Hz power source with an peak voltage of 170 V? (b) What is the resistance of a 100-W bulb?
An AC power supply that produces a maximum voltage of ?Vmax = 100 V is connected to a 24.0- ? resistor. The current and the resistor voltage are respectively measured with an ideal AC ammeter and an ideal AC voltmeter, as shown in figure. What does each meter read? Note that an ideal ammeter has

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