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physics
modern physics
Physics 10th edition David Young, Shane Stadler - Solutions
The rear window of a van is coated with a layer of ice at 0 °C. The density of ice is 917 kg/m3. The driver of the van turns on the rear-window defroster, which operates at 12 V and 23 A. The defroster directly heats an area of 0.52 m2 of the rear window. What is the maximum thickness of ice
A piece of Nichrome wire has a radius of 6.5 × 10-4 m. It is used in a laboratory to make a heater that uses 4.00 × 102 W of power when connected to a voltage source of 120 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.
According to Equation 20.7, an ac voltage V is given as a function of time t by V = V0 sin 2πft, where V0 is the peak voltage and f is the frequency (in hertz). For a frequency of 60.0 Hz, what is the smallest value of the time at which the voltage equals one-half of the peak value?
The rms current in a copy machine is 6.50 A, and the resistance of the machine is 18.6 V. What are (a) The average power and (b) The peak power delivered to the machine?
The rms current in a 47-Ω resistor is 0.50 A. What is the peak value of the voltage across this resistor?
A 550-W space heater is designed for operation in Germany, where household electrical outlets supply 230 V (rms) service. What is the power output of the heater when plugged into a 120-V (rms) electrical outlet in a house in the United States? Ignore the effects of temperature on the heater's
Review Conceptual Example 7 as an aid in solving this problem. A portable electric heater uses 18 A of current. The manufacturer recommends that an extension cord attached to the heater receive no more than 2.0 W of power per meter of length. What is the smallest radius of copper wire that can be
The recovery time of a hot water heater is the time required to heat all the water in the unit to the desired temperature. Suppose that a 52-gal (1.00 gal = 3.79 × 10-3 m3) unit starts with cold water at 11 °C and delivers hot water at 53 °C. The unit is electric and utilizes a resistance heater
A coffee-maker contains a heating element that has a resistance of 14 Ω. This heating element is energized by a 120-V outlet. What is the current in the heating element?
To save on heating costs, the owner of a greenhouse keeps 660 kg of water around in barrels. During a winter day, the water is heated by the sun to 10.0 °C. During the night the water freezes into ice at 0.0 °C in nine hours. What is the minimum ampere rating of an electric heating system (240 V)
A 60.0-W lamp is placed in series with a resistor and a 120.0-V source. If the voltage across the lamp is 25 V, what is the resistance R of the resistor?
Multiple-Concept Example 9 discusses the physics principles used in this problem. Three resistors, 2.0, 4.0, and 6.0 Ω, are connected in series across a 24-V battery. Find the power delivered to each resistor.
The current in a 47-Ω resistor is 0.12 A. This resistor is in series with a 28-Ω resistor, and the series combination is connected across a battery. What is the battery voltage?
Multiple-Concept Example 9 reviews the concepts that are important to this problem. A light bulb is wired in series with a 144-Ω resistor, and they are connected across a 120.0-V source. The power delivered to the light bulb is 23.4 W. What is the resistance of the light bulb? Note that there are
One heater uses 340 W of power when connected by itself to a battery. Another heater uses 240 W of power when connected by itself to the same battery. How much total power do the heaters use when they are both connected in series across the battery?
Two resistances, R1 and R2, are connected in series across a 12-V battery. The current increases by 0.20 A when R2 is removed, leaving R1 connected across the battery. However, the current increases by just 0.10 A when R1 is removed, leaving R2 connected across the battery. Find (a) R1 and (b) R2.
Suppose that the resistance between the walls of a biological cell is 5.0 × 109 Ω. (a) What is the current when the potential difference between the walls is 75 mV? (b) If the current is composed of Na+ ions (q = +e), how many such ions flow in 0.50 s?
A coffee-maker (14 Ω) and a toaster (19 Ω) are connected in parallel to the same 120-V outlet in a kitchen. How much total power is supplied to the two appliances when both are turned on?
For the three-way bulb (50 W, 100 W, 150 W) discussed in Conceptual Example 11, find the resistance of each of the two filaments. Assume that the wattage ratings are not limited by signify cant figures, and ignore any heating effects on the resistances.
The drawing shows three different resistors in two different circuits. The battery has a voltage of V = 24.0 V, and the resistors have values of R1 = 50.0 Ω, R2 = 25.0 Ω, and R3 = 10.0 Ω.(a) For the circuit on the left, determine the current through and the
A 16-Ω loudspeaker, an 8.0-Ω loudspeaker, and a 4.0-Ω loudspeaker are connected in parallel across the terminals of an amplifier. Determine the equivalent resistance of the three speakers, assuming that they all behave as resistors.
Two identical resistors are connected in parallel across a 25-V battery, which supplies them with a total power of 9.6 W. While the battery is still connected, one of the resistors is heated so that its resistance doubles. The resistance of the other resistor remains unchanged. Find (a) The initial
A coffee cup heater and a lamp are connected in parallel to the same 120-V outlet. Together, they use a total of 111 W of power. The resistance of the heater is 4.0 × 102 Ω. Find the resistance of the lamp.
Two resistors have resistances R1 and R2. When the resistors are connected in series to a 12.0-V battery, the current from the battery is 2.00 A. When the resistors are connected in parallel to the battery, the total current from the battery is 9.00 A. Determine R1 and R2.
A car battery has a rating of 220 ampere · hours (A · h). This rating is one indication of the total charge that the battery can provide to a circuit before failing. (a) What is the total charge (in coulombs) that this battery can provide? (b) Determine the maximum current that the battery can
The drawing shows two circuits, and the same battery is used in each. The two resistances RA in circuit A are the same, and the two resistances RB in circuit B are the same. Knowing that the same total power is delivered in each circuit, find the ratio RB/RA for the circuits.
The rear window defogger of a car consists of thirteen thin wires (resistivity = 88.0 × 10-8 Ω·m) embedded in the glass. The wires are connected in parallel to the 12.0-V battery, and each has a length of 1.30 m. The defogger can melt 2.10 × 10-2 kg of ice at 0 °C into water at 0 °C in two
A 60.0-V resistor is connected in parallel with a 120.0-Ω resistor. This parallel group is connected in series with a 20.0-Ω resistor. The total combination is connected across a 15.0-V battery. Find (a) The current and (b) The power delivered to the 120.0-Ω resistor.
Find the equivalent resistance between points A and B in the drawing.
The circuit in the drawing contains three identical resistors. Each resistor has a value of 10.0 Ω. Determine the equivalent resistance between the points a and b, b and c, and a and c.
Find the equivalent resistance between the points A and B in the drawing.
A square, current-carrying loop is placed in a uniform magnetic field with the plane of the loop parallel to the magnetic field (see the drawing). The dashed line is the axis of rotation. The magnetic field exerts _______.(a) A net force and a net torque on the loop(b) A net force, but not a net
The drawing shows four situations in which two very long wires are carrying the same current, although the directions of the currents may be different. The point P in the drawings is equidistant from each wire. Which one (or more) of these situations gives rise to a zero net magnetic field at P?(a)
Three long, straight wires are carrying currents that have the same magnitude. In C the current is opposite to the current in A and B. The wires are equally spaced. Each wire experiences a net force due to the other two wires. Which wire experiences a net force with the greatest magnitude?(a) A(b)
At a location near the equator, the earth's magnetic field is horizontal and points north. An electron is moving vertically upward from the ground. What is the direction of the magnetic force that acts on the electron? (a) North (b) East (c) South (d) West (e) The magnetic force is zero.
Three particles are moving perpendicular to a uniform magnetic field and travel on circular paths (see the drawing). The particles have the same mass and speed. List the particles in order of their charge magnitude, largest to smallest.(a) 3, 2, 1(b) 3, 1, 2(c) 2, 3, 1(d) 1, 3, 2(e) 1, 2, 3
The drawing shows the circular paths of an electron and a proton. These particles have the same charge magnitudes, but the proton is more massive. They travel at the same speed in a uniform magnetic field , which is directed into the page everywhere. Which particle follows the larger circle, and
One component of a magnetic field has a magnitude of 0.048 T and points along the +x axis, while the other component has a magnitude of 0.065 T and points along the -y axis. A particle carrying a charge of +2.0 × 10-5 C is moving along the +z axis at a speed of 4.2 × 103 m/s. (a) Find the
An ionized helium atom has a mass of 6.6 × 10-27 kg and a speed of 4.4 × 105 m/s. It moves perpendicular to a 0.75-T magnetic field on a circular path that has a 0.012-m radius. Determine whether the charge of the ionized atom is +e or +2e.
A charged particle with a charge-to-mass ratio of |q|/m = 5.7 × 108 C/kg travels on a circular path that is perpendicular to a magnetic field whose magnitude is 0.72 T. How much time does it take for the particle to complete one revolution?
A charged particle enters a uniform magnetic field and follows the circular path shown in the drawing.(a) Is the particle positively or negatively charged? Why?(b) The particle's speed is 140 m/s, the magnitude of the magnetic field is 0.48 T, and the radius of the path is 960 m. Determine the mass
A proton is projected perpendicularly into a magnetic field that has a magnitude of 0.50 T. The field is then adjusted so that an electron will follow a circular path of the same radius when it is projected perpendicularly into the field with the same velocity that the proton had. What is the
Suppose that an ion source in a mass spectrometer produces doubly ionized gold ions (Au2+), each with a mass of 3.27 × 10-25 kg. The ions are accelerated from rest through a potential difference of 1.00 kV. Then, a 0.500-T magnetic field causes the ions to follow a circular path. Determine the
An a-particle has a charge of +2e and a mass of 6.64 × 10-27 kg. It is accelerated from rest through a potential difference that has a value of 1.20 × 106 V and then enters a uniform magnetic field whose magnitude is 2.20 T. The α-particle moves perpendicular to the magnetic field at all times.
(a) A proton, traveling with a velocity of 4.5 × 106 m/s due east, experiences a magnetic force that has a maximum magnitude of 8.0 × 10-14 N and a direction of due south. What are the magnitude and direction of the magnetic field causing the force? (b) Repeat part (a) assuming the proton is
Particle 1 and particle 2 have masses of m1 = 2.3 × 10-8 kg and m2 = 5.9 × 10-8 kg, but they carry the same charge q. The two particles accelerate from rest through the same electric potential difference V and enter the same magnetic field, which has a magnitude B. The particles travel
Two of the isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 × 10-27 kg and 21.59 × 10-27 kg, respectively. These two isotopes are singly ionized (+e), each given a speed of 6.667 × 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is
The ion source in a mass spectrometer produces both singly and doubly ionized species, X+ and X2+. The difference in mass between these species is too small to be detected. Both species are accelerated through the same electric potential difference, and both experience the same magnetic field,
Review Conceptual Example 2 as an aid in understanding this problem. A velocity selector has an electric field of magnitude 2470 N/C, directed vertically upward, and a horizontal magnetic field that is directed south. Charged particles, traveling east at a speed of 6.50 × 103 m/s, enter the
Conceptual Example 4 provides background pertinent to this problem. An electron has a kinetic energy of 2.0 × 10-17 J. It moves on a circular path that is perpendicular to a uniform magnetic field of magnitude 5.3 × 10-5 T. Determine the radius of the path.
A positively charged particle of mass 7.2 × 10-8 kg is traveling due east with a speed of 85 m/s and enters a 0.31-T uniform magnetic field. The particle moves through one-quarter of a circle in a time of 2.2 × 10-3 s, at which time it leaves the field heading due south. All during the motion the
Review Conceptual Example 2 as background for this problem. A charged particle moves through a velocity selector at a constant speed in a straight line. The electric field of the velocity selector is 3.80 × 103 N/C, while the magnetic field is 0.360 T. When the electric field is turned off, the
Refer to Check Your Understanding Question 10 before starting this problem. Suppose that the target discussed there is located at the coordinates x = -0.10 m and y = -0.10 m. In addition, suppose that the particle is a proton and the magnetic field has a magnitude of 0.010 T. The speed at which the
At New York City, the earth's magnetic field has a vertical component of 5.2 × 10-5 T that points downward (perpendicular to the ground) and a horizontal component of 1.8 × 10-5 T that points toward geographic north (parallel to the ground). What are the magnitude and direction of the magnetic
A straight wire in a magnetic field experiences a force of 0.030 N when the current in the wire is 2.7 A. The current in the wire is changed, and the wire experiences a force of 0.047 N as a result. What is the new current?
A horizontal wire of length 0.53 m, carrying a current of 7.5 A, is placed in a uniform external magnetic field. When the wire is horizontal, it experiences no magnetic force. When the wire is tilted upward at an angle of 19°, it experiences a magnetic force of 4.4 × 10-3 N. Determine the
The drawing shows a wire composed of three segments, AB, BC, and CD. There is a current of I = 2.8 A in the wire. There is also a magnetic field (magnitude = 0.26 T) that is the same everywhere and points in the direction of the +z axis. The lengths of the wire segments are LAB = 1.1 m, LBC = 0.55
Two insulated wires, each 2.40 m long, are taped together to form a two-wire unit that is 2.40 m long. One wire carries a current of 7.00 A; the other carries a smaller current I in the opposite direction. The two-wire unit is placed at an angle of 65.0° relative to a magnetic field whose
A loop of wire has the shape of a right triangle (see the drawing) and carries a current of I = 4.70 A. A uniform magnetic field is directed parallel to side AB and has a magnitude of 1.80 T.(a) Find the magnitude and direction of the magnetic force exerted on each side of the triangle.(b)
A copper rod of length 0.85 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring that has a spring constant of k = 75 N/m. A magnetic field with a strength of 0.16 T is oriented perpendicular to the surface of the table.(a)
A charge of -8.3 μC is traveling at a speed of 7.4 × 106 m/s in a region of space where there is a magnetic field. The angle between the velocity of the charge and the field is 52°. A force of magnitude 5.4 × 10-3 N acts on the charge. What is the magnitude of the magnetic field?
A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.20 m and a mass of 0.080 kg. A uniform magnetic field of magnitude 0.070 T is directed from the ceiling to the floor. When a current of I = 42 A exists in the wire, the wire swings upward and,
The two conducting rails in the drawing are tilted upward so they each make an angle of 30.0° with respect to the ground. The vertical magnetic field has a magnitude of 0.050 T. The 0.20-kg aluminum rod (length = 1.6 m) slides without friction down the rails at a constant velocity. How much
Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field as in Figure 21.19. Coil 1 has a radius of 5.0 cm and rotates in a 0.18-T field. Coil 2 rotates in a 0.42-T field. Each coil experiences the same maximum torque. What is the radius (in cm)
The 1200-turn coil in a dc motor has an area per turn of 1.1 × 10-2 m2. The design for the motor specifies that the magnitude of the maximum torque is 5.8 N · m when the coil is placed in a 0.20-T magnetic field. What is the current in the coil?
Two circular coils of current-carrying wire have the same magnetic moment. The first coil has a radius of 0.088 m, has 140 turns, and carries a current of 4.2 A. The second coil has 170 turns and carries a current of 9.5 A. What is the radius of the second coil?
A wire has a length of 7.00 × 10-2 m and is used to make a circular coil of one turn. There is a current of 4.30 A in the wire. In the presence of a 2.50-T magnetic field, what is the maximum torque that this coil can experience?
The coil of wire in the drawing is a right triangle and is free to rotate about an axis that is attached along side AC. The current in the loop is I = 4.70 A, and the magnetic field (parallel to the plane of the loop and side AB) is B = 1.80 T.(a) What is the magnetic moment of the loop, and(b)
Two pieces of the same wire have the same length. From one piece, a square coil containing a single loop is made. From the other, a circular coil containing a single loop is made. The coils carry different currents. When placed in the same magnetic field with the same orientation, they experience
You have a wire of length L = 1.00 m from which to make the square coil of a dc motor. The current in the coil is I = 1.7 A, and the magnetic field of the motor has a magnitude of B = 0.34 T. Find the maximum torque exerted on the coil when the wire is used to make a single-turn square coil and a
When a charged particle moves at an angle of 25° with respect to a magnetic field, it experiences a magnetic force of magnitude F. At what angle (less than 90°) with respect to this field will this particle, moving at the same speed, experience a magnetic force of magnitude 2F?
A square coil and a rectangular coil are each made from the same length of wire. Each contains a single turn. The long sides of the rectangle are twice as long as the short sides. Find the ratio tsquare/trectangle of the maximum torques that these coils experience in the same magnetic field when
The coil in Figure 21.19a contains 410 turns and has an area per turn of 3.1 × 10-3 m2. The magnetic field is 0.23 T, and the current in the coil is 0.26 A. A brake shoe is pressed perpendicularly against the shaft to keep the coil from turning. The coefficient of static friction
In the model of the hydrogen atom created by Niels Bohr, the electron moves around the proton at a speed of 2.2 × 106 m/s in a circle of radius 5.3 × 10-11 m. Considering the orbiting electron to be a small current loop, determine the magnetic moment associated with this motion.
A long solenoid has a length of 0.65 m and contains 1400 turns of wire. There is a current of 4.7 A in the wire. What is the magnitude of the magnetic field within the solenoid?
A long solenoid has 1400 turns per meter of length, and it carries a current of 3.5 A. A small circular coil of wire is placed inside the solenoid with the normal to the coil oriented at an angle of 90.0° with respect to the axis of the solenoid. The coil consists of 50 turns, has an area of 1.2
Two rigid rods are oriented parallel to each other and to the ground. The rods carry the same current in the same direction. The length of each rod is 0.85 m, and the mass of each is 0.073 kg. One rod is held in place above the ground, while the other fl oats beneath it at a distance of 8.2 × 10-3
Two long, straight wires are separated by 0.120 m. The wires carry currents of 8.0 A in opposite directions, as the drawing indicates. Find the magnitude of the net magnetic field at the points labeled(a) A and(b) B.
A particle that has an 8.2 μC charge moves with a velocity of magnitude 5.0 × 105 m/s along the +x axis. It experiences no magnetic force, although there is a magnetic field present. The maximum possible magnetic force that the charge could experience has a magnitude of 0.48 N. Find the magnitude
A long, straight wire carrying a current of 305 A is placed in a uniform magnetic field that has a magnitude of 7.00 × 10-3 T. The wire is perpendicular to the field. Find a point in space where the net magnetic field is zero. Locate this point by specifying its perpendicular distance from the
Two circular coils are concentric and lie in the same plane. The inner coil contains 140 turns of wire, has a radius of 0.015 m, and carries a current of 7.2 A. The outer coil contains 180 turns and has a radius of 0.023 m. What must be the magnitude and direction (relative to the current in the
A small compass is held horizontally, the center of its needle a distance of 0.280 m directly north of a long wire that is perpendicular to the earth's surface. When there is no current in the wire, the compass needle points due north, which is the direction of the horizontal component of the
Two infinitely long, straight wires are parallel and separated by a distance of one meter. They carry currents in the same direction. Wire 1 carries four times the current that wire 2 carries. On a line drawn perpendicular to both wires, locate the spot (relative to wire 1) where the net magnetic
The drawing shows two perpendicular, long, straight wires, both of which lie in the plane of the paper. The current in each of the wires is I = 5.6 A. Find the magnitudes of the net magnetic fields at points A and B.
The drawing shows two wires that both carry the same current of I = 85.0 A and are oriented perpendicular to the plane of the paper. The current in one wire is directed out of the paper, while the current in the other is directed into the paper. Find the magnitude and direction of the net magnetic
The drawing shows two long, straight wires that are suspended from a ceiling. The mass per unit length of each wire is 0.050 kg/m. Each of the four strings suspending the wires has a length of 1.2 m. When the wires carry identical currents in opposite directions, the angle between the strings
Suppose that a uniform magnetic field is everywhere perpendicular to this page. The field points directly upward toward you. A circular path is drawn on the page. Use Ampère's law to show that there can be no net current passing through the circular surface.
The wire in Figure 21.37 carries a current of 12 A. Suppose that a second long, straight wire is placed right next to this wire. The current in the second wire is 28 A. Use Ampère’s law to find the magnitude of the magnetic field at a distance of r = 0.72 m from the wires when the currents
A magnetic field has a magnitude of 1.2 × 10-3 T, and an electric field has a magnitude of 4.6 × 103 N/C. Both fields point in the same direction. A positive 1.8 μC charge moves at a speed of 3.1 × 106 m/s in a direction that is perpendicular to both fields. Determine the magnitude of the net
A very long, hollow cylinder is formed by rolling up a thin sheet of copper. Electric charges flow along the copper sheet parallel to the axis of the cylinder. The arrangement is, in effect, a hollow tube of current I. Use Ampère's law to show that the magnetic field (a) Is μ0I / (2πr) outside
In a certain region, the earth's magnetic field has a magnitude of 5.4 × 10-5 T and is directed north at an angle of 58° below the horizontal. An electrically charged bullet is fired north and 11° above the horizontal, with a speed of 670 m/s. The magnetic force on the bullet is 2.8 × 10-10 N,
A very long, straight wire carries a current of 0.12 A. This wire is tangent to a single-turn, circular wire loop that also carries a current. The directions of the currents are such that the net magnetic field at the center of the loop is zero. Both wires are insulated and have diameters that can
Multiple-Concept Example 7 discusses how problems like this one can be solved. A +6.00 μC charge is moving with a speed of 7.50 × 104 m/s parallel to a very long, straight wire. The wire is 5.00 cm from the charge and carries a current of 67.0 A in a direction opposite to that of the moving
The x, y, and z components of a magnetic field are Bx = 0.10 T, By = 0.15 T, and Bz = 0.17 T. A 25-cm wire is oriented along the z axis and carries a current of 4.3 A. What is the magnitude of the magnetic force that acts on this wire?
In a lightning bolt, a large amount of charge flows during a time of 1.8 × 10-3 s. Assume that the bolt can be treated as a long, straight line of current. At a perpendicular distance of 27 m from the bolt, a magnetic field of 8.0 × 10-5 T is measured. How much charge has flowed during the
A charge is moving perpendicular to a magnetic field and experiences a force whose magnitude is 2.7 × 10-3 N. If this same charge were to move at the same speed and the angle between its velocity and the same magnetic field were 38°, what would be the magnitude of the magnetic force that the
Two charged particles move in the same direction with respect to the same magnetic field. Particle 1 travels three times faster than particle 2. However, each particle experiences a magnetic force of the same magnitude. Find the ratio |q1|/|q2| of the magnitudes of the charges.
The drawing shows four insulated wires overlapping one another, forming a square with 0.050-m sides. All four wires are much longer than the sides of the square. The net magnetic field at the center of the square is 61 μT. Calculate the current I.
A particle has a charge of q = 15.60 μC and is located at the coordinate origin. As the drawing shows, an electric field of Ex = +245 N/C exists along the +x axis. A magnetic field also exists, and its x and y components are Bx = +1.80 T and By = +1.40 T. Calculate the force (magnitude and
Two parallel rods are each 0.50 m in length. They are attached at their centers to either end of a spring (spring constant = 150 N/m) that is initially neither stretched nor compressed. When 950 A of current is in each rod in the same direction, the spring is observed to be compressed by 2.0 cm.
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