Questions and Answers of Essential University Physics

A conducting loop of area 240 cm2 and resistance 12 Ω is perpendicular to a spatially uniform magnetic field and carries a 320-mA induced current. At what rate is the magnetic field changing?
A circular wire loop 45 cm in diameter has resistance 120 Ω and lies in a horizontal plane. A uniform magnetic field points vertically downward, and in 25 ms it increases linearly from 5.0 mT to 55
Find the magnetic flux through a 5.0-cm-diameter circular loop oriented with the loop normal at 36° to a uniform 75-mT magnetic field.
Show that the volt is the SI unit for the rate of change of magnetic flux, making Faraday’s law dimensionally correct. Your result also shows why the unit of flux itself can be expressed as Vs.
A toroid is a solenoid-like coil bent into a circle (Fig. 26.52a). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us
A toroid is a solenoid-like coil bent into a circle (Fig. 26.52a). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us
A toroid is a solenoid-like coil bent into a circle (Fig. 26.52a). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us
A toroid is a solenoid-like coil bent into a circle (Fig. 26.52a). Toroids are the configuration of choice in magnetic-confinement nuclear fusion experiments, which, if successful, could provide us
Your roommate is sold on “magnet therapy,” a sham treatment using small bar magnets attached to the body. You skeptically ask your roommate how this is supposed to work. He mumbles something
Derive Equation 26.20 by considering the current sheet to be made of infinitely many infinitesimal line currents. B = zuoJs (field of an infinite current sheet) (26.20)
You’re an engineer at a nuclear power plant, and one of your colleagues has drawn up plans to reroute the conductors carrying current from the plant’s electric generator. Your colleague wants to
A magnetic dipole ?(vector) = ?i? is on the axis of a circular current loop of radius a oriented as shown in Fig. 26.17a, a distance x from the center. Differentiate Equation 26.16 to find the force
Repeat the calculation in Problem 69 for a solenoid of finite length L and cross-sectional radius a to find the magnetic field strength at the center of the solenoid?s axis. Data From Problem
Find an expression for the magnetic field at the center of a square loop of side a carrying current I.
A long, flat conducting ribbon of width w is parallel to a long, straight wire; its near edge is a distance a from the wire (Fig. 26.51). Wire and ribbon carry the same current I; it?s distributed
The structure shown in Fig. 26.50 is made from conducting rods. The upper horizontal rod (mass 22 g, length 95 cm) is free to slide vertically on the uprights while maintaining electrical contact. A
You’re developing a system to orient an orbiting telescope. The system uses three perpendicular coils, with torques developed in Earth’s magnetic field when current passes through them. Weight
A disk of radius a carries uniform surface charge density σ and rotates with angular speed ω about the disk axis. Show that the magnetic field at the disk’s center is 1/2μ0σωα.
A solid conducting wire of radius R runs parallel to the z-axis and carries a current density given by J(vector) = J0(1 - r/R)k̂, where J0 is a constant and r is the distance from the wire axis.
A long, hollow conducting pipe of radius R and length l carries a uniform current I flowing around the pipe (Fig. 26.49). Find expressions for the magnetic field(a) inside(b) outside the pipe.? ? R
A circular wire loop of radius 15 cm and negligible thickness carries a 2.0-A current. Use suitable approximations to find the magnetic field of this loop(a) In the loop plane, 1.0 mm outside the
Indium antimonide (InSb) is a semiconductor commonly used in Hall-effect devices because of its relatively large Hall coefficient. A magnetic-field sensor is made from a 50?m-thick strip of InSb,
A coaxial cable (see Fig. 26.47) consists of a 1.0-mm-diameter inner conductor and a 0.20-mm-thick outer conductor with interior diameter 1.0 cm. A 100-mA current flows down the inner conductor and
The largest lightning strikes have peak currents of around 250 kA, flowing in essentially cylindrical channels of ionized air. How far from such a flash would the resulting magnetic field be equal to
Derive Equation 26.21 for the solenoid field by considering the solenoid to be made of infinitesimal current loops. Use Equation 26.9 for the loop fields, and integrate over all loops. Hola? B =
You have 10 m of 0.50-mm-diameter copper wire and a battery capable of passing 15 A through the wire. What magnetic field strengths could you obtain(a) inside a 2.0-cm-diameter solenoid wound with
A solenoid used in a plasma physics experiment is 10 cm in diameter, is 1.0 m long, and carries a 35-A current to produce a 100-mT magnetic field.(a) How many turns are in the solenoid?(b) If the
A long, hollow conducting pipe of radius R carries a uniform current I along the pipe, as shown in Fig. 26.46. Use Amperes law to find the magnetic field strength (a) inside and (b) outside the
A long conducting rod of radius R carries a nonuniform current density J = J0r/R, where J0 is a constant and r is the radial distance from the rod’s axis. Find expressions for the magnetic field
A long, straight wire carries a 25-A current. A 10-cm by 15-cm rectangular wire loop carrying 850 mA is 3.0 cm from the wire, as shown in Fig. 26.45. Find the magnitude and direction of the net
You and a friend get lost while hiking, so your friend pulls out a magnetic compass to get re-oriented. However, you?re standing right under a power line carrying 1.5 kA toward magnetic north; it?s
A 20-cm-long conducting rod with mass 18 g is suspended by wires of negligible mass (Fig. 26.41). A uniform magnetic field of 0.15 T points horizontally into the page, as shown. An external circuit
A wire of negligible resistance is bent into a rectangle as in Fig. 26.40, and a battery and resistor are connected as shown. The right-hand side of the circuit extends into a region containing a
Show that Equations 26.18 and 26.19 give the same results when evaluated at the wire?s surface. Hol B field outside any current distribution with line symmetry / (26.18) Holr B = field inside a
The magnetic field of in Fig. 26.39 has microwaves magnitude 75 ?T, but its direction reverses abruptly. Find the current encircled by the rectangular loop shown. B(vector) 20 cm 15 cm Figure 26.39
Stray voltage is a serious problem on dairy farms, often resulting from corroded wiring or poor wiring practices. These conditions can produce several volts between the ground and metal watering
Stray voltage is a serious problem on dairy farms, often resulting from corroded wiring or poor wiring practices. These conditions can produce several volts between the ground and metal watering
Stray voltage is a serious problem on dairy farms, often resulting from corroded wiring or poor wiring practices. These conditions can produce several volts between the ground and metal watering
Stray voltage is a serious problem on dairy farms, often resulting from corroded wiring or poor wiring practices. These conditions can produce several volts between the ground and metal watering
In the circuit of Fig. 25.42 the switch is initially open and the capacitor is uncharged. Find expressions for the current I supplied by the battery (a) just after the switch is closed and (b) a long
In Problem 60, take C1 = C2 = C, and find the current through R2 as a function of time. Use the node and loop laws to get a differential equation for the current, and use the initial conditions on
An electrochemical impulse traveling along the cell modeled in Fig. 25.41 changes the value of ε3 so now it supplies a 40-nA upward current. Assuming the rest of the circuit remains as described in
Figure 25.41 shows a portion of a circuit used to model muscle cells and neurons. All resistors have the same value R = 1.5 M?, and the emfs are ?1 = 75 mV, ?2 = 45 mV, and ?3 = 20 mV. Find the
Figure 25.40 shows the voltage across a capacitor that?s charging through a 4700? resistor in the circuit of Fig. 25.18. Use the graph to determine(a) the battery voltage,(b) the time constant,(c)
The circuit in Fig. 25.39 extends forever to the right, and all the resistors have the same value R. Show that the equivalent resistance measured across the two terminals at left is R(1 +??5)/2. ww
Find the equivalent resistance between A and B for the circuits in Fig. 25.38. A- R1. R. R1, B. B- B (а) (b) (e) FIGURE 25.38 Problem 71
With all values except ?2 as given in the preceding problem,(a) find ?2 such that there is no current in this battery.(b) What are the currents in R1 and R3 under these conditions? ww R3 ww R2 ww
In Fig. 25.37, take ?1 = 12.0 V, ?2 = 6.00 V, ?3 = 3.00 V, R1 = 1.00 ?, R2 = 2.00 ?, and R3 = 4.00 ?. Find the current in R2 and give its direction. ww R3 ww R2 ww FIGURE 25.37 Problems 63 and 64
In Fig. 25.36, the switch is initially open and both capacitors are initially uncharged. All resistors have the same value R. Find expressions for the current in R2?(a) just after the switch is
In Fig. 25.35 the 2.0?F capacitor is charged to 150 V, while the 1.0?F capacitor is initially uncharged. Switch S is then closed. Find the total energy dissipated in the resistor as the circuit comes
In Fig. 25.34, what are the meter readings when an ideal(a) Voltmeter (b) Ammeter is connected between A and B? 18 kN ww A 48 VE : 36 kn -B ww
The voltage across the 30k? resistor in Fig. 25.33 is measured with(a) a 50k? voltmeter,(b) a 250k? voltmeter,(c) a 10M? digital meter. What does each read, to two significant figures? 30 kΩ ww 100
Find all three currents in the circuit of Fig. 25.13 with the values given, but with battery ?2 reversed. E = 6 V & = 9 V R1 = 20ŠR3 = 10; R2 = 42 (a) Node A R Loop) R2 Loopa Node B Loop 3 (b) +
In Fig. 25.32, find the equivalent resistance measured between A and B. A. R. 2R R 2R B- FIGURE 25.32 Problem 49
What’s the ammeter reading in Fig. 25.31? 20 20 6 V 20 Ω
In Fig. 25.30, how much power is dissipated in the 4Ω resistor? 10 ww- 6 VE 29
In the circuit of Fig. 25.30, find(a) the current supplied by the battery(b) the current through the 6? resistor. 10 6 V= 203 4ng 6n FIGURE 25.30 Problems 46 and 47
In Fig. 25.29, R1 is a variable resistor and the other two resistors have equal resistances R.(a) Find an expression for the voltage across R1,(b) sketch a graph of this voltage as R1 varies from 0
Take ε = 12 V and R1 = 270 Ω in Fig. 25.4. (a) What’s the resistance R2 if there’s 4.5 V across it? (b) What will be the power dissipation in R2? (a) Current from R1 can't go anywhere but
You company is designing a battery-based backup power source, and your job is to assess its safety. You know that under damp or sweaty conditions, the resistance between two points of unbroken skin
In Fig. 25.28, take all resistors to be 1 kΩ. Find the current in the vertical resistor when a 6.0-V battery is connected between A and B. A Ww ww C ww B ww
In Fig. 25.28, all resistors have the same value, R. What will be the resistance measured(a) Between A and B(b) Between A and C? A Ww ww C ww B ww
An ammeter with 100Ω resistance is inserted in the circuit of Fig. 25.27. By what percentage is the measured current in error because of the nonzero meter resistance? 5 kN ww- + 150 V= 10 k2
A voltmeter with 200kΩ resistance is used to measure the voltage across the 10kΩ resistor in Fig. 25.27. By what percentage is the measurement in error because of the finite meter
What’s the current through the 3Ω resistor in Fig. 25.26? 5Ω 6 V두 9 V ww
Figure 24.20 shows a truncated cone of material with resistivity r. Assume the equipotentials are planes parallel to the two faces, and integrate over slices of thickness dx like the one shown to
A circular pan of radius b has a plastic bottom and metallic sidewall of height h. It?s filled with a solution of resistivity r. A metal disk of radius a and height h is at the center, as shown in
The resistivity of copper as a function of temperature is given approximately by ? = ?0[1 + a(T - T0)], where ?0 is Table 24.1?s entry for 20?C, T0 = 20?C, and a = 4.3x10-3 ?C-1 . Find the
Use Table 24.1 to determine the conductivity of(a) Copper (b) Seawater. Table 24.1 Resistivities Material Resistivity (. m) Metallic conductors (20°C) Aluminum 2.65 X 10-8 Соpper 1.68 X 10-8
Nuclear fusion could provide humankind with limitless energy, making a gallon of seawater the energy equivalent of 300 gallons of gasoline. The National Ignition Facility (NIF) at Lawrence Livermore
Nuclear fusion could provide humankind with limitless energy, making a gallon of seawater the energy equivalent of 300 gallons of gasoline. The National Ignition Facility (NIF) at Lawrence Livermore
Nuclear fusion could provide humankind with limitless energy, making a gallon of seawater the energy equivalent of 300 gallons of gasoline. The National Ignition Facility (NIF) at Lawrence Livermore
Nuclear fusion could provide humankind with limitless energy, making a gallon of seawater the energy equivalent of 300 gallons of gasoline. The National Ignition Facility (NIF) at Lawrence Livermore
A capacitor consists of two long concentric metal cylinders (Fig. 23.15). Find an expression for its capacitance in terms of the dimensions shown. -L- FIGURE 23.15 Problem 60
In Fig. 23.14, find the energy stored in the 1?F capacitor when a 50-V battery is connected between A and B. 3.0 μF A 2.0 μF 1.0 µF HE 2.0 µF B• FIGURE 23.14 Problems 45 and 46
What?s the equivalent capacitance measured between A and B in Fig. 23.14? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3.0 μF A 2.0 μF 1.0 µF HE 2.0 µF B• FIGURE 23.14 Problems 45 and 46
Standard electrocardiography measures time-dependent potential differences between multiple points on the body, giving cardiologists multiple perspectives on the heart?s electrical activity. In
Standard electrocardiography measures time-dependent potential differences between multiple points on the body, giving cardiologists multiple perspectives on the heart?s electrical activity. In
Use Equation 22.6 to calculate the electric field on the perpendicular bisector of a dipole, and show that your result is equivalent to Equation 20.6a. k(2aq) cos0 _ kp cos 0 V(r, 0) =- (dipole
The annulus of in Fig. 22.25 carries a uniform surface charge density s. Find an expression for the potential at an arbitrary point P on its axis. FIGURE 22.25 Problem 57
Your radio station needs a new coaxial cable to connect the transmitter and antenna. One possible cable consists of a 2.0-mm diameter inner conductor and an outer conductor with diameter 1.6 cm and
Coaxial cables are widely used with audio-visual technology, electronic instrumentation, and radio broadcasting, because they minimize interference with or from signals traveling on the cable.
Coaxial cables are widely used with audio-visual technology, electronic instrumentation, and radio broadcasting, because they minimize interference with or from signals traveling on the cable.
Coaxial cables are widely used with audio-visual technology, electronic instrumentation, and radio broadcasting, because they minimize interference with or from signals traveling on the cable.
Three parallel wires of length l each carry current I in the same direction. They’re positioned at the vertices of an equilateral triangle of side a, and oriented perpendicular to the triangle.
You and a friend get lost while hiking, so your friend pulls out a magnetic compass to get re-oriented. However, you’re standing right under a power line carrying 1.5 kA toward magnetic north;
A single piece of wire carrying current I is bent so it includes a circular loop of radius a, as shown in Fig. 26.43. Find an expression for the magnetic field at the loop center. FIGURE 26.43
Your company is developing a device incorporating a 20-cm diameter coil carrying 0.50 A that, when properly oriented, will just cancel Earth’s 50μT magnetic field at the coil’s center. How much
A wire carrying 1.5 A passes through a 48-mT magnetic field. The wire is perpendicular to the field and makes a quarter-circle turn of radius 21 cm in the field region, as shown in Fig. 26.42. Find
Nuclear magnetic resonance (NMR) is a technique for analyzing chemical structures and also the basis of magnetic resonance imaging used for medical diagnosis. NMR relies on sensitive measurements of
A simple electric motor consists of a 220-turn coil, 4.2 cm in diameter, mounted between the poles of a magnet that produces a 95-mT field. When a 15-A current flows in the coil, what are(a) the
A single-turn wire loop 10 cm in diameter carries a 12-A current. It experiences a 0.015 Nm torque when the normal to the loop plane makes a 25° angle with a uniform magnetic field. Find the
A rectangular copper strip measures 1.0 mm in the direction of a uniform 2.4-T magnetic field. When the strip carries a 6.8-A current perpendicular to the field, a 1.2μV Hall potential develops
You’re designing a prosthetic ankle that includes a miniature electric motor containing a 150-turn circular coil 15 mm in diameter. The motor needs to develop a maximum torque of 3.1 mNm. The
An electron is moving in a uniform 0.25-T magnetic field; its velocity components parallel and perpendicular to the field are both 3.1 Mm/s.(a) What’s the radius of the electron’s spiral path?(b)
90-cm-diameter cyclotron with a 2.0-T magnetic field is used to accelerate deuterium nuclei (one proton plus one neutron).(a) At what frequency should the dee voltage be alternated?(b) What’s the
Show that the orbital radius of a charged particle moving at right angles to a magnetic field B can be written r = √12Km/qB, where K is the kinetic energy in joules, m the particle’s mass, and q
A beam of electrons moving in the x-direction at 8.7 Mm/s enters a region where a uniform 180-G magnetic field points in the y-direction. The boundary of the field region is perpendicular to the
A simplified model of Earth’s magnetic field has it originating in a single current loop at the outer edge of the planet’s liquid core (radius 3000 km). What current would give the 62μT field
A proton moving with velocity v1(vector) = 3.6x104ĵ m/s experiences a magnetic force of 7.4x10-16î N. A second proton moving on the x-axis experiences a magnetic force of 2.8x10-16ĵ N. Find the

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