Question: Two circular loops lie side by side

> You are studying a solenoid of unknown resistance and inductance. You connect it in series with a 50.0 Ω resistor, a 25.0-V battery that has negligible internal resistance, and a switch. Using an ideal voltmeter, you measure and digit

> During a summer internship as an electronics technician, you are asked to measure the self-inductance L of a solenoid. You connect the solenoid in series with a 10.0-Ω resistor, a battery that has negligible internal resistance, and a

> In the circuit shown in Fig. P30.66, neither the battery nor the inductors have any appreciable resistance, the capacitors are initially uncharged, and the switch S has been in position 1 for a very long time. Fig. P30.66: (a). What is the current in

> Certain bacteria (such as Aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. If a transmission line carrying 100 A is laid

> In the circuit shown in Fig. P30.65, switch S is closed at time t = 0. Fig. P30.65: (a). Find the reading of each meter just after S is closed. (b). What does each meter read long after S is closed? 40.0 N 5.0 Ω 10.0 2 15.0 N 20.0 mH 10.0 mH 25.

> After the current in the circuit of Fig. P30.63 has reached its final, steady value with switch S1 closed and S2 open, switch S2 is closed, thus short-circuiting the inductor. (Switch S1 remains closed. See Problem 30.63 for numerical values of the circu

> Consider the circuit shown in Fig. P30.63. Let

> In the circuit shown in Fig. P30.61,

> In the circuit shown in Fig. P30.60, switch S1 has been closed for a long enough time so that the current reads a steady 3.50 A. Suddenly, switch S2 is closed and S1 is opened at the same instant. Figure P30.60: (a). What is the maximum charge that t

> In the circuit shown in Fig. P30.59, switch S is closed at time t = 0 with no charge initially on the capacitor. Fig. P30.59: (a). Find the reading of each ammeter and each voltmeter just after S is closed. (b). Find the reading of each meter after

> In the circuit shown in Fig. P30.58, find the reading in each ammeter and voltmeter Figure P30.58: (a). just after switch S is closed and (b). after S has been closed a very long time. (A3 100.0 0 15.0 mH (V2 (A2) 50.0 2 50.0 V 75.0 N V3 (A) 000

> A metal rectangle is close to a long, straight, current-carrying wire, with two of its sides parallel to the wire. If the current in the long wire is decreasing, is the rectangle repelled by or attracted to the wire? Explain why this result is consistent

> In the circuit shown in Fig. P30.57, the switch S has been open for a long time and is suddenly closed. Neither the battery nor the inductors have any appreciable resistance. What do the ammeter and the voltmeter read Fig. P30.57: (a). just after S is

> A 6.40-nF capacitor is charged to 24.0 V and then disconnected from the battery in the circuit and connected in series with a coil that has L = 0.0660 H and negligible resistance. After the circuit has been completed, there are current oscillations. (a)

> Two parallel wires are 5.00 cm apart and carry currents in opposite directions, as shown in Fig. E28.12. Find the magnitude and direction of the magnetic field at point P due to two 1.50-mm segments of wire that are opposite each other and each 8.00 cm f

> Consider the circuit shown in Fig. Q26.12. What happens to the brightnesses of the bulbs when the switch S is closed if the battery Fig. Q26.12: (a). has no internal resistance and (b). has nonnegligible internal resistance? Explain why. ww S. +

> A 7.00-µF capacitor is initially charged to a potential of 16.0 V. It is then connected in series with a 3.75-mH inductor. (a). What is the total energy stored in this circuit? (b). What is the maximum current in the inductor? What is the charge on the

> An inductor with inductance L = 0.200 H and negligible resistance is connected to a battery, a switch S, and two resistors, R1 = 8.00 Ω and R2 = 6.00 Ω (Fig. P30.52). The battery has emf 48.0 V and negligible inter

> An inductor with inductance L = 0.300 H and negligible resistance is connected to a battery, a switch S, and two resistors, R1 = 12.0 and R2 = 16.0 (Fig. P30.50). The battery has emf 96.0 V and negligible internal resistance. S is closed at t = 0. Fi

> Consider the circuit in Fig. 30.11 with both switches open. At t = 0 switch S1 is closed while switch S2 is left open. Fig. 30.11: (a). Use Eq. (30.14) to derive an equation for the rate PR at which electrical energy is being consumed in the resistor

> Consider the coaxial cable of Problem 30.46. The conductors carry equal currents i in opposite directions. Problem 30.46: A small solid conductor with radius a is supported by insulating, nonmagnetic disks on the axis of a thin-walled tube with inner

> Which graph in Fig. P29.74 best represents the time t dependence of the current i induced in the brain tissue, assuming that this tissue can be modeled as a resistive circuit? (The units of i are arbitrary.) Figure P29.74: (a). A; (b). B; (c). C;

> It may be desirable to increase the maximum induced current in the brain tissue. In Fig. P29.73, which time-dependent graph of the magnetic field B in the coil achieves that goal? Assume that everything else remains constant. Figure P29.73: (a). A;

> Consider the brain tissue at the level of the dashed line to be a series of concentric circles, each behaving independently of the others. Where will the induced emf be the greatest? (a). At the center of the dashed line; (b). at the periphery of the d

> Consider the situation in Exercise 29.21. In part (a), find the direction of the force that the large circuit exerts on the small one. Explain how this result is consistent with Lenz’s law. Exercise 29.21: A type-II superconductor in an external field

> In part (a) of the figure, a current pulse increases to a peak and then decreases to zero in the direction shown in the stimulating coil. What will be the direction of the induced current (dashed line) in the brain tissue? Figure a: (a). 1; (b). 2;

> A long, straight wire lies along the z-axis and carries a 4.00-A current in the +z-direction. Find the magnetic field (magnitude and direction) produced at the following points by a 0.500-mm segment of the wire centered at the origin: (a). x = 2.00 m, y

> A square, conducting, wire loop of side L, total mass m, and total resistance R initially lies in the horizontal xy-plane, with corners at (x, y, z) = (0, 0, 0), (0, L, 0), (L, 0, 0), and (L, L, 0). There is a uniform, upward magnetic field

> A metal bar with length L, mass m, and resistance R is placed on frictionless metal rails that are inclined at an angle

> You measure the magnitude of the external force

> You are conducting an experiment in which a metal bar of length 6.00 cm and mass 0.200 kg slides without friction on two parallel metal rails (Fig. P29.67). A resistor with resistance R = 0.800 Ω is connected across one end of the rails so that the bar,

> You are evaluating the performance of a large electromagnet. The magnetic field of the electromagnet is zero at t = 0 and increases as the current through the windings of the electromagnet is increased. You determine the magnetic field as a function of t

> A capacitor has two parallel plates with area A separated by a distance d. The space between plates is filled with a material having dielectric constant K. The material is not a perfect insulator but has resistivity

> The magnetic field

> An airplane propeller of total length L rotates around its center with angular speed

> A rectangular loop with width L and a slide wire with mass m are as shown in Fig. P29.61. A uniform magnetic field

> A student asserted that if a permanent magnet is dropped down a vertical copper pipe, it eventually reaches a terminal velocity even if there is no air resistance. Why should this be? Or should it?

> A +6.00-µC point charge is moving at a constant 8.00 × 106 m/s in the +y-direction, relative to a reference frame. At the instant when the point charge is at the origin of this reference frame, what is the magnetic-field vector

> A 25.0-cm-long metal rod lies in the xy-plane and makes an angle of 36.90 with the positive x-axis and an angle of 53.10 with the positive y-axis. The rod is moving in the +x-direction with a speed of 6.80 m / s. The rod is in a uniform magnetic field

> A slender rod, 0.240 m long, rotates with an angular speed of 8.80 rad/s about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform magnetic field with a magnitude of 0.650 T. (a). What is

> A circular conducting ring with radius r0 = 0.0420 m lies in the xy-plane in a region of uniform magnetic field

> The long, straight wire shown in Fig. P29.57a carries constant current I. A metal bar with length L is moving at constant velocity

> A bar of length L = 0.36 m is free to slide without friction on horizontal rails as shown in Fig. P29.56. A uniform magnetic field B = 2.4 T is directed into the plane of the figure. At one end of the rails there is a battery with emf

> A very long, cylindrical wire of radius R carries a current I0 uniformly distributed across the cross section of the wire. Calculate the magnetic flux through a rectangle that has one side of length W running down the center of the wire and another side

> A conducting rod with length L = 0.200 m, mass m = 0.120 kg, and resistance R = 80.0 Ω moves without friction on metal rails as shown in Fig. 29.11. A uniform magnetic field with magnitude B = 1.50 T is directed into the plane of the figure. The rod is

> A flexible circular loop 6.50 cm in diameter lies in a magnetic field with magnitude 1.35 T, directed into the plane of the page as shown in Fig. P29.53. The loop is pulled at the points indicated by the arrows, forming a loop of zero area in 0.250 s.

> You are shipwrecked on a deserted tropical island. You have some electrical devices that you could operate using a generator but you have no magnets. The earth’s magnetic field at your location is horizontal and has magnitude 8.0 × 10-5 T, and you decide

> In Fig. P29.51 the loop is being pulled to the right at constant speed v. A constant current I flows in the long wire, in the direction shown. Fig. P29.51: (a). Calculate the magnitude of the net emf a く-r→ b

> An electron and a proton are each moving at 735 km/s in perpendicular paths as shown in Fig. E28.8. At the instant when they are at the positions shown, find the magnitude and direction of (a). the total magnetic field they produce at the origin; (b).

> Suppose the loop in Fig. P29.50 is Fig. P29.50: (a). rotated about the y-axis; (b). rotated about the x-axis; (c). rotated about an edge parallel to the z-axis. What is the maximum induced emf in each case if A = 600 cm2, A X. 3

> The solenoid is removed from the enclosure and then used in a location where the earth’s magnetic field is 50 µT and points horizontally. A sample of bacteria is placed in the center of the solenoid, and the same current is applied that produced a magnet

> To use a larger sample, the experimenters construct a solenoid that has the same length, type of wire, and loop spacing but twice the diameter of the original. How does the maximum possible magnetic torque on a bacterium in this new solenoid compare with

> What current is needed in the wire so that the magnetic field experienced by the bacteria has a magnitude of 150

> A wide, long, insulating belt has a uniform positive charge per unit area

> Two long, straight conducting wires with linear mass density λ are suspended from cords so that they are each horizontal, parallel to each other, and a distance d apart. The back ends of the wires are connected to each other by a slack, low

> A pair of long, rigid metal rods, each of length 0.50 m, lie parallel to each other on a frictionless table. Their ends are connected by identical, very lightweight conducting springs with unstretched length l0 and force constant k (Fig. P28.78). When a

> You use a tesla meter (a Hall-effect device) to measure the magnitude of the magnetic field at various distances from a long, straight, thick cylindrical copper cable that is carrying a large constant current. To exclude the earth’s mag

> As a summer intern at a research lab, you are given a long solenoid that has two separate windings that are wound close together, in the same direction, on the same hollow cylindrical form. You must determine the number of turns in each winding. The sole

> Positive point charges q = +8.00 µC and q' = +3.00 µC are moving relative to an observer at point P, as shown in Fig. E28.6. The distance d is 0.120 m, v = 4.50 × 106 m/s, and v' = 9.00 × 106 m/s Fig.

> A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a current whose current density is

> In Fig. 29.8, if the angular speed v of the loop is doubled, then the frequency with which the induced current changes direction doubles, and the maximum emf also doubles. Why? Does the torque required to turn the loop change? Explain. Fig. 29.8: (

> Long, straight conductors with square cross section, each carrying current I, are laid side by side to form an infinite current sheet with current directed out of the plane of the page (Fig. P28.74). A second infinite current sheet is a distance d below

> Long, straight conductors with square cross sections and each carrying current I are laid side by side to form an infinite current sheet (Fig. P28.73). The conductors lie in the xy-plane, are parallel to the y-axis, and carry current in the +y-direction.

> A circular loop has radius R and carries current I2 in a clockwise direction (Fig. P28.72). The center of the loop is a distance D above a long, straight wire. What are the magnitude and direction of the current I1 in the wire if the magnetic field at th

> A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a current whose current density is

> The wire shown in Fig. P28.70 is infinitely long and carries a current I. Calculate the magnitude and direction of the magnetic field that this current produces at point P. Fig. P28.70:

> A long, straight wire with a circular cross section of radius R carries a current I. Assume that the current density is not constant across the cross section of the wire, but rather varies as J =

> Calculate the magnetic field (magnitude and direction) at a point P due to a current I = 12.0 A in the wire shown in Fig. P28.68. Segment BC is an arc of a circle with radius 30.0 cm, and point P is at the center of curvature of the arc. Segment DA is an

> Figure P28.67 is a sectional view of two circular coils with radius a, each wound with N turns of wire carrying a current I, circulating in the same direction in both coils. The coils are separated by a distance a equal to their radii. In this configurat

> Several charges enter a uniform magnetic field directed into the page. (a). What path would a positive charge q moving with a velocity of magnitude v follow through the field? (b). What path would a positive charge q moving with a velocity of magnitude

> Two long, parallel wires hang by 4.00-cm-long cords from a common axis (Fig. P28.65). The wires have a mass per unit length of 0.0125 kg/m and carry the same current in opposite directions. What is the current in each wire if the cords hang at an angle o

> The long, straight wire AB shown in Fig. P28.64 carries a current of 14.0 A. The rectangular loop whose long edges are parallel to the wire carries a current of 5.00 A. Find the magnitude and direction of the net force exerted on the loop by the magnetic

> Your physics study partner asks you to consider a parallelplate capacitor that has a dielectric completely filling the volume between the plates. He then claims that Eqs. (29.13) and (29.14) show that the conduction current in the dielectric equals the d

> Two long, straight, parallel wires are 1.00 m apart (Fig. P28.63). The wire on the left carries a current I1 of 6.00 A into the plane of the paper. Fig. P28.63: (a). What must the magnitude and direction of the current I2 be for the net field at poin

> An electric bus operates by drawing direct current from two parallel overhead cables, at a potential difference of 600 V, and spaced 55 cm apart. When the power input to the bus’s motor is at its maximum power of 65 hp, (a). what current does it draw an

> An electron is moving in the vicinity of a long, straight wire that lies along the x-axis. The wire has a constant current of 9.00 A in the -x-direction. At an instant when the electron is at point (0, 0.200 m, 0) and the electron’s velocity is

> A long, straight wire carries a 13.0-A current. An electron is fired parallel to this wire with a velocity of 250 km/s in the same direction as the current, 2.00 cm from the wire. (a). Find the magnitude and direction of the electron’s initial accelerati

> A long, straight wire carries a current of 8.60 A. An electron is traveling in the vicinity of the wire. At the instant when the electron is 4.50 cm from the wire and traveling at a speed of 6.00 × 104 m/s directly toward the wire, what are the magnitude

> Two long, parallel transmission lines, 40.0 cm apart, carry 25.0-A and 75.0-A currents. Find all locations where the net magnetic field of the two wires is zero if these currents are in (a). the same direction and (b). the opposite direction.

> At a particular instant, charge q1 = +4.80 × 10-6 C is at the point (0, 0.250 m, 0) and has velocity

> An alpha particle (charge +2e) and an electron move in opposite directions from the same point, each with the speed of 2.50 × 105 m/s (Fig. E28.4). Find the magnitude and direction of the total magnetic field these charges produce at point P

> A pair of point charges, q = +8.00 µC and q' = -5.00 µC, are moving as shown in Fig. P28.55 with speeds v = 9.00 × 104 m/s and v' = 6.50 × 104 m/s. When the charges are at the locations shown in the figure, what are the magnitude and direction of (a). t

> The large magnetic fields used in MRI can produce forces on electric currents within the human body. This effect has been proposed as a possible method for imaging “biocurrents” flowing in the body, such as the current that flows in individual nerves. Fo

> Which of following elements is a candidate for MRI? (a). 12C6; (b). 16O8; (c). 40Ca20; (d). 31P15.

> In the situation shown in Fig. 29.18, would it be appropriate to ask how much energy an electron gains during a complete trip around the wire loop with current I'? Would it be appropriate to ask what potential difference the electron moves through during

> If a proton is exposed to an external magnetic field of 2 T that has a direction perpendicular to the axis of the proton’s spin, what will be the torque on the proton? (a). 0; (b). 1.4 × 10-26 N ∙ m; (c). 2.8 × 10-26 N ∙ m; (d). 0.7 × 10-26 N ∙ m.

> A particle with mass m and positive charge q starts from rest at the origin shown in Fig. P27.82. There is a uniform electric field

> A particle with charge 2.15 µC and mass 3.20 × 10-11 kg is initially traveling in the +y-direction with a speed v0 = 1.45 × 105 m/s. It then enters a region containing a uniform magnetic field that is directed into,

> You are using a type of mass spectrometer to measure charge-to-mass ratios of atomic ions. In the device, atoms are ionized with a beam of electrons to produce positive ions, which are then accelerated through a potential difference V. (The final speed o

> A circular loop of wire with area A lies in the xy-plane. As viewed along the z-axis looking in the z-direction toward the origin, a current I is circulating clockwise around the loop. The torque produced by an external magnetic field

> The neutron is a particle with zero charge. Nonetheless, it has a nonzero magnetic moment with z-component 9.66 × 10-27 A ∙ m2. This can be explained by the internal structure of the neutron. A substantial body of evidence

> An electron moves at 0.100c as shown in Fig. E28.3. Find the magnitude and direction of the magnetic field this electron produces at the following points, each 2.00 mm from the electron: Fig. E28.3: (a). points A and B; (b). point C; (c). point D.

> It was shown in Section 27.7 that the net force on a current loop in a uniform magnetic field is zero. But what if B S is not uniform? Figure P27.75 shows a square loop of wire that lies in the xy-plane. The loop has corners at (0, 0), (0, L), (L, 0), an

> The lower end of the thin uniform rod in Fig. P27.74 is attached to the floor by a frictionless hinge at point P. The rod has mass 0.0840 kg and length 18.0 cm and is in a uniform magnetic field B = 0.120 T that is directed into the page. The rod is held

> It was shown in Section 27.7 that the net force on a current loop in a uniform magnetic field is zero. The magnetic force on the voice coil of a loudspeaker (see Fig. 27.28) is nonzero because the magnetic field at the coil is not uniform. A voice coil i

> A uniform bar has mass 0.0120 kg and is 30.0 cm long. It pivots without friction about an axis perpendicular to the bar at point a (Fig. P27.72). The gravitational force on the bar acts in the –y-direction. The bar is in a uniform magne

> Example 29.6 discusses the external force that must be applied to the slidewire to move it at constant speed. If there were a break in the left-hand end of the U-shaped conductor, how much force would be needed to move the slidewire at constant speed? As

> The loop of wire shown in Fig. P27.71 forms a right triangle and carries a current I = 5.00 A in the direction shown. The loop is in a uniform magnetic field that has magnitude B = 3.00 T and the same direction as the current in side PQ of the loop. Fi

> A uniform bar of length L carries a current I in the direction from point a to point b (Fig. P27.70). The bar is in a uniform magnetic field that is directed into the page. Consider the torque about an axis perpendicular to the bar at point a that is due

> The rectangular loop of wire shown in Fig. P27.69 has a mass of 0.15 g per centimeter of length and is pivoted about side ab on a frictionless axis. The current in the wire is 8.2 A in the direction shown. Find the magnitude and direction of the magnetic