A particle with initial velocity
> A rectangle measuring 30.0 cm by 40.0 cm is located inside a region of a spatially uniform magnetic field of 1.25 T, with the field perpendicular to the plane of the coil (Fig. E29.26). The coil is pulled out at a steady rate of 2.00 cm/s traveling perpe
> The magnetic force acting on a charged particle can never do work because at every instant the force is perpendicular to the velocity. The torque exerted by a magnetic field can do work on a current loop when the loop rotates. Explain how these seemingly
> A thin, 50.0-cm-long metal bar with mass 750 g rests on, but is not attached to, two metallic supports in a uniform 0.450-T magnetic field, as shown in Fig. E27.37. A battery and a 25.0-Ω resistor in series are connected to the supports. Fi
> Two closed loops A and C are close to a long wire carrying a current I (Fig. E29.17). Fig. E29.17: (a). Find the direction (clockwise or counterclockwise) of the current induced in each loop if I is steadily decreasing. (b). While I is decreasing, wh
> The current I in a long, straight wire is constant and is directed toward the right as in Fig. E29.16. Conducting loops, A, B, C, and D are moving, in the directions shown, near the wire. Fig. E29.16: (a). For each loop, is the direction of the induc
> A circular loop of wire is in a region of spatially uniform magnetic field, as shown in Fig. E29.15. The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or counterclockwise) of the induced current in the loop w
> A circular loop of wire with radius r = 0.0250 m and resistance R = 0.390 Ω is in a region of spatially uniform magnetic field, as shown in Fig. E29.23. The magnetic field is directed into the plane of the figure. At t = 0, B = 0. The
> A circular loop of wire with radius r = 0.0480 m and resistance R = 0.160 Ω is in a region of spatially uniform magnetic field, as shown in Fig. E29.22. The magnetic field is directed out of the plane of the figure. The magnetic field
> A small, circular ring is inside a larger loop that is connected to a battery and a switch (Fig. E29.21). Use Lenz’s law to find the direction of the current induced in the small ring Fig. E29.21: / / (a). just after switch S is closed; (b). after S
> A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as shown in Fig. E29.20. Terminals a and b of winding A may be connected to a battery through a reversing switch. State whether the induced current in the resis
> Using Lenz’s law, determine the direction of the current in resistor ab of Fig. E29.19 when Fig. E29.19: (a). switch S is opened after having been closed for several minutes; (b). coil B is brought closer to coil A with the switch
> The current in Fig. E29.18 obeys the equation I(t) = I0 e-bt, where b > 0. Find the direction (clockwise or counterclockwise) of the current induced in the round coil for t > 0. Fig. E29.18:
> A closely wound search coil (see Exercise 29.3) has an area of 3.20 cm2, 120 turns, and a resistance of 60.0 Ω. It is connected to a charge-measuring instrument whose resistance is 45.0 Ω. When the coil is rotated quickly from a position parallel to a un
> An electromagnet produces a magnetic field of 0.550 T in a cylindrical region of radius 2.50 cm between its poles. A straight wire carrying a current of 10.8 A passes through the center of this region and is perpendicular to both the axis of the cylindri
> Will the capacitors in the circuits shown in Fig. Q26.18 charge at the same rate when the switch S is closed? If not, in which circuit will the capacitors charge more rapidly? Explain. Fig. Q26.18: (a) R S. (b)
> One practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. The coil is initially held with its plane perpendicular to a magnetic field. The coil is then either quickly rotated a quarter-turn about a diamet
> A flat, rectangular coil of dimensions l and w is pulled with uniform speed v through a uniform magnetic field B with the plane of its area perpendicular to the field (Fig. E29.14). Fig. E29.14: (a). Find the emf induced in this coil. (b). If the sp
> In a region of space, a magnetic field points in the +x-direction (toward the right). Its magnitude varies with position according to the formula Bx = B0 + bx, where B0 and b are positive constants, for x > 0. A flat coil of area A moves with uniform spe
> A closely wound rectangular coil of 80 turns has dimensions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 37.0° with a magnetic field of 1.70 T to a position perpendicular to the field. The rotation ta
> A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendic
> A flat, circular, steel loop of radius 75 cm is at rest in a uniform magnetic field, as shown in an edge-on view in Fig. E29.8. The field is changing with time, according to B(t) = (1.4 T) e-(0.057 s-1)t. Fig. E29.8: (a). Find the emf induced in the
> A long solenoid with 60 turns of wire per centimeter carries a current of 0.15 A. The wire that makes up the solenoid is wrapped around a solid core of silicon steel (Km = 5200). (The wire of the solenoid is jacketed with an insulator so that none of the
> A solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius b and outer radius c (Fig. E28.43). The central conductor and tube carry equal currents I in opposite directions. The currents are distrib
> An ideal toroidal solenoid (see Example 28.10) has inner radius r1 = 15.0 cm and outer radius r2 = 18.0 cm. The solenoid has 250 turns and carries a current of 8.50 A. What is the magnitude of the magnetic field at the following distances from the center
> A long wire carrying 4.50 A of current makes two 90 bends, as shown in Fig. E27.35. The bent part of the wire passes through a uniform 0.240-T magnetic field directed as shown in the figure and confined to a limited region of space. Find the magnitude an
> A toroidal solenoid has an inner radius of 12.0 cm and an outer radius of 15.0 cm. It carries a current of 1.50 A. How many equally spaced turns must it have so that it will produce a magnetic field of 3.75 mT at points within the coils 14.0 cm from its
> Each of the lettered points at the corners of the cube in Fig. Q27.12 represents a positive charge q moving with a velocity of magnitude v in the direction indicated. The region in the figure is in a uniform magnetic field B , parallel to the x-axis and
> A solenoid is designed to produce a magnetic field of 0.0270 T at its center. It has radius 1.40 cm and length 40.0 cm, and the wire can carry a maximum current of 12.0 A. (a). What minimum number of turns per unit length must the solenoid have? (b). Wh
> Repeat Exercise 28.43 for the case in which the current in the central, solid conductor is I1, the current in the tube is I2, and these currents are in the same direction rather than in opposite directions. Exercise 28.43: A solid conductor with radius
> Figure E28.40 shows, in cross section, several conductors that carry currents through the plane of the figure. The currents have the magnitudes I1 = 4.0 A, I2 = 6.0 A, and I3 = 2.0 A, and the directions shown. Four paths, labeled a through d, are shown.
> A closed curve encircles several conductors. The line integral
> Calculate the magnitude of the magnetic field at point P of Fig. E28.35 in terms of R, I1, and I2. What does your expression give when I1 = I2? Fig. E28.35: R P R
> The magnetic field around the head has been measured to be approximately 3.0 × 10-8 G. Although the currents that cause this field are quite complicated, we can get a rough estimate of their size by modeling them as a single circular current loop 16 cm (
> In a 1.25-T magnetic field directed vertically upward, a particle having a charge of magnitude 8.50 µC and initially moving northward at 4.75 km/s is deflected toward the east. (a). What is the sign of the charge of this particle? Make a sketch to illus
> A particle of mass 0.195 g carries a charge of -2.50 × 10-8 C. The particle is given an initial horizontal velocity that is due north and has magnitude 4.00 × 104 m/s. What are the magnitude and direction of the minimum magnetic field that will keep the
> A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 1.50 km/s in the +x-direction experiences a force of 2.25 × 10-16 N in the +y-direction, and an electron moving at 4.75 km/s in
> A particle with charge -5.60 nC is moving in a uniform magnetic field
> Two concentric circular loops of wire lie on a tabletop, one inside the other. The inner wire has a diameter of 20.0 cm and carries a clockwise current of 12.0 A, as viewed from above, and the outer wire has a diameter of 30.0 cm. What must be the magnit
> An electron moves at 1.40 × 106 m/s through a region in which there is a magnetic field of unspecified direction and magnitude 7.40 × 10-2 T. (a). What are the largest and smallest possible magnitudes of the acceleration of the electron due to the magne
> A 1500-W electric heater is plugged into the outlet of a 120-V circuit that has a 20-A circuit breaker. You plug an electric hair dryer into the same outlet. The hair dryer has power settings of 600 W, 900 W, 1200 W, and 1500 W. You start with the hair d
> The heating element of an electric dryer is rated at 4.1 kW when connected to a 240-V line. (a). What is the current in the heating element? Is 12-gauge wire large enough to supply this current? (b). What is the resistance of the dryer’s heating element
> You connect a battery, resistor, and capacitor as in Fig. 26.20a, where R = 12.0Ω and C = 5.00 × 10-6 F. The switch S is closed at t = 0. When the current in the circuit has magnitude 3.00 A, the charge on the capacitor i
> A 4.60-µF capacitor that is initially uncharged is connected in series with a 7.50-k Ω resistor and an emf source with
> You connect a battery, resistor, and capacitor as in Fig. 26.20a, where
> How could the direction of a magnetic field be determined by making only qualitative observations of the magnetic force on a straight wire carrying a current?
> A capacitor is charged to a potential of 12.0 V and is then connected to a voltmeter having an internal resistance of 3.40 M Ω. After a time of 4.00 s the voltmeter reads 3.0 V. What are (a). the capacitance and (b). the time constant of the circuit?
> In the circuit shown in Fig. E26.51, C = 5.90 µF,
> A 12.0-µF capacitor is charged to a potential of 50.0 V and then discharged through a 225-Ω resistor. How long does it take the capacitor to lose (a). half of its charge and (b). half of its stored energy?
> A single circular current loop 10.0 cm in diameter carries a 2.00-A current. (a). What is the magnetic field at the center of this loop? (b). Suppose that we now connect 1000 of these loops in series within a 500-cm length to make a solenoid 500 cm lon
> In the circuit in Fig. E26.49 the capacitors are initially uncharged, the battery has no internal resistance, and the ammeter is idealized. Find the ammeter reading Fig. E26.49: (a). just after the switch S is closed and (b). after S has been closed
> A 1.50-µF capacitor is charging through a 12.0-Ω resistor using a 10.0-V battery. What will be the current when the capacitor has acquired 1 4 of its maximum charge? Will it be 1 4 of the maximum current?
> In the circuit shown in Fig. E26.47 each capacitor initially has a charge of magnitude 3.50 nC on its plates. After the switch S is closed, what will be the current in the circuit at the instant that the capacitors have lost 80.0% of their initial stored
> A resistor and a capacitor are connected in series to an emf source. The time constant for the circuit is 0.780 s. (a). A second capacitor, identical to the first, is added in series. What is the time constant for this new circuit? (b). In the original
> An emf source with
> A 12.4-µF capacitor is connected through a 0.895-M resistor to a constant potential difference of 60.0 V. (a). Compute the charge on the capacitor at the following times after the connections are made: 0, 5.0 s, 10.0 s, 20.0 s, and 100.0 s. (b). Comput
> In the circuit shown in Fig. E26.43 both capacitors are initially charged to 45.0 V. Fig. E26.43: (a). How long after closing the switch S will the potential across each capacitor be reduced to 10.0 V, and (b). what will be the current at that time?
> A resistor consists of three identical metal strips connected as shown in Fig. Q26.8. If one of the strips is cut out, does the ammeter reading increase, decrease, or stay the same? Why? Fig. Q26.8: A
> The resistance of a galvanometer coil is 25.0 Ω, and the current required for full-scale deflection is 500 µA. (a). Show in a diagram how to convert the galvanometer to an ammeter reading 20.0 mA full scale, and compute the shunt resistance. (b). Show
> A galvanometer having a resistance of 25.0 Ω has a 1.00-Ω shunt resistance installed to convert it to an ammeter. It is then used to measure the current in a circuit consisting of a 15.0- Ω resistor connected across the terminals of a 25.0-V battery
> A closely wound, circular coil with radius 2.40 cm has 800 turns. (a). What must the current in the coil be if the magnetic field at the center of the coil is 0.0770 T? (b). At what distance x from the center of the coil, on the axis of the coil, is th
> A circuit consists of a series combination of 6.00-kΩ and 5.00-kΩ resistors connected across a 50.0-V battery having negligible internal resistance. You want to measure the true potential difference (that is, the potential difference without the meter
> The resistance of the coil of a pivotedcoil galvanometer is 9.36 , and a current of 0.0224 A causes it to deflect full scale. We want to convert this galvanometer to an ammeter reading 20.0 A full scale. The only shunt available has a resistance of 0.025
> In the circuit shown in Fig. E26.25 find Fig. E26.25: (a). the current in resistor R; (b). the resistance R; (c). the unknown emf E. (d). If the circuit is broken at point x, what is the current in resistor R? 28.0 V R + 4.00 A ww X 6.00 N 6.0
> The batteries shown in the circuit in Fig. E26.24 have negligibly small internal resistances. Find the current through Fig. E26.24: (a). the 30.0-Ω resistor; (b). the 20.0-Ω resistor; (c). the 10.0-V battery. 30.0 20.0 N
> In the circuit shown in Fig. E26.23, ammeter A1 reads 10.0 A and the batteries have no appreciable internal resistance. Fig. E26.23: (a). What is the resistance of R? (b). Find the readings in the other ammeters. (A2) 40.0 N R (A) (A4 (A3 20.0 N
> In the circuit shown in Fig. E26.34, the 6.0-Ω resistor is consuming energy at a rate of 24 J/s when the current through it flows as shown. Fig. E26.34: (a). Find the current through the ammeter A. (b). What are the polarity and emf E of
> In the circuit shown in Fig. E26.33 all meters are idealized and the batteries have no appreciable internal resistance. Fig. E26.33: (a). Find the reading of the voltmeter with the switch S open. Which point is at a higher potential: a or b? (b). Wi
> In the circuit shown in Fig. E26.32 both batteries have insignificant internal resistance and the idealized ammeter reads 1.50 A in the direction shown. Find the emf
> A battery with no internal resistance is connected across identical light bulbs as shown in Fig. Q26.7. When you close the switch S, will the brightness of bulbs B1 and B2 change? If so, how will it change? Explain. Fig. Q26.7: B B1 B2
> In the circuit shown in Fig. E26.31 the batteries have negligible internal resistance and the meters are both idealized. With the switch S open, the voltmeter reads 15.0 V. Fig. E26.31: (a). Find the emf 30.0 N A 20.0 + T 25.0 V 50.0 V 75.0 Ω E =
> Three very long parallel wires each carry current I in the directions shown in Fig. E28.28. If the separation between adjacent wires is d, calculate the magnitude and direction of the net magnetic force per unit length on each wire. Fig. E28.28: / /
> The 5.00-V battery in Fig. E26.28 is removed from the circuit and replaced by a 15.00-V battery, with its negative terminal next to point b. The rest of the circuit is as shown in the figure. Find Fig. E26.28: (a). the current in each branch and (b)
> The 10.00-V battery in Fig. E26.28 is removed from the circuit and reinserted with the opposite polarity, so that its positive terminal is now next to point a. The rest of the circuit is as shown in the figure. Find Fig. E26.28: (a). the current in e
> In the circuit shown in Fig. E26.28, find Fig. E26.28: (a). the current in each branch and (b). the potential difference Vab of point a relative to point b.
> In the circuit shown in Fig. E26.27, find Fig. E26.27: (a). the current in the 3.00-Ω resistor; (b). the unknown emfs 2.00 A R 4.00 N 3.00 N 6.00 N 3.00 A | 5.00 A ww
> Find the emfs E1 and E2 in the circuit of Fig. E26.26, and find the potential difference of point b relative to point a. Fig. E26.26: 1.00 N 20.0 V 6.00 N 1.00 A | 1.00 Ω ε 4.00 Ω a A|| 1.00 N E2 2.00 N
> For the circuit shown in Fig. E26.7 find the reading of the idealized ammeter if the battery has an internal resistance of 3.26 Ω. Fig. E26.7: 45.0 N 25.0 V 18.0 N ww 15.0 N A,
> For the circuit shown in Fig. E26.6 both meters are idealized, the battery has no appreciable internal resistance, and the ammeter reads 1.25 A. Fig. E26.6: (a). What does the voltmeter read? (b). What is the emf E of the battery? 25.0 N (A 15.0
> A triangular array of resistors is shown in Fig. E26.5. What current will this array draw from a 35.0-V battery having negligible internal resistance if we connect it across Fig. E26.5: (a). ab; (b). bc; (c). ac? (d). If the battery has an interna
> A machine part has a resistor X protruding from an opening in the side. This resistor is connected to three other resistors, as shown in Fig. E26.2. An ohmmeter connected across a and b reads 2.00 Ω. What is the resistance of X? Fig. E26.2:
> If two resistors R1 and R2 (R2 > R1) are connected in parallel as shown in Fig. Q26.6, which of the following must be true? In each case justify your answer. Fig. Q26.6: / / (a). I1 = I2. (b). I3 = I4. (c). The current is greater in R1 than in R2.
> When the polarity of the voltage applied to a dc motor is reversed, the direction of motion does not reverse. Why not? How could the direction of motion be reversed?
> A uniform wire of resistance R is cut into three equal lengths. One of these is formed into a circle and connected between the other two (Fig. E26.1). What is the resistance between the opposite ends a and b? Fig. E26.1: a b
> A 60-W, 120-V light bulb and a 200-W, 120-V light bulb are connected in series across a 240-V line. Assume that the resistance of each bulb does not vary with current. (Note: This description of a light bulb gives the power it dissipates when connected t
> Two light bulbs have constant resistances of 400 Ω and 800 Ω. If the two light bulbs are connected in series across a 120-V line, find (a). the current through each bulb; (b). the power dissipated in each bulb; (c). the total power dissipated in both
> In the circuit shown in Fig. E26.20, the rate at which R1 is dissipating electrical energy is 15.0 W. Fig. E26.20: (a). Find R1 and R2. (b). What is the emf of the battery? (c). Find the current through both R2 and the 10.0-Ω resistor.
> In the circuit in Fig. E26.19, a 20.0-Ω resistor is inside 100 g of pure water that is surrounded by insulating styrofoam. If the water is initially at 10.0°C, how long will it take for its temperature to rise to 58.0°C?
> In the circuit shown in Fig. E26.18,
> You are a technician testing the operation of a cyclotron. An alpha particle in the device moves in a circular path in a magnetic field
> You are a research scientist working on a high-energy particle accelerator. Using a modern version of the Thomson e/m apparatus, you want to measure the mass of a muon (a fundamental particle that has the same charge as an electron but greater mass). The
> A resistor with R = 850 Ω is connected to the plates of a charged capacitor with capacitance C = 4.62 µF. Just before the connection is made, the charge on the capacitor is 6.90 mC. (a). What is the energy initially stored in the capacitor? (b). What
> How many turns does this typical MRI magnet have? (a). 1100; (b). 3000; (c). 4000; (d). 22,000.
> A long, horizontal wire AB rests on the surface of a table and carries a current I. Horizontal wire CD is vertically above wire AB and is free to slide up and down on the two vertical metal guides C and D (Fig. E28.32). Wire CD is connected through the s
> A tank containing a liquid has turns of wire wrapped around it, causing it to act like an inductor. The liquid content of the tank can be measured by using its inductance to determine the height of the liquid in the tank. The inductance of the tank chang
> In the circuit shown in Fig. E26.17, the voltage across the 2.00-Ω resistor is 12.0 V. What are the emf of the battery and the current through the 6.00-Ω resistor? Fig. E26.17: /
> In the circuit shown in Fig. P30.61,
> Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 45.0 W. What power would be dissipated if the three resistors were connected in parallel across the sa
> The wire semicircles shown in Fig. P28.66 have radii a and b. Calculate the net magnetic field (magnitude and direction) that the current in the wires produces at point P. Fig. P28.66: b P ->
> A wire 25.0 cm long lies along the z-axis and carries a current of 7.40 A in the +z-direction. The magnetic field is uniform and has components Bx = -0.242 T, By = -0.985 T, and Bz = -0.336 T. (a). Find the components of the magnetic force on the wire.
> A dielectric of permittivity 3.5 × 10-11 F/m completely fills the volume between two capacitor plates. For t > 0 the electric flux through the dielectric is (8.0 × 103 V ∙ m/s3) t3. The dielectric is ideal and nonmagnetic; the conduction current in the d
