Question: Find the emfs E1 and E2 in

> 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-kΩ 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 MΩ. 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

> A particle with initial velocity

> 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

> 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

> A person with body resistance between his hands of 10 k Ω accidentally grasps the terminals of a 14-kV power supply. (a). If the internal resistance of the power supply is 2000 Ω, what is the current through the person’s body? (b). What is the power di

> The average bulk resistivity of the human body (apart from surface resistance of the skin) is about 5.0 Ω ∙ m. The conducting path between the hands can be represented approximately as a cylinder 1.6 m long and 0.10 m in diameter. The skin resistance can

> Figure P28.62 shows an end view of two long, parallel wires perpendicular to the xy-plane, each carrying a current I but in opposite directions. Figure P28.62: (a). Copy the diagram, and draw vectors to show the a P x- a (XI

> The wires in a household lamp cord are typically 3.0 mm apart center to center and carry equal currents in opposite directions. If the cord carries direct current to a 100-W light bulb connected across a 120-V potential difference, what force per meter d

> A particle of charge q > 0 is moving at speed v in the +z-direction through a region of uniform magnetic field

> A charged capacitor with C = 590 µF is connected in series to an inductor that has L = 0.330 H and negligible resistance. At an instant when the current in the inductor is i = 2.50 A, the current is increasing at a rate of di/dt = 73.0 A/s. During the cu

> Consider the circuit shown in Fig. E26.16. The current through the 6.00-Ω resistor is 4.00 A, in the direction shown. What are the currents through the 25.0-Ω and 20.0-Ω resistors? Fig. E26.16: 4.00 A 6.00 N ww 2

> The magnetic poles of a small cyclotron produce a magnetic field with magnitude 0.85 T. The poles have a radius of 0.40 m, which is the maximum radius of the orbits of the accelerated particles. (a). What is the maximum energy to which protons (q = 1.60

> An L-C circuit consists of a 60.0-mH inductor and a 250-µF capacitor. The initial charge on the capacitor is 6.00 µC, and the initial current in the inductor is zero. (a). What is the maximum voltage across the capacitor? (b). What is the maximum curre

> Your latest invention is a car alarm that produces sound at a particularly annoying frequency of 3500 Hz. To do this, the car-alarm circuitry must produce an alternating electric current of the same frequency. That’s why your design includes an inductor

> A very long, straight solenoid with a crosssectional area of 2.00 cm2 is wound with 90.0 turns of wire per centimeter. Starting at t = 0, the current in the solenoid is increasing according to i(t) = (0.160 A/s2) t2. A secondary winding of 5 turns encirc

> A small solid conductor with radius a is supported by insulating, nonmagnetic disks on the axis of a thin-walled tube with inner radius b. The inner and outer conductors carry equal currents i in opposite directions. (a). Use Ampere’s law to find the ma

> A coil has 400 turns and self-inductance 7.50 mH. The current in the coil varies with time according to i = (680 mA) cos (pt/0.0250 s). (a). What is the maximum emf induced in the coil? (b). What is the maximum average flux through each turn of the coi

> One solenoid is centered inside another. The outer one has a length of 50.0 cm and contains 6750 coils, while the coaxial inner solenoid is 3.0 cm long and 0.120 cm in diameter and contains 15 coils. The current in the outer solenoid is changing at 49.2

> Two long, parallel wires are separated by a distance of 2.50 cm. The force per unit length that each wire exerts on the other is 4.00 × 10-5 N/m, and the wires repel each other. The current in one wire is 0.600 A. (a). What is the current in the second

> An inductor is connected to the terminals of a battery that has an emf of 16.0 V and negligible internal resistance. The current is 4.86 mA at 0.940 ms after the connection is completed. After a long time, the current is 6.45 mA. What are (a). the resist

> An L-R-C series circuit has L = 0.450 H, C = 2.50 × 10-5 F, and resistance R. (a). What is the angular frequency of the circuit when R = 0? (b). What value must R have to give a 5.0% decrease in angular frequency compared to the value calculated in par

> An L-R-C series circuit has L = 0.600 H and C = 3.00 µF. (a). Calculate the angular frequency of oscillation for the circuit when R = 0. (b). What value of R gives critical damping? (c). What is the oscillation frequency

> In the circuit of Fig. E26.15, each resistor represents a light bulb. Let R1 = R2 = R3 = R4 = 4.50 Ω and

> An L-C circuit containing an 80.0-mH inductor and a 1.25-nF capacitor oscillates with a maximum current of 0.750 A. Calculate: (a). the maximum charge on the capacitor and (b). the oscillation frequency of the circuit. (c). Assuming the capacitor had

> In an L-C circuit, L = 85.0 mH and C = 3.20 µF. During the oscillations the maximum current in the inductor is 0.850 mA. (a). What is the maximum charge on the capacitor? (b). What is the magnitude of the charge on the capacitor at an instant when the c

> In Fig. 30.11 switch S1 is closed while switch S2 is kept open. The inductance is L = 0.380 H, the resistance is R = 48.0 Ω, and the emf of the battery is 18.0 V. At time t after S1 is closed, the current in the circuit is increasing

> A 35.0-V battery with negligible internal resistance, a 50.0Ω resistor, and a 1.25-mH inductor with negligible resistance are all connected in series with an open switch. The switch is suddenly closed. (a). How long after closing the switch will the cu

> In a proton accelerator used in elementary particle physics experiments, the trajectories of protons are controlled by bending magnets that produce a magnetic field of 4.80 T. What is the magnetic-field energy in a 10.0-cm3 volume of space where B = 4.80

> An air-filled toroidal solenoid has 300 turns of wire, a mean radius of 12.0 cm, and a cross-sectional area of 4.00 cm2. If the current is 5.00 A, calculate: (a). the magnetic field in the solenoid; (b). the self-inductance of the solenoid; (c). the en

> Two long, parallel wires are separated by a distance of 0.400 m (Fig. E28.29). The currents I1 and I2 have the directions shown. Fig. E28.29: (a). Calculate the magnitude of the force exerted by each wire on a 1.20-m length of the other. Is the force

> An air-filled toroidal solenoid has a mean radius of 15.0 cm and a cross-sectional area of 5.00 cm2. When the current is 12.0 A, the energy stored is 0.390 J. How many turns does the winding have?