(II) I f 65 MW of power at 45 kV (rms) arrives at atown

What would be the advantage, in Faradays experiments (Fig. 29-1), of using coils with many turns?

What is the difference between magnetic flux and magnetic field?

Suppose you are holding a circular ring of wire and suddenly thrust a magnet, south pole first, away from you toward the center of the circle. Is a current induced in the wire? Is a current induced when the magnet is held steady within the ring? Is a current induced when you withdraw the magnet? In each case, if your answer is yes, specify the direction.

Two loops of wire are moving in the vicinity of a very long straight wire carrying a steady current as shown in Fig. 29-33. Find the direction of the induced current in each loop.

Ts there, a forrp between the two loons HisriisseH in

Suppose you are looking along a line through the centers of two circular (but separate) wire loops, one behind the other. A battery is suddenly connected to the front loop, establishing a clockwise current, (a) Will a current be induced in the second loop? (b) If so, when does this current start? (c) When does it stop? (d) In what direction is this current? (ie) Is there a force between the two loops? ( /) If so, in what direction?

The battery mentioned in Question 6 is disconnected. Will a current be induced in the second loop? If so, when does it start and stop? In what direction is this current?

In what direction w ill the current flow in Fig. 29-12a if the rod moves to the left, which decreases the area of the loop to the left?

In Fig. 29-34, determine the direction of the induced current in resistor RA (a) when coil B is moved toward coil A, (b) when is moved away from A, Coil B (c) when the resistance /omnonovrx s* Rb is increased.

In situations where a small signal must travel over a distance, a shielded cable is used in which the signal wire is surrounded by an insulator and then enclosed by a cylindrical conductor carrying the return current (Fig. 28-12). Why is a shield necessary?

What is the advantage of placing the two insulated electric wires carrying ac close together or even twisted about each other?

Which object w ill fall faster in a nonuniform magnetic field, a conducting loop with radius or a straight wire of length 1/2?

A region where no magnetic field is desired is surrounded by a sheet of low-resistivity metal, (a) Will this sheet shield the interior from a rapidly changing magnetic field outside? Explain. (b) Will it act as a shield to a static magnetic field? (c) What if the sheet is superconducting (resistivity = 0)?

A cell phone charger contains a transformer. Why cant you just buy one universal charger to charge your old cell phone, your new cell phone, your drill, and your toy electric train?

An enclosed transformer has four wire leads coming from it. How could you determine the ratio of turns on the two coils without taking the transformer apart? How would you know which wires paired with which?

The use of higher-voltage lines in homes say, 600 V or 1200 V would reduce energy waste. Why are they not used?

A transformer designed for a 120-V ac input w ill often burn out if connected to a 120-V dc source. Explain. [Hint: The resistance of the primary coil is usually very low.]

Explain why, exactly, the lights may dim briefly when a refrigerator motor starts up. When an electric heater is turned on, the lights may stay dimmed as long as the heater is on. Explain the difference.

Use Fig. 29-15 plus the right-hand rules to show why the counter torque in a generator opposes the motion.

Will an eddy current brake (Fig. 29-21) work on a copper or aluminum wheel, or must the wheel be ferromagnetic? Explain

It has been proposed that eddy currents be used to help sort solid waste for recycling. The waste is first ground into tiny pieces and iron removed with a dc magnet. The waste then is allowed to slide down an incline over permanent magnets. How w ill this aid in the separation of nonferrous metals (Al, Cu, Pb, brass) from nonmetallic materials?

The pivoted metal bar with slots in Fig. 29-35 falls much more quickly through a magnetic field than does a solid bar. Explain.

If an aluminum sheet is held between the poles of a large bar magnet, it requires some force to pull it out of the magnetic field even though the sheet is not ferromagnetic and does not touch the pole faces. Explain.

A bar magnet falling inside a vertical metal tube reaches a terminal velocity even if the tube is evacuated so that there is no air resistance. Explain

A metal bar, pivoted at one end, oscillates freely in the absence of a magnetic field; but in a magnetic field, its oscillations are quickly damped out. Explain. (This magnetic damping is used in a number of practical devices.)

Since a magnetic microphone is basically like a loudspeaker, could a loudspeaker (Section 27-6) actually serve as a microphone? That is, could you speak into a loudspeaker and obtain an output signal that could be amplified? Explain. Discuss, in light of your response, how a microphone and loudspeaker differ in construction.

(I) The moving rod in Fig. 29-12b is 13.2 cm long and generates an emf of 120 mV while moving in a 0.90-T magnetic field. What is its speed?

(I) The moving rod in Fig. 29-12b is 12.0 cm long and is pulled at a speed of 15.0 cm/s. I f the magnetic field is 0.800 T, calculate the emf developed

(II) In Fig. 29-12a, the rod moves to the right with a speed of 1.3 m/s and has a resistance of 2.5 fl. The rail separation is = 25.0 cm. The magnetic field is 0.35 T, and the resistance of the U-shaped conductor is 25.0 XI at a given instant. Calculate (a) the induced emf, (b) the current in the U-shaped conductor, and (c) the external force needed to keep the rods velocity constant at that instant

(II) If the U-shaped conductor in Fig. 29-12a has resistivity p, whereas that of the moving rod is negligible, derive a formula for the current I as a function of time. Assume the rod starts at the bottom of the U at t = 0, and moves with uniform speed v in the magnetic field B. The cross-sectional area of the rod and all parts of the U is A.

(II) Suppose that the U-shaped conductor and connecting rod in Fig. 2 9-12a are oriented vertically (but still in contact) so that the rod is falling due to the gravitational force. Find the terminal speed of the rod if it has mass m = 3.6 grams, length i = 18 cm, and resistance R = 0.001312. It is falling in a uniform horizontal field B = 0.060 T. Neglect the resistance of the U-shaped conductor.

(II) When a car drives through the Earths magnetic field, an emf is induced in its vertical 75.0-cm-long radio antenna. If the Earths field (5.0 X 10-5 T) points north with a dip angle of 45, what is the maximum emf induced in the antenna and which direction(s) w ill the car be moving to produce this maximum value? The cars speed is 30.0 m/s on a horizontal road.

(II) A conducting rod rests on two long frictionless parallel rails in a magnetic field B (_L to the rails and rod) as in Fig. 29-44. (a) I f the rails are horizontal and the rod is given an in itia l push, w ill the rod travel at constant speed even though a magnetic field is present? (b ) Suppose at t = 0, when the rod has speed v = v0 , the two rails are connected electrically by a wire from point a to point b. Assuming the rod has resistance R and the rails have negligible resistance, determine the speed of the rod as a function of time. Discuss your answer.

( I ll) Suppose a conducting rod (mass ra, resistance R) rests on two frictionless and resistanceless parallel rails a distance I apart in a uniform magnetic field B (_L to the rails and to the rod) as in Fig. 29-44. A t t = 0, the rod is at rest and a source of emf is connected to the points a and b. Determine the speed of the rod as a function of time if (a) the source puts out a constant current I, (b) the source puts out a constant emf %. (c) Does the rod reach a terminal speed in either case? I f so, what is it?

I ll) A short section of wire, of length a, is moving with velocity v, parallel to a very long wire carrying a current I as shown in Fig. 29-45. The near end of the wire section is a distance b from the long wire. Assuming the vertical wire is very long compared to a + b, determine the emf between the ends of the short section. Assume v is (a) in the same direction as I, (b) in the opposite direction to I.

(I) The generator of a car idling at 875-rpm produces 12.4 V. What w ill the output be at a rotation speed of 1550 rpm assuming nothing else changes?

(I) A simple generator is used to generate a peak output voltage of 24.0 V. The square armature consists of windings that are 5.15 cm on a side and rotates in a field of 0.420 T at a rate of 60.0 rev/s. How many loops of wire should be wound on the square armature?

(II) A simple generator has a 480-loop square coil 22.0 cm on a side. How fast must it turn in a 0.550-T field to produce a 120-V peak output?

(II) Show that the rms output of an ac generator is Vrms = N A B a ) / \/ l where w = li r f .

(II) A 250-loop circular armature coil with a diameter of 10.0 cm rotates at 120 rev/s in a uniform magnetic field of strength 0.45 T. What is the rms voltage output of the generator? What would you do to the rotation frequency in order to double the rms voltage output?

(I) The back emf in a motor is 72 V when operating at 1200 rpm. What would be the back emf at 2500 rpm if the magnetic field is unchanged?

(I) A motor has an armature resistance of 3.05 fi. I f it draws 7.20 A when running at fu ll speed and connected to a 120-V line, how large is the back emf?

(II) What w ill be the current in the motor of Example 29-10 if the load causes it to run at half speed?

(II) The back emf in a motor is 85 V when the motor is operating at 1100 rpm. How would you change the motors magnetic field if you wanted to reduce the back emf to 75 V

(II) A dc generator is rated at 16 kW, 250 V, and 64 A when it rotates at 1000 rpm. The resistance of the armature windings is 0.400. (a) Calculate the no-load voltage at 1000 rpm (when there is no circuit hooked up to the generator). (b ) Calculate the full-load voltage (i.e. at 64 A ) when the generator is run at 750 rpm. Assume that the magnitude of the magnetic field remains constant.

(I) A transformer has 620 turns in the primary coil and 85 in the secondary coil. What kind of transformer is this, and by what factor does it change the voltage? By what factor does it change the current?

(I) Neon signs require 12 kV for their operation. To operate from a 240-V line, what must be the ratio of secondary to primary turns of the transformer? What would the voltage output be if the transformer were connected backward?

(II) A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 7.5 A to the train, (a) What voltage is present across the tracks? (b ) Is the transformer step-up or step-down?

(II) The output voltage of a 75-W transformer is 12 V, and the input current is 22 A. (a) Is this a step-up or a step-down transformer? (b ) By what factor is the voltage multiplied?

(II) I f 65 MW of power at 45 kV (rms) arrives at a town from a generator via 3.0-fl transmission lines, calculate (a) the emf at the generator end of the lines, and (b) the fraction of the power generated that is wasted in the lines.

(II) Assume a voltage source supplies an ac voltage of amplitude V0 between its output terminals. I f the output terminals are connected to an external circuit, and an ac current of amplitude / 0 flows out of the terminals, then the equivalent resistance of the external circuit is Req = Vq/ I 0. (a) I f a resistor R is connected directly to the output terminals, what is R eq? (b) I f a transformer with Np and N$ turns in its primary and secondary, respectively, is placed between the source and the resistor as shown in Fig. 29-46, what is Req? [Transformers can be used in ac circuits to alter the apparent resistance of circuit elements, such as loud speakers, in order to maximize transfer of power.]

( Ill) Design a dc transmission line that can transmit 225 MW of electricity 185 km with only a 2.0% loss. The wires are to be made of aluminum and the voltage is 660 kV.

( Ill) Suppose 85 kW is to be transmitted over two 0.100-ft lines. Estimate how much power is saved if the voltage is stepped up from 120 V to 1200 V and then down again, rather than simply transmitting at 120 V. Assume the transformers are each 99% efficient.

(II) In a circular region, there is a uniform magnetic field B pointing into the page (Fig. 29-47). An xy coordinate system has its origin at the circular regions center. A free positive point charge +<2 = 1.0 juC is initially at rest at a position x = +10 cm on the x axis. If the magnitude of the magnetic field is now decreased at a rate of -0.10 T/s, what force (magnitude and direction) w ill act on +Q7

(II) The betatron, a device used to accelerate electrons to high energy, consists of a circular vacuum tube placed in a magnetic field (Fig. 29-48), into which electrons are injected. The electromagnet produces a field that (1) keeps the electrons in their circular orbit inside the tube, and (2) increases the speed of the electrons when B changes. (a) Explain how the electrons are accelerated. (See Fig. 29-48.) (b) In what direction are the electrons moving in Fig. 29-48 (give directions as if looking down from above)? (c) Should B increase or decrease to accelerate the electrons? (d) The magnetic field is actually 60 Hz ac; show that the electrons can be accelerated only during \ of a cycle (asos)- (During this time they make hundreds of thousands of revolutions and acquire very high energy

( Ill) Show that the electrons in a betatron, Problem 55 and Fig. 29-48, are accelerated at constant radius if the magnetic field B0 at the position of the electron orbit in the tube is equal to half the average value of the magnetic field (i?avg) over the area of the circular orbit at each moment: B0 = |i? avg. (This is the reason the pole faces have a rather odd shape, as indicated in Fig. 29-48.)

( Ill) Find a formula for the net electric field in the moving rod of Problem 34 as a function of time for each case, (a) and (b).

Suppose you are looking at two current loops in the plane of the page as shown in Fig. 29-49. When the switch S is closed in the left-hand coil, (a) what is the direction of the induced current in the other loop? (b) What is the situation after a long time? (c) What is the direction of the induced current in the right-hand loop if that loop is quickly pulled horizontally to the right (S having been closed for a long time)?

A square loop 27.0 cm on a side has a resistance of 7.50 fi. It is initially in a 0.755-T magnetic field, with its plane perpendicular to B, but is removed from the field in 40.0 ms. Calculate the electric energy dissipated in this process.

Power is generated at 24 kV at a generating plant located 85 km from a town that requires 65 MW of power at 12 kV. Two transmission lines from the plant to the town each have a resistance of 0.10 ft/km . What should the output voltage of the transformer at the generating plant be for an overall transmission efficiency of 98.5%, assuming a perfect transformer?

A circular loop of area 12 m2 encloses a magnetic field perpendicular to the plane of the loop; its magnitude is B(t) = (10T/s). The loop is connected to a 7.5-ft resistor

The primary windings of a transformer which has an 85% efficiency are connected to 110-V ac. The secondary windings are connected across a 2.4-ft, 75-W lightbulb. (a) Calculate the current through the primary windings of the transformer, (b) Calculate the ratio of the number of primary windings of the transformer to the number of secondary windings of the transformer.

A pair of power transmission lines each have a 0.80-ft resistance and carry 740 A over 9.0 km. If the rms input voltage is 42 kV, calculate (a) the voltage at the other end, (b) the power input, (c) power loss in the lines, and (d) the power output.

Show that the power loss in transmission lines, PL , is given by Pl = {Pj )2Rl/V 2, where PT is the power transmitted to the user, V is the delivered voltage, and RL is the resistance of the power lines.

A high-intensity desk lamp is rated at 35 W but requires only 12 V. It contains a transformer that converts 120-V household voltage, (a) Is the transformer step-up or stepdown? (b) What is the current in the secondary coil when the lamp is on? (c) What is the current in the primary coil? (d) What is the resistance of the bulb when on?

Two resistanceless rails rest 32 cm apart on a 6.0 ramp. They are joined at the bottom by a 0.60-ft resistor. A t the top a copper bar of mass 0.040 kg (ignore its resistance) is laid across the rails. The whole apparatus is immersed in a

A coil with 150 turns, a radius of 5.0 cm, and a resistance of 12 O surrounds a solenoid with 230 turns/cm and a radius of 4.5 cm; see Fig. 29-50. The current in the solenoid changes at a constant rate from 0 to 2.0 A in 0.10 s. Calculate the magnitude and direction of the induced current in the 150-turn coil.

A search coil for measuring B (also called a flip coil) is a small coil with N turns, each of cross-sectional area A. It is connected to a so-called ballistic galvanometer, which is a device to measure the total charge Q that passes through it in a short time. The flip coil is placed in the magnetic field to be measured with its face perpendicular to the field. It is then quickly rotated 180 about a diameter. Show that the total charge Q that flows in the induced current during this short flip time is proportional to the magnetic field B. In particular, show that B is given by B = QR 2NA where R is the total resistance of the circuit, including that of the coil and that of the ballistic galvanometer which measures the charge Q.

A ring with a radius of 3.0 cm and a resistance of 0.025 f l is rotated about an axis through its diameter by 90 in a magnetic field of 0.23 T perpendicular to that axis. What is the largest number of electrons that would flow past a fixed point in the ring as this process is accomplished?

A flashlight can be made that is powered by the induced current from a magnet moving through a coil of wire. The coil and magnet are inside a plastic tube that can be shaken causing the magnet to move back and forth through the coil. Assume the magnet has a maximum field strength of 0.05 T. Make reasonable assumptions and specify the size of the coil and the number o f turns necessary to ligh t a standard 1-watt, 3-V flashlight bulb.

A small electric car overcomes a 250-N friction force when traveling 35 km/h. The electric motor is powered by ten 12-V batteries connected in series and is coupled directly to the wheels whose diameters are 58 cm. The 270 armature coils are rectangular, 12 cm by 15 cm, and rotate in a 0.60-T magnetic field, (a) How much current does the motor draw to produce the required torque? (b ) What is the back emf? (c) How much power is dissipated in the coils? (d) What percent of the input power is used to drive the car?

What is the energy dissipated as a function of time in a circular loop of 18 turns of wire having a radius of 10.0 cm and a resistance of 2.0 XI if the plane of the loop is perpendicular to a magnetic field given by B(t) - B0e,-t/r

A thin metal rod of length rotates with angular velocity (o about an axis through one end (Fig. 29-51). The rotation axis is perpendicular to the rod and is parallel to a uniform magnetic field B. Determine the emf developed between the ends of the rod.

The magnetic field of a shunt-wound dc motor is produced by field coils placed in parallel with the armature coils. Suppose that the field coils have a resistance of 36.0 O and the armature coils 3.00 Cl. The back emf at fu ll speed is 105 V when the motor is connected to 115 V dc. (a) Draw the equivalent circuit for the situations when the motor is just starting and when it is running fu ll speed, (b) What is the total current drawn by the motor at start up? (c) What is the total current drawn when the motor runs at fu ll speed?

Apply Faradays law, in the form of Eq. 29-8, to show that the static electric field between the plates of a parallel-plate r 1 capacitor cannot drop abruptly to zero at the edges, but must, in fact, fringe. Use the path shown dashed in Fig. 29-52.

A circular metal disk of radius R rotates with angular velocity co about an axis through its center perpendicular to its face. The disk rotates in a uniform magnetic field B whose direction is parallel to the rotation axis. Determine the emf induced between the center and the edges

What is the magnitude and direction of the electric field at each point in the rotating disk of Problem 76?

A circular-shaped circuit of radius r, containing a resistance R and capacitance C, is situated with its plane perpendicular to a spatially uniform magnetic field B directed into the page (Fig. 29-53). Starting at time t = 0, the voltage difference V\>a = Va across the capacitor plates is observed to increase with time t according to = K)(l - e~t/T), where V0 and t are positive constants. Determine dB /d t, the rate at which the magnetic field magnitude changes with time. Is B becoming larger or smaller as time increases?

In a certain region of space near Earths surface, a uniform horizontal magnetic field of magnitude B exists above a level defined to be y = 0. Below y = 0, the field abruptly becomes zero (Fig. 29-54). A vertical square wire loop has resistivity p, mass density pm, diameter d, and side length t It is initia lly at rest with its lower horizontal side at y = 0 and is then allowed to fall under gravity, with its plane perpendicular to the direction of the magnetic field. (a) While the loop is s till partially immersed in the magnetic field (as it falls into the zero-field region), determine the magnetic drag force that acts on it at the moment when its speed is v. (b) Assume that the loop achieves a terminal velocity vT before its upper horizontal side exits the field. Determine a formula for v^. (c) I f the loop is made of copper and B = 0.80 T, find v j.

Ill) In an experiment, a coil was mounted on a low-friction cart that moved through the magnetic field B of a permanent magnet. The speed of the cart v and the induced voltage V were simultaneously measured, as the cart moved through the magnetic field, using a computer-interfaced motion sensor and a voltmeter. The Table below shows the collected data: Speed, v (m/s) 0.367 0.379 0.465 0.623 0.630 Induced voltage, V (V) 0.128 0.135 0.164 0.221 0.222 (a) Make a graph of the induced voltage, V, vs. the speed, v. Determine a best-fit linear equation for the data. Theoretically, the relationship between V and v is given by V = B N lv where N is the number of turns of the coil, B is the magnetic field, and is the average of the inside and outside widths of the coil. In the experiment, B = 0.126 T, N = 50, and = 0.0561 m. (b) Find the % error between the slope of the experimental graph and the theoretical value for the slope, (c) For each of the measured speeds v, determine the theoretical value of V and find the % error of each.