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3. Two small spheres are charged with +16 and 4 units of electricity. With what, force will they attract each other when at a distance of 4 cm.?

4. If the two spheres of the previous problem are made to touch and are then returned to their former positions, with what force will they act on each other? Will this force be attraction or repulsion?

5. Why is the capacity of a conductor greater when another conductor connected to the earth is near it than when it stands alone?

6. A Leyden jar is placed on a glass plate and 10 units of electricity placed on the inner coating. The knob is then connected to a gold-leaf electroscope. Will the leaves of the electroscope stand farther apart now or after the outside coating has been connected to the earth?

CHAPTER XIV. 1. Why would an electromagnet made by winding bare wire on a bare iron core be worthless as a magnet?

2. The plane of a suspended loop of wire is east and west. A current is sent through it, passing from east to west on the upper side. What will happen to the loop if it is perfectly free to turn?

3. When a strong current is sent through a suspended-coil galvanometer, what position will the coil assume?

4. If the earth's magnetism is due to a surface charge rotating with the earth, must this charge be positive or negative in order to produce the sort of magnetic poles which the earth has? (This is actually the present theory of the earth's magnetism.)

5. Why must a galvanometer which is to be used for measuring voltages have a high resistance?

6. Why is the E. M. F. of a cell equal to the P. D. of its terminals when on open circuit? (Explain by reference to the water analogy of § 318.)

7. Can you prove from a consideration of Ohm's law that when wires of different resistances are inserted in series in a circuit, the P.D.'s between the ends of the various wires are proportional to the resistances of these wires?

8. How long a piece of No. 30 copper wire will have the same resistance as a meter of No. 30 German-silver wire? (See table of specific resistances, p. 262.)

9. The diameter of No. 20 wire is 31.96 mils (1 mil = .001 in.) and that of No. 30 wire 10.025 mils. Compare the resistances of equal lengths of No. 20 and No. 30 German-silver wires.

10. What length of No. 30 copper wire will have the same resistance as 20 ft. of No. 20 copper wire?

11. What length of No. 20 German-silver wire will have the same resistance as 100 ft. of No. 30 copper wire?

12. A galvanometer has a resistance of 588 ohms. If only one fiftieth of the current in the main circuit is to be allowed to pass through the moving coil, what must be the resistance of the shunt?

13. Ten pieces of wire, each having a resistance of 5 ohms, are connected in parallel (see Fig. 278). If the junction a is connected to one terminal of a Daniell cell and b to the other, what is the total current which will flow through the circuit when the E. M. F. of the cell is 1 volt and its resistance 2 ohms?

14. If a certain Daniell cell has an internal resistance of 2 ohms and an E. M. F. of 1.08 volts, what current will it send through an ammeter whose resistance is negligible? What current will it send through a copper wire of 2 ohms resistance? through a German-silver wire of 100 ohms resistance?

15. A Daniell cell indicates a certain current when connected to a galvanometer of negligible resistance. When a piece of No. 20 Germansilver wire is inserted into the circuit, it is found to require a length of 5 ft. to reduce the current to one half its former value. Find the resistance of the cell in ohms, No. 20 German-silver wire having a resistance of 190.2 ohms per 1000 ft.

16. A coil of unknown resistance is inserted in series with a considerable length of No. 30 German-silver wire and joined to a Daniell cell. When the terminals of a high-resistance galvanometer are touched to the wire at points 10 ft. apart, the deflection is found to be the same as when they are touched across the terminals of the unknown resistance. What is the resistance of the unknown coil? (See § 316, p. 263.)

17. How do we calculate the power consumed in any part of an electric circuit? What horse power is required to run an incandescent lamp carrying .5 ampere at 110 volts?

18. An electric soldering iron allows 5 amperes to flow through it when connected to an E. M. F. of 110 volts. What will it cost, at 12 cents per kilowatt hour, to operate the iron 6 hr. per day for 5 da.?

19. An electric motor developed 2 horse power when taking 16.5 amperes at 110 volts. Find the efficiency of the motor. (One horse power = 746 watts.)

CHAPTER XV. 1. If the coil of a sensitive galvanometer is set to swinging while the circuit through the coil is open, it will continue to swing for a long time; but if the coil is short-circuited, it will come to rest after a very few oscillations. Why? (The experiment may easily be tried. Remember that currents are induced in the moving coil. Apply Lenz's law.)

2. Show that if the reverse of Lenz's law were true, a motor once started would run of itself and do work; that is, it would furnish a case of perpetual motion.

3. If a series-wound dynamo is running at a constant speed, what effect will be produced on the strength of the field magnets by diminishing the external resistance and thus increasing the current? What will be the effect on the E. M. F.? (Remember that the whole current goes around the field magnets.) (See § 357.)

4. If a shunt-wound dynamo is run at constant speed, what effect will be produced on the strength of the field magnets by reducing the external resistance? What effect will this have on the E. M. F.?

5. In an incandescent-lighting system the lamps are connected in parallel across the mains. Every lamp which is turned on, then, diminishes the external resistance. Explain from a consideration of Problems 3 and 4 why a compound-wound dynamo (Fig. 318) keeps the P.D. between the mains constant.

6. When an electric fan is first started, the current through it is much greater than it is after the fan has attained its normal speed. Why?

7. If the pressure applied at the terminals of a motor is 500 volts, and the back pressure, when running at full speed, is 450 volts, what is the current flowing through the armature, its resistance being 10 ohms?

8. Two successive coils on the armature of a multipolar alternator are cutting lines of force which run in opposite directions. How does it happen that the currents generated flow through the wires in the same direction? (Fig. 310.)

9. A multipolar alternator has 20 poles and rotates 200 times per minute. How many alternations per second will be produced in the circuit?

10. With the aid of the dynamo rule explain why, in Figs. 313 and 315, the current in the conductors under the north poles is moving toward the observer and that in the conductors under the south poles away from the observer.

CHAPTER XVI. 1. A bullet fired from a rifle with a speed of 1200 ft. per second is heard to strike the target 6 sec. afterwards. What is the distance to the target, the temperature of the air being 20° C.? (Let x= the distance to the target.)

2. A church bell is ringing at a distance of mi. from one man and mi. from another. How much louder would it appear to the second man than to the first if no reflections of the sound took place? 3. A stone is dropped into a well 200 m. deep. At 20° C. how much time will elapse before the sound of the splash is heard at the top?

4. As a circular saw cuts into a block of wood the pitch of the note given out falls rapidly. Why?

5. A clapper strikes a bell once every two seconds. How far from the bell must a man be in order that the clapper may appear to hit the bell at the exact instant at which each stroke is heard?

6. The note from a piano string which makes 300 vibrations per second passes from indoors, where the temperature is 20° C., to outdoors, where it is 0° C. What is the difference in centimeters between the wave lengths indoors and outdoors?

7. A man riding on an express train moving at the rate of 1 mi. per minute hears a bell ringing in a tower in front of him. If the bell makes 280 vibrations per second, how many pulses will strike his ear per second, the velocity of sound being 1120 ft. per second? (The number of extra impulses received per second by the ear is equal to the number of wave lengths contained in the distance traveled per second by the train.) What effect has this upon the pitch? Had he been going from the bell at this rate, how many pulses per second would have reached his ear? How would this affect the pitch?

8. Explain the loud noise that results from singing the right pitch of note into the bunghole of an empty barrel.

9. Why do the echoes which are prominent in empty halls often disappear when the hall is full of people?

CHAPTER XVII. 1. What is the wave length of middle C when the speed of sound is 1152 ft. per second?

2. What is the pitch of a note whose wave length is 5.4 in., the speed being 1152 ft. per second?

3. A wire gives out the note C when the tension on it is 4 kg. What tension will be required to give out the note G?

4. A wire 50 cm. long gives out 400 vibrations per second. How many vibrations will it give when the length is reduced to 10 cm.? What syllable will represent this note if do represents the first note?

5. Two strings, each 6 ft. long, make 256 vibrations per second. If one of the strings is lengthened 1 in., how many beats per second will be heard?

6. If a vibrating string is found to produce the note C' when stretched by a force of 10 lb., what must be the force exerted to cause it to produce (a) the note E? (b) the note G?

7. When water is poured into a deep bottle, why does the pitch of the sound rise as the bottle fills?

8. Show what relation exists between the wave lengths of a note and the lengths of the shortest closed and open pipes which will respond to this note.

9. What must be the length of a closed organ pipe which produces the note E? (Take the speed of sound as 340 m. per second.)

10. What is the first overtone which can be produced in an open G organ pipe?

11. What is the first overtone which can be produced by a closed C organ pipe?

CHAPTER XVIII. 1. If the opaque body in Fig. 382 is moved nearer to the screen ef, how does the penumbra change?

2. The diameter of the moon is 2000 mi., that of the sun 860,000 mi., and the sun is 93,000,000 mi. away. What is the length of the moon's umbra?

3. If the distance from the center of the earth to the center of the moon were exactly equal to the length of the moon's umbra, over how wide a strip on the earth's surface would the sun be totally eclipsed at any one time?

4. Look at the reflected image of an electric-light filament in a piece of red glass. Why are there two images, one red and one white?

5. Show by a diagram and explanation what is meant by critical angle. 6. The vertical diameter of the sun appears noticeably less than its horizontal diameter just before rising and just before setting because of refraction due to the earth's atmosphere. Explain.

7. In what direction must a fish look in order to see the setting sun? (See Fig. 485.)

FIG. 485. To an eye under water all external objects appear to lie within a cone whose angle is 97°



FIG. 486. Prism glass

8. Fig. 486 represents a section of a plate of prism glass. Explain why glass of this sort is so much more efficient than ordinary window glass in illuminating the rears of dark stores on the ground floor in narrow streets.

9. In which medium, water or air, does light travel the faster? Give reasons for your answer.

10. Does a man above the surface of water appear to a fish below it farther from or nearer to the surface than he actually is? Make an explanatory wave diagram.

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