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generate for a certain number of hours; in stationary cells it is ordinarily 8 hours. Cells are rated also in ampere-hours. An 80-ampere-hour cell will give, approximately, 10 amperes for 8 hours, 5 amperes for 16 hours, 1 ampere for 80 hours, and so on. The Edison cell. In this cell

Volts

2.0

Charge at normal rate

1.6

1.2

0.8

0.4

Discharge at
normal rate

nickel-plated steel plates are immersed in a solution of potassium hydroxide. The Edison cell does not have as high an efficiency as the lead cell, and its electromotive force is not only lower but also less constant. Its average electromotive force on discharge is 1.2 volts, while that of the lead cell is about 2 volts. However, it can be completely discharged without injury, and may be left for some time in this condition. In general the Edison cell will stand rougher usage than the lead cell. The curves in Fig. 273 show the terminal voltage on charge and discharge.

PROBLEMS

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Hours

FIG. 273

1. The electrochemical equivalent of copper is 0.000329 gm. per coulomb. How many grams will be deposited by 1 ampere flowing for 1 hr.?

2. How many amperes are needed to deposit 3 gm. of silver in an hour? (The electrochemical equivalent of silver = 0.001118 gm. per coulomb.)

3. If 20 amperes are passed through acidulated water for 5 min., how many grams of hydrogen are liberated? (The electrochemical equivalent of hydrogen is 0.00001046.)

4. An electrolytic cell has a counter electromotive force of 2 volts and a resistance of 4 ohms. This is connected to a battery of 4 volts and an internal resistance of 1 ohm. (a) Find the current in the circuit. (b) Find the number of grams of hydrogen deposited in 20 min. if the electrochemical equivalent

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5. The electrochemical equivalent of hydrogen is m/e (equation (72), sect. 455). According to Millikan, e = 1.591 × 10-19 coulombs. Compute the value of the mass of the hydrogen atom.

6. Taking the electrochemical equivalent of silver as 0.0011180 gm. per coulomb, compute the electrochemical equivalent of oxygen (use the atomic weights and valences given in section 454).

CHAPTER XXXII

MAGNETIC FIELDS OF CURRENTS; MECHANICAL FORCES ON CONDUCTORS IN MAGNETIC FIELDS

Introduction, 460. Quantitative relations between current and strength of magnetic field; definition of unit current, 461. The mechanical force acting on a current-carrying wire placed in a magnetic field, 462. Summary of facts about current-magnetic-field forces, 463. The force on a straight wire in a uniform magnetic field, 464. The attraction or repulsion of two parallel wires, 465. Coils of wire in magnetic fields, 466. The moving-coil galvanometer, 467. Direct-current ammeters, 468. Direct-current voltmeters, 469. Electric motors, 470. Summary, 471.

460. Introduction. It is worth while for the student to recall certain facts about magnetic fields produced by electric charges in motion, and about forces acting on coils of wire carrying a current when they are placed in magnetic fields. A number of these facts were stated in Chapter XXVII, but no full explanation was given of the relation between them. They may be summarized

as follows:

1. When a current flows through a wire, a magnetic field is formed around the wire. Forces act on magnets brought near the wire.

2. The relation between the direction of the current and the direction of the magnetic field produced by the current is given by the right-hand rule (sect. 405). It is important that each student be familiar with this rule.

3. Currents flowing through coils, or helixes, of wire produce relatively strong fields inside these coils. When iron is placed inside a coil which has a current flowing through it, the iron becomes magnetized by induction (electromagnet).

4. If a current flows through a coil suspended in a magnetic field, there will be rotational forces (torques) acting on the coil. The rotation of the coil of a galvanometer or of an ammeter, or the rotation of the armature of an electric motor, is an example of this action.

In Chapter XXVII experiments were described demonstrating the facts given above, but overlooking several important questions, among which are the following:

1. Why is there a force tending to move a current-carrying conductor when it is placed in a magnetic field?

2. Under what circumstances does this force exist?

3. What is the direction of this force? Does it bear any relation to the direction of the current and to the direction of the magnetic field?

4. On what does the magnitude of this force depend? How can it be made larger ?

The student should be able to answer these questions before he has completed a reading of this chapter.

461. Quantitative relations between current and strength of magnetic field; definition of unit current. When a current flows through a wire, a magnetic field is produced. If the current is made twice as large, the strength of the field at any one place is doubled. In general, the strength of the magnetic field produced | by a current is, at any one place, proportional to that current. This fact is utilized in the measurement of currents: in nearly all cases current is measured by means of the magnetic field it produces.

Not only is current measured by the strength of its magnetic field, but the definition of the C.G.S. unit of current is based on the strength of the field a current produces.

Unit current in the C.G.S. electromagnetic system may be defined as the current that will produce at the center of a circular coil of wire of one turn a magnetic field the strength of which is

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If i units of current flow through the coil, the strength of the magnetic field, H, at the center is

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If the coil has N turns, then

2πΝί

H =

r

(74)

The ampere is one tenth of the C.G.S. electromagnetic unit. Hence a current of 1 ampere will produce a field the strength of which is one tenth as great as that produced by the C.G.S. electromagnetic unit. If I represents the current in amperes, the strength of field at

the center of a circular coil of N turns is

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This equation can be used either to compute the strength of the magnetic field produced at the center of a coil by a current I or, if the strength of the magnetic field is measured, to compute the value of the current.

Strength of magnetic field due to a long straight wire. The strength of the magnetic field near a long straight wire is proportional to the current, i, in the wire, and inversely proportional to the distance from the wire. Expressed in the form of an equation,

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where H is the strength of the field, i the current measured in C.G.S. electromagnetic units, and r the distance of the point from the wire. Since 1 ampere is equal to one tenth of a C.G.S. electromagnetic unit, when the current is measured in amperes and indicated by I,

H

21 10r

(75 a)

Strength of magnetic field in a long solenoid. It can be proved that the magnetic field inside a long solenoid, or helix, is very

uniform, and has a strength given by

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where N is the total number of turns, and I is the length of the

solenoid. If the current is measured in amperes,

1

H

4 ΠΙΝ

(76a) Instead of defining unit current from equation (73), some prefer to use equation (75) or (76). The logical process is to choose some equation as the fundamental one and to define the unit of current from it. Then all the other equations which state the strength of the magnetic field produced by currents flowing in various-shaped circuits must be derived from the fundamental equation. But the methods are not simple, and no attempt is made here to show how any one of equations (73), (75), and (76) can be derived from any one of the others.

462. The mechanical force acting on a current-carrying wire placed in a magnetic field. In Fig. 274, AB represents a wire placed in the magnetic field of a magnet. When a current flows along this wire, there will be a force acting on the wire. This force A will not be one of attraction nor of repulsion, but the wire will be pushed either toward the student or away from him, depending on the direction of the current. The direction of the force will be at right angles to the wire and also at right angles to the magnetic field produced by the magnet.

N

B

FIG. 274

The existence of this force is one of the most important facts of electricity and magnetism. In order to distinguish it from other forces that may be acting on the wire, it is called the current-magnetic-field force.

The current-magnetic-field force can be shown experimentally whenever a wire that is sufficiently flexible is used. The carbon filament of an incandescent lamp is usually flexible enough to show a deflection when a pole of a magnet is brought near. Another method is to suspend a loop of light tinsel wire; or, if ordinary wire is used, it can be suspended as shown in Fig. 275. The loop is suspended by means of hooks made by bending the ends of the bare wires, the hooks being turned in such a direction that they do not interfere with the swinging of the loop. Heavy wire should not be used.

Fig. 276 shows a sectional view of Fig. 275; that is, a section formed by a perpendicular plane cutting the wire. The section of the wire is at P. Let us suppose that the current in the wire of

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