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11. Given two bars of metal identical in appearance, one of which is magnetized. What is the simplest method of determining which of the bars is magnetized?

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12. Two identical bar magnets 10 cm long of magnetic moment M - 400 each are arranged with their axes parallel to the earth's magnetic field // . - 0.2 (Fig. P15-12). Using the approximate formula for the field perpendicular to the axis of a bar magnet, locate the points of zero intensity.


We now turn to the examination • • • of the action of two magnets on each other and we shall see that they both come under the law of the mutual action of two electric currents, if we conceive one of these currents as set up at every point of a line drawn on the surface of a magnet from one pole to the other, in planes perpendicular to the axis of the magnet, so that from the simple comparison of facts it seems to me impossible to doubt that there are really such currents about the axis of a magnet • • •

— A Mmi': Marie Ampere.

One of the greatest contributions to the understanding of magnetic phenomena was made by Oersted (1777-1851). From his accidental discovery of the effect of a current on a compass, the concept of a magnetic pole was completely revised. But let us read his own report. The following excerpt was taken from a pamphlet published by him in 1820. The translation was made by Rev. J. E. Kempe.

The first experiments on the subject which I undertake to illustrate were set on foot in the classes for electricity, galvanism, and magnetism, which were held by me in the winter just past. By these experiments it seemed to be shown that the magnetic needle was moved from its position by the help of a galvanic apparatus, and that, when the galvanic circuit was closed, but not when open, as certain very celebrated physicists in vain attempted several years ago. As, however, these experiments were conducted with somewhat defective apparatus, and, on that account, the phenomena which were produced did not seem clear enough for the importance of the subject, I got my friend Esmarch, the King's Minister of Justice, to join me, that the experiments might be repeated and extended with the great galvanic apparatus which we fitted up together.

In reviewing my experiments I will pass over everything which, though they conduced to the discovery of the reason of the thing, yet, when this is discovered, cannot any further illustrate it. Those things, therefore, which clearly demonstrate the reason of the thing, let us take for granted.

The galvanic apparatus which we made use of consists of 20 rectangular copper receptacles, the length and height of which are alike 12 inches, the breadth, however, scarcely exceeding 2| inches. Every receptacle is furnished with two copper plates, so inclined that they can carry a copper bar which supports a zinc plate in the water of the next receptacle. The water of the receptacles contains 1/60 of its weight of

a/rid and likewise 1 60 of its weight of nitric acid. The part of each plate which it immersed in the solution if square, the side being about 10 inches long. Even smaller apparatus may be used, provided they are able to make a metallic wire red hot.

Let the opposite poles of the galvanic apparatus be joined by a metallic wire, which, for brevity, we wOl call hereafter the joining conductor or eLse the joining wire. To the effect, however, which takes place in this conductor and surrounding space. we will give the name of electric conflict

Let the rectilinear part of this wire be placed in a horizontal position over the magnetic needle duly suspended, and parallel to it. If necessary, the joining wire can be so bent that the suitable part of it may obtain the position necessary for the experiment. These things being thus arranged the magnetic needle will be moved, and indeed, under that part of the joining wire which receives electricity most immediately from the negative end of the galvanic apparatus, will decline towards the west.

If the distance of the joining wire from the magnetic needle does not exceed f of an inch, the declination of the needle makes an angle of about 45°. If the distance is increased the angles decrease as the distances increase. The declination, however, varies according to the efficiency of the apparatus.

The joining wire can change its place either eastward or westward, provided it keeps a position parallel to the needle, without any other change of effect than as respects magnitude; and thus the effect can by no means be attributed to attraction, for the same pole of the magnetic needle which approaches the joining wire while it is placed at the east side of it ought to recede from the same when it occupies a position at the west side of it if these declinations depended upon attractions or repulsions.

The joining conductor may consist of several metallic wires or bands connected together. The kind of metal does not alter the effects, except, perhaps, as regards quantity. We have employed with equal success wires of platinum, gold, silver, copper, iron, bands of lead and tin, a mass of mercury. A conductor is not wholly without effect when water interrupts, unless the interruption embraces a space of several inches in length.

The effects of the joining wire on the magnetic needle pass through glass, metal, wood, water, resin, earthenware, stones; for if a plate of glass, metal, or wood be interposed, they are by no means destroyed, nor do they disappear if plates of glass, metal, and wood be simultaneously interposed; indeed, they seem to be scarcely lessened. The result is the same if there is interposed a disc of amber, a plate of porphyry, an earthenware vessel, even if filled with water. Our experiments have also shown that the effects already mentioned are not changed if the magnetic needle is shut up in a copper box filled with water. It is unnecessary to state that the passing of the effects through all these materials in electricity and galvanism has never before been observed. The effects, therefore, which take place in electric conflict are as different as possible from the effects of the electric force or another.

If the joining wire is placed in a horizontal plane under the magnetic needle, all the effects are the same as in the plane over the needle, only MAGNETIC FIELD AT CENTER OF A CIRCULAR LOOP 169

in an inverse direction, for the pole of the magnetic needle under which is that part of the joining wire which receives electricity most immediately from the negative end of the galvanic apparatus will decline towards the east.

That these things may be more easily remembered let us use this formula: the pole over which negative electricity enters is turned towards the west, that under which it enters towards the east.

Ampere's law

In 1820, the year following Oersted's discovery, Andre" Marie Ampere performed further experiments on the magnetic effect of a current. He formulated part of his work in an equation which now bears his name. Consider an element of a conductor of length dl, carrying a current i (Fig. 16-1). Ampere showed experimentally that the field set up at any point such as P, due to this element, can be expressed by the equation



Fig. 16-1.

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where <t> is the angle betweenjthe element dl and the line r, drawn from dTto the point P,_and K is a constant depending upon the units chosenT^ If i is measured in amperes, r and I in centimeters, and H in oersteds, then K becomes 1/10.

The-element-of- the magnetic field is a vector, with a direction jUways at right angles to .hothjthe current element and the radius vector_j%_ A simple rule for determining the direction of the field is to hold the right hand as though grasping the wire carrying the current, the fingers being curved around the wire and the thumb pointing in the direction of the current. The fingers will then point in the direction of the magnetic field. The magnetic field around a wire is circular. Ampere's law is a fundamental connection between electric currents and magnetic fields.


Magnetic field at the center of a circular loop

The magnetic field H at the center of a circular loop of wire of radius a carrying a current of i amperes (Fig. 16-2) can be found by integrating equation 16-1. In this case the radius, r, has a constant value of a, and the angle <t> between r and dl is ir/2 at all points, making sin <t> = 1. Then

Fig. 16-2.

This equation is used as the basis of the definition of the electromagnetic unit of current. If we let K = 1 in Ampere's law we have H = 2irI/a. The electromagnetic unit of current (emu) is defined as a current in a circular loop of 1-cm radius that will produce a field intensity of 2ir oersteds at its center. The practical unit of current, the ampere, is then 1/10 the emu of current, and, since 1 coulomb = 3 X 10' esu, 1 emu of current equals 3-x 1010 esu of current. This


Fio. 16-3.

ratio between the emu and the esu of current is just the velocity of light as was developed by Maxwell.

The magnetic lines of force due to the current loop are indicated in Fig. 16 -3a and 6.

If there is more than one turn of wire in the coil, the expression for the field at the center is H = 2irni/l0a where n is the number of turns. This follows since the magnetic field due to each of the turns is in the same direction at the center, and therefore the fields can be added numerically by scalar addition.

Magnetic field along the axis of a circular current

The magnetic field at a point P a distance of x centimeters away

from the center of a single turn of a coil, and lying on the axis of the coil, can also be determined by a consideration of Ampere's law (Fig. 16-4).

. Consider an element dl on the


coil. Since the magnetic field due

°' '"' to this element is at right angles to

both r and dl, draw the vector dH. The value of dH given by Am

pere's law is

,,. i dl sin <t> idl / . ir\


An element, dl', diametrically opposite, will produce a magnetic field at P in the direction dH'. Since the normal components of these

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