It is easily shown by direct experiment that the lines of force in which this field urges our unit pole form circles round the wire that carries the current, so that a pole is urged, not to or from the wire, but continually round and round it (the wire being assumed straight). Each line of force is a closed circle (not a spiral), lying in a plane perpendicular to the rectilineal wire, and having its centre in this wire. The field is weaker further from the wire, and stronger nearer to the wire.

As with the electrostatic field in Chapter X. §§ 13 and 14, so with a magnetic field we can mark out a certain number of lines of force and leave in the field such a selection that the number piercing 1 sq. cm. held perpendicularly to the lines at any place in the field measures the strength of the field at that place, i.e. gives the number of dynes with which a unit magnetic pole would be urged at that place.

Experiments. (i.) A hole is bored (with a bow drill and turpentine) in a sheet of glass, and a wire carrying a current is passed through this hole perpendicularly to the glass plate.

On passing a strong current, and scattering iron filings on the plate, these latter will (on tapping the plate) be observed to arrange themselves in con

centric circles about the hole as centre. If the wire be not perpendicular to the plate, the lines will be ellipse-shaped. This indicates that the lines of force are circles lying in planes perpendicular to the wire.

(ii.) If the wire lie on the plate, we find the filings arranged in straight lines perpendicular to the wire. These straight lines are the sections of the

concentric circles, made by the plate.

Now let a magnetic needle, so balanced as to turn any way, be placed near such a current; and let us for the present consider only the field due to the current, leaving the earth's field out of the question. It is clear that the needle can be in equilibrium only when it lies in the plane passing through its point of suspension and perpendicular to the wire carrying the current; and when, further, its poles are equidistant from the wire. If it is very small it may be said to come to rest when it lies in (or is tangent to) one of the above circular lines of force. (Compare Chapter II. § 11.) In such a position its poles are urged by equal forces tending in opposite directions round the wire; these equal forces being inclined at equal angles with the needle, since this forms a chord of the circular line of force.

This pair of forces will direct the needle as stated, and will also give a resultant urging the needle broadside-on towards the wire. The reader should make the above clear to himself by means of a figure.

(iii.) A magnetic needle is fixed on a cork, and so floats on the surface of water. To one side of the needle is placed a wire perpendicularly to the surface of the water, and a strong current is passed through the wire. It is better so to place the wire, and to pass the current in such a direction that the action of the current is not opposed to that of the earth, but acts with it. It will then be observed that the needle will be dragged into a position in which its poles lie on the circumference of a circle which has for its centre the point where the wire cuts the water, i.e. lie on the same circular line of force; and that then the needle will be urged broadside-on towards the wire.

(iv.) In the same way are steel or iron filings urged broadside-on towards a wire carrying a current, and caused to adhere to it, the filings having become 'magnetic needles' by the inductive action of the field. They are thus arranged in very close circles round the wire. (In the case of a magnetised steel wire the filings adhere end-on, pointing along the lines of force that in this case radiate from the wire.)

§ 2. The and - Directions of the Lines of Force. It is easily shown, by experiment with a magnetic needle, that the + and directions of the lines of force are given by either of the following rules.

(I.) Ampère's rule. If one swims with the current (i.e. so that it flows from feet to head) and looks at a n-seeking (or +) pole, this will be urged to one's left hand. A s-seeking (or -) pole will be urged to one's right hand.'

T

b.

Oersted's experiment.—The historic experiment of Oersted illustrates well this rule of Ampère. The figure here given sufficiently explains this simple experiment.

(II.) Another form of the rule is often very useful. No one who has driven in an ordinary (or right-handed) screw can forget how the hand turns

as tne screw advances away from the person driving it. As one drives it from one, the hand turns as do the hands of a clock that faces one. Now the above experimental rule of Ampère means that if the current advances with the screw, a + pole is urged round it in the direction in which the screw turns. And since the direction in which a + pole is urged gives us the + direction of the lines of force, we may give the following rule.

The direction of the lines of force about a wire carrying a current is associated with the direction of the current in just the same way as the direction of rotation of an ordinary (or right-handed) screw is associated with the direction of the onward movement of the

screw.

(III.) Field due to a circle of wire carrying a current.-If the wire be bent into a circle it will easily be understood that at the centre of the circle all the lines of force there combine to give a line of force running perpendicularly to the plane of the circle. To any side of this line the lines of force bend away; they ultimately curve completely round the wire and run into themselves again. Thus there is, if we wish to be very exact, only one straight line of force, viz. that which runs through the centre of the circle perpendicularly to its plane. [Mathematicians would say that the two ends of this line join at infinity, so that it also forms a 'closed curve.'] But practically, if we take a portion of the field that is near the centre of the circular current and is small as compared with the diameter of the circle, we may consider this portion to be uniform, and to have its lines all running perpendicular to the plane of the circle.

A little consideration will show us that the same 'right-handed screw relation' holds here in this somewhat converse case.

If we

follow this central line of force in its + direction (¿.e. if we travel as a pole is urged), then the current round the circle is associated with our direction of movement as the direction of rotation of a screw is associated with its onward movement. E.g., if we face a circle in which the current goes clock-wise (i.e. as do the hands of a clock when we face it) our + pole is urged towards this circle.

§ 3. Simple Form of Galvanometer.—If we balance a magnetic needle so that it moves in a horizontal plane, it will come to rest when it is in the plane of the magnetic meridian. If we deflect it from this position of rest, there will be a couple due to the horizontal component of the earth's field tending to restore it to its original position of rest.

Now let a loop of wire be passed round the needle, above and below it, so that its plane coincides with the plane of the magnetic meridian. The figure here given exhibits

this simple arrangement.

If a current be passed round this wire loop, it is easy to see that the upper and the lower wires give fields about the needle in the same direction, tending to set it at right angles to the plane of the loop, i.e. at right angles to the plane of m the magnetic meridian.

Now the earth's couple is greatest

a

when the needle stands E. and W., and is zero when the needle stands N. and S.; while the converse is the case with the current's couple.

Hence the needle will settle at some angle 0 of deflexion from the magnetic meridian; the magnitude of (cæteris paribus) depending upon the current-strength.

Such is the principle of the galvanometer. In §§ 5, 6, 12, 13, 14, 15, we shall describe instruments designed for measurement of currents. In $$ 7, 8, 9, 10, 11, the instruments described are mainly for detection of very small currents. (For further general remarks on galvanometers, see § 16.)

$ 4. Relation of Strength of Field to Current-Strength.It can be shown that strength of field is (cateris paribus) directly

proportional to strength of current; the strength of field being measured, e.g., by the vibration method of Chapter III. §§ 3 and 6.

We make a vertical frame, round which insulated wire may be wound, and place it in the plane of the magnetic meridian. In the centre of this frame the needle vibrates under the field due to earth and current together.

We then try the effect of having one, two, three, &c., turns of wire round the frame. By including in the circuit a rheostat, by means of which more or less resistance may be introduced, and an auxiliary galvanometer whose deflexion we thus keep constant, we can insure the constancy of the current that we employ.

We then compare the fields, as in Chapter III. § 3, and show that the above law holds. It is easy to show that the field depends strictly upon current-strength and not upon current-density; that is, upon the quantity per second passing over any section of the conductor, not upon whether this current forms (so to speak) a broad slow stream or a quick narrow one.

Experiment.-One way of proving the above is to show that when a current flows through a thick wire, and returns through a thin wire wound round the former, the total resultant magnetic field is zero. This is another example of proving equality by means of the 'zero method.'

The reader will observe that from this it follows, as assumed above, that with the same current n turns of wire act as one turn carrying n times this current. Hence, the law stated at the beginning of this section is proved by the method given, in which we employ one, two, three, &c., turns of wire.

$5. The Tangent Galvanometer. The simplest form of true galvanometer (or current-measurer) is that called the tangentgalvanometer. Referring to § 2 (III.), we shall see that about the centre of a circular wire carrying a current the field may be considered uniform. Or, if a needle whose length is small as compared with the diameter of the circle (see note (iii.) at end of this section) be suspended at the centre, then, however much it be deflected it will remain practically in the same strength of field as long as the current remains constant.

If then we can measure the strength of this field by the amount of deflexion, we measure at the same time the current that gives rise to the field; whereas, if the needle were too long or situated unsymmetrically with respect to the circle, the needle would, for