ELECTRO-DYNAMICS. 



ELECTRO-DYNAMICS. 



the zinc end of the pile being a constant source of positive electricity 

 and the copper end of negative, a rod communicating with wires con- 

 nected respectively with these extremities will have a current of 

 positive electricity from the zinc to the copper, and a negative current 

 in a contrary direction ; but as it is simultaneously permeated by both, 

 when we speak of the direction of a current we shall understand that 

 of the positive current to avoid ambiguity. 



Two parallel currents which are directed in the same way attract each 

 other, but when directed in opposite ways they repel. 



When rectilineal currents form mutually an angle, the species of 

 action which they exercise may be thus defined : " Two portions of 

 currents will attract if they are both approaching or both receding 

 from the vertex of the angle which they form ; but when one approaches 

 and the other recedes from that angle, then they repel : " the same law 

 holds in the limiting case of parallelism. 



of rotation will be continued in the upper semicircle ; for the force is 

 attractive in the angle D'"E"'B, and repulsive in D'"E'"A. Hence a 



Let two currents cross each other, as A E B, c E D, and suppose the 

 directions of the currents to be those indicated by the arrows in the 

 figure ; then, according to this law, the force between c E, E B, is re- 

 pulsive ; and that between c E, E A, attractive ; if, therefore, A B is 

 fixed, and c E D moveable, we ought to have c E tending towards A E, 

 and for the same reason, D E tending towards E B ; the rod c E D, there- 

 fore, has a rotatory motion impressed on it until it is placed parallel 

 with A B : this is confirmed by experiment. 



If we now consider two currents to form a very obtuse angle, one of 

 them approaching, and the other receding from the vertex, we have 

 repulsion ; let the obtuse angle be increased to 180, and in this extreme 

 case the two currents merge into one : hence it follows that the con- 

 secutive parts of one and the same current exercise a mutual repulsion 

 on each other. 



The actions exercised by a rectilineal current and by a sinuous 

 current, which have generally the same direction and are terminated at 

 the same extremities, are equal, the intensity of action being supposed 

 the same in both cases ; thus, if we suspend a moveable conductor 

 between a rectilineal and a sinuous conductor disposed so as to repel 

 the first, this, after a little oscillation about its mean place, will finally 

 rest in the middle of the interval between the conductors. 



Let u now consider the action of "an indefinite current A B, on a 

 terminated current c E, which is directed towards E ; the direction of 

 A B being that indicated in the figure. 



The portion B E of the indefinite current repels E o, in consequence 

 of the contrary direction of the current in the latter. Let us represent 

 this force in magnitude and direction by 017= c o ; also A E attracts c E ; 

 the force may be represented by C.F, similarly situated with c o ; but 

 eg, the repulsive force of B E, i drawn without the angle B E c ; and 

 c I, or the attractive force of A E, must be drawn within the angle 

 A c. If we now compound the forces c r, c o, they will manifestly 

 produce a resultant c H parallel to the indefinite current A B. Hence 

 the terminated current will be urged by a force parallel to the other, 

 and in a contrary direction ; and by similar reasoning it is easily seen 

 that if the direction of the current o E were contrary to that indicated 

 by the arrow, or receded from A B, then the whole force in o E would 

 be in the mme direction as the current A B, and parallel to it. 



I . t us suppose c D to be a conductor moveable round an axis at c in 

 the plaie D i/o", and suppose the direction of its current to be from 

 c towards D, and that of an indefinite conductor A B to be similar and 

 parallel ; then A B attracting o D will turn it round o into the position 

 c D', and the force on the angle c E' B is then repulsive, and in o E' A 

 attractive ; hence c D' will further turn round, and the same direction 



continued rotation will be produced. This rotation will be in the con- 

 trary direction if we change the direction of the current either in A B 

 or CD; or if, without changing the current, we transfer A B to the 

 opposite side of c D : hence if A B be placed so as to meet the axis c, 

 there will be no rotation ; hence also if the terminated current be 

 moveable round its middle point there will be no rotation, since both 

 its halves tend to rotate in contrary ways. It is easy to analyse in the 

 same manner the action of an indefinite conductor on a closed current 

 by considering its action on each of the parts, the general effect being 

 to bring the moveable conductor into a position of equilibrium in a 

 plane parallel to the indefinite conductor. 



Instead of a single closed circuit we may suppose any number of 

 them connected together after an invariable manner. The action of an 

 indefinite current will still tend to bring that system into a plane 

 parallel to its direction. These systems have been called electro- 

 dynamic cylinders and also canals of currents. 



In consequence of the electro-chemical causes which are so widely 

 diffused through the globe, electrical currents are generated, which 

 give its polarity to the magnet, and which, as is well known, are 

 sufficient to generate continued rotation of given currents. 



It has been found by Ampere that the actions of similar conductors 

 on points similarly situated are equal ; and that a closed conductor 

 exercises no action on a circular conductor moveable round a central 



is. 



In seeking for the true laws of elementary action of currents, a 

 decomposition similar to that of the parallelepiped of forces may be 

 employed ; that is, for the action of an elementary current we may 

 substitute the actions of the three sides of a parallelepiped terminated 

 at the same extremities; for, as before stated, if we preserve the 

 direction of the currents we shall not alter the action by substituting 

 any sinuous for a plane conductor with the same extremities. 



We will now show how the law of force between the elements of 

 currents may be obtained, which, when once known, will reduce all the 

 phenomena to mathematical calculation. 



To determine the law of force tending to or from any element of an 

 electrical current, when points of another current are taken at dif- 

 ferent distances but in a given direction : 



Let Si, !/ be the elements of two electrical currents, of which the 

 intensities are i, i', their distance a unit, and / the force mutually 

 exercised in the line forming their middle points; hence / = it' 

 fi !'. 



Let S<r Sir' be portions of similar currents to the former, but of 

 which the linear dimensions are v times as great, and since their mutual 

 distance is also v times as great ; this force is diminished in proportion 

 to some function of v, as <f> (v} : hence /' = ii' $<r. So'. <f> (v). 



Now Sff=vSs 



Hence 7 = ^ 



ta' v^i'; th eref ore 

 f'=ii' v* Ss 8s'. <t> (if). 



We should have the same proportions if, instead of elements, we took 

 conductors of any lengths but still similar, for this is equivalent merely 

 to integrating the above expressions after decomposing the forces in 

 fixed directions; and since we have experimentally in this case 



f = /', it follows that Q (v) = ; that is, the law is the inverse 



square of the distance, as in statical electricity ; but we must observe 

 that the directions of the currents are here supposed to make given 

 angles with the joining line v. 



The following theorems are taken from Mr. Murphy's ' Electricity,' 

 to which we refer for the demonstrations, which are by no means diffi- 

 cult to persons a little acquainted with the differential and integral 

 calculus. 



Let a right line v join the middles of the elements Si, Si' of two 

 currents, being inclined respectively to those elements at the angles 

 6, ff, the planes of which angles are mutually inclined at an angle $, and 



