THE MAGNETIC MEASUREMENT OF CURRENT. 27 



A/ acts on m is equal and opposite* to this. Therefore, ignoring 

 algebraic signs, we have: 



m-kH = A/ XI X -sin0 



from which equation (i) follows at once. 



Proposition. The intensity of the magnetic field at a given 

 point in the neighborhood of a given coil of wire is proportional 

 to the strength of the current in the coil, and the direction of the 

 field at that point is fixed. That is to say, if the strength of the 

 current is doubled, the intensity of the field will be everywhere 

 doubled, but the direction of the field will be everywhere the 

 same as before. The trend of the lines of force of the magnetic 

 field due to a coil or circuit depends only on the shape and size 

 of the coil or circuit, not at all on the strength of the current.f 



19. Magnetic field due to a long straight wire. The lines of 

 force of the magnetic field surrounding a long straight electric 

 wire are circles with their planes at right angles to the wire and 



* A curious absurdity is involved here. Figure 22 shows an edgewise view of 

 Fig. 21 ; F is the force with which m acts on A/, and F f is the equal and op- 

 posite force with which AJ acts on m; and these forces do not have the same 

 line of action. This absurdity is due to the non-physical character of an element 



element of wire 

 seen endwise* 



magnet 



otc/e r/tuu/t5t'\ 



3 > ? 



f 



Fig. 22. 



AZ of an electric circuit. In so far as magnetic effect is concerned, an electric circuit 

 is always complete. Thus the increasing electrical stress in the dielectric of a 

 condenser which is being charged is equivalent magnetically to a flow of current 

 through the dielectric of the condenser. 



The impossible consequences of the physical absurdity in equation (i) of Art. 18 

 always disappear when the equation is integrated around a complete circuit. 



t This proposition may be established by an argument based upon equation (i) 

 above, the essential point being that when equation (i) is integrated the constant 

 factor I can be taken from under the integral sign. 



