Page:Electricity (1912) Kapp.djvu/161

Rh instrument may be made suitable for measuring currents of widely different magnitude. The deflected part $$i$$ of the total current passes through the wires of the coil, and those parts of the winding which lie parallel to the surface of the cylindrical armature are subject to the influence of the induction in the air space between armature and poles. The dynamic force of the current is $$Bli$$, where $$l$$ represents the total length of wire within the air space. The coil will thus be deflected against the controlling force of the spring, and since the deflection of a spring is proportional to the deflecting force, the excursion of the pointer over the scale is proportional to the current. The sense in which the pointer is deflected indicates at the same time the direction of the current.

Up to the present we have considered the dynamic action between a current and a magnetic field, but we have still to consider the dynamic action between two currents. For this purpose we go back to Biot-Savart's law and apply it to the case of a very long straight conductor. What is the induction at a small distance $$a$$ from the axis of the wire? This problem can only be solved by the use of the calculus, and therefore it must