Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/354

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717.] In the construction of a sensitive galvanometer the aim of every part of the arrangement is to produce the greatest possible deflexion of the magnet by means of a given small electromotive force acting between the electrodes of the coil.

The current through the wire produces the greatest effect when it is placed as near as possible to the suspended magnet. The magnet, however, must be left free to oscillate, and therefore there is a certain space which must be left empty within the coil. This defines the internal boundary of the coil.

Outside of this space each winding must be placed so as to have the greatest possible effect on the magnet. As the number of windings increases, the most advantageous positions become filled up, so that at last the increased resistance of a new winding diminishes the effect of the current in the former windings more than the new winding itself adds to it. By making the outer windings of thicker wire than the inner ones we obtain the greatest magnetic effect from a given electromotive force.

718.] We shall suppose that the windings of the galvanometer are circles, the axis of the galvanometer passing through the centres of these circles at right angles to their planes.

Let $$r \sin \theta$$ be the radius of one of these circles, and $$r \cos \theta$$ the distance of its centre from the centre of the galvanometer, then, if $$l$$ is the length of a portion of wire coinciding with this circle, and $$\gamma$$ the current which flows in it, the magnetic force at the centre of the galvanometer resolved in the direction of the axis is

If we write Rhthis expression becomes $$\gamma \frac{l}{x^2}$$.

Hence, if a surface be constructed similar to those represented in section in Fig. 52, whose polar equation is Rhwhere $$x_1$$ is any constant, a given length of wire bent into the form of a circular arc will produce a greater magnetic effect when it lies within this surface than when it lies outside it.