Page:Elementary Text-book of Physics (Anthony, 1897).djvu/356

342 be seen that the relation between the current and the lines of force is also that between the lines of force and the current; that is, the direction of the lines of force and the direction of the current are related as the directions of translation and rotation of a right-handed screw. A simple rule equivalent to these others is as follows: Let the conductor carrying the current be grasped with the right hand and the thumb extended along it in the direction of the current; the fingers then point in the direction of the lines of force.

In accordance with the views prevalent at the time, Biot supposed that the action of the current upon a magnet pole was due to the independent action of each element of the current. He showed that the results of his experiments were consistent with the assumption that a force acts between a magnet pole $$m$$ and an element $$ds$$ of the current $$i,$$ at the distance $$r$$ from the magnet pole and making an angle a with $$r,$$ equal to $$\frac{mi \sin \alpha \, ds}{r^2}\cdot$$ At present we no longer consider the current as acting at a distance in accordance with this formula, but consider it rather as setting up a magnetic field, and we express its action upon a magnet pole in terms of the field which it nets up. We will return to the consideration of Biot's formula after developing this method.

It was shown by Ampère, and later by Weber, that a very small closed plane circuit sets up a magnetic field similar to that about a small magnet placed with its centre at the centre of the circuit, with its axis normal to the plane of the circuit. This magnet may be replaced by a magnetic shell with its edge coincident with the circuit, without altering the magnetic field. At all points outside the shell its magnetic field is similar to the magnetic field set up by the current; at those points in the field occupied by the substance of the shell the conditions are not the same in both cases. The potential of a shell at a point outside it is $$j \omega$$ (§ 243), where $$j$$ is the strength of the shell and $$\omega$$ is the solid angle subtended by the shell. This is also the potential of the current, if the current be measured in such units that the current strength $$i = j.$$ Now a shell of finite area may be built up of a number of elementary