Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/284

Rh placed in a field of magnetic force whose components are $$\alpha$$, $$\beta$$, $$\gamma$$, is Rh

Hence, if the force urging the element to move without rotation in the direction of $$x$$ is $$X_1 \, dx\, dy\, dz$$,Rhand if the moment of the couple tending to turn the element about the axis of $$x$$ from $$y$$ towards $$z$$ is $$L\, dx\, dy\, dz$$,Rh

The forces and the moments corresponding to the axes of $$y$$ and $$z$$ may be written down by making the proper substitutions.

640.] If the magnetized body carries an electric current, of which the components are $$u$$, $$v$$, $$w$$, then, by equations C, Art. 603, there will be an additional electromagnetic force whose components are $$X_2$$, $$Y_2$$, $$Z_2$$, of which $$X_2$$ is Rh

Hence, the total force, $$X$$, arising from the magnetism of the molecule, as well as the current passing through it, is Rh

The quantities $$a$$, $$b$$, $$c$$ are the components of magnetic induction, and are related to $$\alpha$$, $$\beta$$, $$\gamma$$, the components of magnetic force, by the equations given in Art. 400,

The components of the current, $$u$$, $$v$$, $$w$$, can be expressed in terms of $$\alpha$$, $$\beta$$, $$\gamma$$ by the equations of Art. 607, Hence