The Electric Field of a Magnetized Spheroid Rotating about the Axis of Magnetization

Electrostatic Potential Due to a Rotating Magnetized Spheroid.—Taking the axis of symmetry as both the axis of rotation and the direction of magnetization, and assuming that the gradient of the potential is at each point equal to $\frac{\left[v·B\right]}{c}$ where $v$ is the velocity, $B$ the induction and $c$ the speed of light, formulæ are derived for the potential at any point on the surface or outside of it ($a$) when the spheroid is insulated and uncharged as a whole and ($b$) when the axis is kept earthed. In the latter case the change of potential of the surface as a result of reversing the magnetization is equal to $\frac{2B\omega b^2}{3c}$, where $\omega$ is the angular speed and $2b$ is the maximum diameter. This change may be measured by the resulting change of potential of a stationary shell surrounding the spheroid. For example, in the case of a long iron cylinder (which is approximately equivalent to a spheroid of the same maximum diameter) of 4 cm. radius, with an induction of 18,000 e.m.u. and revolving 100 times a second, the change of potential of a cylindrical shell of 4.5 cm. radius would be about 0.9 volt.