= Depolarization factor of a dielectric ellipsoid
{title2=$E_{{\rm in},i}=E_{0,i}/[1+N_i(\epsilon_r-1)]$}
For a homogeneous linear isotropic <dielectric> in <vacuum>, $P_i=\epsilon_0(\epsilon_r-1)E_{{\rm in},i}$. Combining this with the <depolarization field> and the imposed uniform <electric field> gives $E_{{\rm in},i}=E_{0,i}/[1+N_i(\epsilon_r-1)]$. A <sphere> has $N_i=1/3$. An infinite slab has $N=1$ normal to its faces and $N=0$ in its plane. A very long circular rod has $N=0$ along its axis and $N=1/2$ transverse to it. Slab and rod statements are limiting geometries, with end effects neglected; a finite cylinder does not generally have an exactly uniform internal <electric field>.
Back to article page
