= Offset uniformly charged spherical shells
{title2=$r=\sqrt{x^2+a^2/4}$}
Place a fixed shell of radius $a$ and charge $-q$ at $(0,a/2)$ and a fixed shell of radius $2a$ and charge $+q$ at $(0,-a/2)$. On the positive $x$ axis their centre distances coincide. The electrostatic <shell theorem> makes the <electric field> vanish until $x=\sqrt3a/2$, gives magnitude $k_eq/(x^2+a^2/4)$ until $x=\sqrt{15}a/2$, and gives $k_eqa/(x^2+a^2/4)^{3/2}$ thereafter. At each ideal charged surface the field has distinct one-sided limits. The net charge is zero but the <electric dipole moment> is $-qa\hat{\mathbf y}$.
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