= Solution
An <electric dipole> consists of equal and opposite <electric charges> separated by a displacement $\mathbf d$. Its <electric dipole moment> is $\mathbf p=q\mathbf d$, directed from negative to positive <electric charge>. At distances large compared with the separation, its leading <electric potential> and <electric field> are
$$
\boxed{\phi(\mathbf r)=\frac{\mathbf p\cdot\widehat{\mathbf r}}{4\pi\epsilon_0r^2},\qquad \mathbf E=\frac{3(\mathbf p\cdot\widehat{\mathbf r})\widehat{\mathbf r}-\mathbf p}{4\pi\epsilon_0r^3}.}
$$
There is no monopole term because the net <electric charge> is zero. The axial <electric field> points along $\mathbf p$ with magnitude $2p/(4\pi\epsilon_0r^3)$, while the equatorial <electric field> points oppositely with half that magnitude.
A uniform applied <electric field> exerts zero net <force> on an ideal fixed <electric dipole>, but it exerts <torque> $\boldsymbol\tau=\mathbf p\times\mathbf E$. Its orientation-dependent <potential energy> is $U=-\mathbf p\cdot\mathbf E$, so alignment with the <electric field> is stable. A nonuniform applied <electric field> can also exert a net <force>, $\mathbf F=\nabla(\mathbf p\cdot\mathbf E)$ for a fixed permanent <electric dipole moment>.
A permanent <electric dipole moment> exists without an applied <electric field>. An induced <electric dipole moment> instead develops in response to the local <electric field>; in an isotropic linear model $\mathbf p=\alpha\mathbf E$. Creating that induced moment requires accounting for the work of polarization, so its mechanical <potential energy> in a specified applied <electric field> is $-\alpha E^2/2$, rather than $-\alpha E^2$. In matter, the dipole moment per unit volume is the <polarization density> $\mathbf P$.
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