Solution (source code)

= Solution

The point-dipole interaction is
$$
U=\frac1{4\pi\epsilon_0r^3}
[\mathbf p_1\cdot\mathbf p_2-3(\mathbf p_1\cdot\hat{\mathbf r})(\mathbf p_2\cdot\hat{\mathbf r})].
$$
Here $\mathbf p_1\cdot\hat{\mathbf r}=0$. For parallel axes, $\mathbf p_1\cdot\mathbf p_2=p^2$, hence
$$
\boxed{U=\frac{p^2}{4\pi\epsilon_0r^3}=1.20\times10^{-20}\,\mathrm J=+0.0748\,\mathrm{eV}.}
$$
This side-by-side parallel arrangement is repulsive in the point-dipole model.