Find the equipotential surface

A small electric dipole with a dipole moment p=1.2×108 mCp= 1.2\times 10^{-8}~\mbox{m}\cdot\mbox{C} is placed in an external electric field E0=1 V/mE_{0}=1~\mbox{V/m} which is parallel to the dipole, that is, pE0. \vec{p} \parallel \vec{E_{0}}. It turns that in this case one of the equipotential surfaces enclosing the dipole is a sphere. Find the radius RR in meters of this sphere. The electric potential created by a point dipole at a point P is given by the formula ϕ(r)=14πε0prr3 \phi(\vec{r})=\frac{1}{4\pi \varepsilon_{0}} \frac{\vec{p}\cdot \vec{r}}{r^{3}} where r\vec{r} is the radius vector from the center of the dipole to the point P.

Details and assumptions

k=14πϵ0=9×109 m/F k=\frac{1}{4\pi \epsilon_{0}}= 9\times 10^{9}~\text{m/F}

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