# Find the equipotential surface

**Electricity and Magnetism**Level pending

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

**Details and assumptions**

\[ k=\frac{1}{4\pi \epsilon_{0}}= 9\times 10^{9}~\text{m/F}\]