# Flux through the surface of an ellipsoid

I was asked to calculate the flux of the field $$\mathbf A = (1/R^2)\hat r$$ where $$R$$ is the radius, through the surface of the ellipsoid $$\left(\frac{x^2}{a^2}\right) + \left(\frac{y^2}{b^2}\right) + z^2 = 1$$

Without doing the formal calculations (I have never encountered a problem like this), I neverless suspect that it's equivalent to the flux of the same field through the surface of a sphere whose radius is the mean radius of the ellipsoid (i.e. $$4 \pi$$)...am I wrong and/or how to solve?

The field you are asked about is the prominent gravitational / Coulomb field which main characteristics is the fact that its divergence is $$0$$ everywhere except for the origin point $$(0,0,0)$$: $$\nabla\cdot{\mathbf A}=4\pi\delta({\mathbf r}),$$ which is easy to check.
Therefore by divergence theorem the flux over the surface is $$4\pi$$ since the origin point is inside the surface.