Analysis of electric field lines

We have a very short electric dipole with moment $$p$$ placed at the origin. The dipole is pointing towards positive x-axis.

Select a field line that passes though $$(0,1)$$ and trace the entire field line, it should form a closed curve. (Refer to the given figure) The area of the loop in the upper half of the plane is $$\frac{a\pi}{b}$$.

Find $$a+b$$

Details and Assumptions

• Assume the opposite charged particles to be at infinitesimal distance form each other.
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