# Analysis of electric field lines

**Electricity and Magnetism**Level 5

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.