Focused Electric Field

In the xyxy plane, there is a parabola described by y=x2y = x^{2}. The parabola has a uniform linear charge density σ\sigma.

The magnitude of the electric field at the focus of the parabola can be expressed as abkσ\dfrac{a}{b}k\sigma, where kk is the Coulomb constant and aa and bb are coprime positive integers.

Determine a+ba+b.

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