Focused Electric Field

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

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

Determine \(a+b\).

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