# Focused Electric Field

Electricity and Magnetism Level 5

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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