An electron at rest at \(P=(5,3,7)\) moves along a path ending at \(Q=(1,1,1)\) under the influence of the electric field (in newtons per coulomb)

\[
\mathbf{F}(x, y, z)=400\left(x^{2}+z^{2}ight)^{-1}\langle x, 0, zangle
\]

(a) Find a potential function for \(\mathbf{F}\).

(b) What is the electron's speed at point \(Q\) ? Use Conservation of Energy and the value \(q_{e} / m_{e}=-1.76 \times 10^{11}\) \(\mathrm{C} / \mathrm{kg}\), where \(q_{e}\) and \(m_{e}\) are the charge and mass on the electron, respectively.