The electric field, E is:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{-}}{\mathbf{\nabla}}{\mathbf{V}}}$

But,

${\mathbf{\nabla}}{\mathbf{=}}{\mathit{i}}\frac{\mathbf{\partial}}{\mathbf{\partial}\mathbf{x}}{\mathbf{+}}{\mathit{j}}\frac{\mathbf{\partial}}{\mathbf{\partial}\mathbf{y}}{\mathbf{+}}{\mathit{k}}\frac{\mathbf{\partial}}{\mathbf{\partial}\mathbf{z}}$

Now we can express E as:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{-}}{\mathbf{(}}{\mathbf{i}}\frac{\mathbf{\partial}}{\mathbf{\partial}\mathbf{x}}{\mathbf{+}}{\mathbf{j}}\frac{\mathbf{\partial}}{\mathbf{\partial}\mathbf{y}}{\mathbf{+}}{\mathbf{k}}\frac{\mathbf{\partial}}{\mathbf{\partial}\mathbf{z}}{\mathbf{)}}{\mathbf{V}}}$, where V is the electric potential in the region of space.

(II) The electric potential in a region of space varies as V=by/(a^{2}+y^{2}). Determine E.

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