Determine the electric field strength vector if the potential of this field depends upon x - and y - coordinates as :
(i) `V = a(x^2 - y^2)`
(ii) `V = a x y`.

Explanation

To determine the electric field strength vector from the given electric potential functions, we will use the relationship between electric field (E) and electric potential (V). The electric field is given by the negative gradient of the electric potential:

\[ \mathbf{E} = -\nabla V \]

Where \(\nabla\) (nabla) is the gradient operator. In two dimensions (x and y), the gradient can be expressed as:

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