Determine the electric field strength vector if the potential of the field depends on x, y coordinates as $V = a (x^{2} - y^{2})$ , where a is a constant.

\to E = - 2 a (x ˆ i - y ˆ j)

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\to E = - a (x ˆ i - y ˆ j)

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\to E = - \frac{a (x ˆ i - y ˆ j)}{2}

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\to E = - \frac{a (x ˆ i - y ˆ j)}{4}

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Solution

The correct option is A $\to E = - 2 a (x ˆ i - y ˆ j)$

$\to E = - ▽ V$ ( negative of gradient of V)

$\to E = - (\frac{d V}{d x}^i + \frac{d V}{d y}^j) = - a (2 x^i + 2 y^j)$

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