Determine the electric field strength vector if the potential of the field depends on x, y coordinates as $V = a x y$ , where $a$ is a constant.

\to E = - a (y ˆ i + y ˆ j)

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\to E = - a (x ˆ i + y ˆ j)

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\to E = - a (x ˆ i + x ˆ j)

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\to E = - a (y ˆ i + x ˆ j)

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Solution

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

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

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

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Determine the electric field strength vector if the potential of the field depends on x, y coordinates as V=axy , where a is a constant.

The correct option is D →E=−a(yˆi+xˆj) →E=−▽V ( negative of gradient of V) →E=−(dVdx^i+dVdy^j)=−a(y^i+x^j)

Determine the electric field strength vector if the potential of the field depends on x, y coordinates as $V = a x y$ , where $a$ is a constant.

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

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

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