In a certain region of space, the potential is given by
$V = k [2 x^{2} - y^{2} + z^{2}]$ . The electric field at the point $(1, 1, 1)$ has magnitude=

k \sqrt{6}

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2 k \sqrt{6}

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2 \sqrt{3} k

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4 k \sqrt{3}

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Solution

The correct option is A $2 \sqrt{3} k$
$V = [2 x^{2} - y^{2} + z^{2}] \to E = \frac{d v}{d x}^i + \frac{d v}{d y}^j + \frac{d v}{d z}^k \to E = 2 k x^i + k (- 2 y)^j + k (2 z)^k \to E = k [2^i - 2^j + 2^k] [(x, y, z) \equiv (1, 1, 1)] ∣ ∣ ∣ \to E ∣ ∣ ∣ = \sqrt{12} k = 2 \sqrt{3} k$

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