The potential in an electric field has the form $V = a (x^{2} + y^{2} + z^{2})$ . The modulus of the electric field at a point (z,y,x) is

2 a (x^{2} + y^{2} + z^{2})^{\frac{3}{2}}

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2 a \sqrt{x^{2} + y^{2} + z^{2}}

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a \sqrt{x^{2} + y^{2} + z^{2}}

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\frac{2 a}{\sqrt{x^{2} + y^{2} + z^{2}}}

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Solution

The correct option is C $a \sqrt{x^{2} + y^{2} + z^{2}}$
Potential in a electric field $V = a (x^{2} + y^{2} + z^{2})$
electric field at a point $(z, x, y)$
$\frac{d V}{d x} = 2 a x + 0 + 0 = 2 a$ where the point $= \sqrt{x^{2} + y^{2} + z^{2}}$
$\frac{d V}{d x} = a \sqrt{x^{2} + y^{2} + y^{2}}$

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Similar questions

x^{2} + y^{2} + z^{2} = r^{2}

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x^{2} - y^{2} + z^{2} = r^{2}

z^{2} + y^{2} - x^{2} = r^{2}

If $x = r s i n α c o s β, y = r s i n α s i n β$ and $z = r c o s α$ , then

x + y + z = 0

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V = x^{2} + y^{2} + z^{2}

(1, 1, 1)

x^{2} = a + (y - z)^{2}, y^{2} = b + (z - x)^{2}, z^{2} = c + (x - y)^{2} .

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