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Gravitational Field

The gravitati...

Question

The gravitational potential due to a mass distribution is $V = 3 x^{2} y + y^{3} z$ . Find the gravitational field.

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Solution

We know that from definition,

$E = - (\frac{\partial V}{\partial x} i + \frac{\partial V}{\partial y} j + \frac{\partial V}{\partial z} k)$

Thus,

$E = - (6 x y i + 3 (x^{2} + y^{2} z) j + y^{3} k)$

Answer is $E = - 6 x y i - 3 (x^{2} + y^{2} z) j - y^{3} k$ .

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