dP= -- rhodzg
what is the significance of negative sign here? what does this negative sifn signifies in general in any such relation?

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Solution

$d P = - ρ g d z$
In this relation the - sign means that with increase in z the pressure (P) decreases.
In any such relations where there is a - sign means when one variable increases the other decreases.

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E = - \frac{d V}{d r}

\to E = - \frac{\partial V}{\partial x}^i - \frac{\partial V}{\partial y}^j - \frac{\partial V}{\partial z}^k

E = -dV/dr, here the negative sign signifies that

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