Question

write the expression for gradient and divergence​

Answer 1

SOLUTION

TO DETERMINE

The expression for gradient and divergence

EVALUATION

Gradient

Let a scalar field be defined by the scalar function f(x, y, z) of coordinates x , y , z which is also defined and differentiable at each point (x , y , z) in some region of space. Then gradient of the function is defined as

$\displaystyle\nabla f = \bigg(\hat{i} \frac{ \partial}{ \partial x} + \hat{j} \frac{ \partial}{ \partial y} + \hat{k} \frac{ \partial}{ \partial z} \bigg)f$

Divergence

The divergence of a continuously Differentiable vector point function $\vec{F}$ is denoted by $div \vec{F}$ and defined as

$\displaystyle\nabla . \vec{F} = \bigg(\hat{i} \frac{ \partial \vec{F}}{ \partial x} + \hat{j} \frac{ \partial \vec{F}}{ \partial y} + \hat{k} \frac{ \partial \vec{F}}{ \partial z} \bigg)$

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