Question

the gradient of a scalar function φ(x y z) is​

Answer 1

Answer:

. Gradint of a scalar function is the magnitude of the gradient is equal to the maxium rate of change of the scalar field and its direction is along the direction of greatest change in the scalar function.

Answer 2

The gradient of the scalar function φ(x y z) is

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

Given :

The scalar function φ(x y z)

To find :

The gradient of the scalar function φ(x y z)

Solution :

Step 1 of 2 :

Write down the given scalar function

Here the given scalar function is φ(x y z)

Step 2 of 2 :

Find the gradient of the scalar function

Let a scalar field be defined by the scalar function φ(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

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

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