Chapter 14: Q. 21 (page 1150)

compute the divergence of the given vector field.
$F (x, y, z) = x i + y j + z k$

Short Answer

Expert verified

The divergence of the vector field is $div F = 3$

Step by step solution

Introduction

Take the vector field for example.

F (x, y, z) = x i + y j + z k

The goal is to find the divergence of the vector entered.

Apply the formula, $div F = \frac{\partial F_{1}}{\partial x} + \frac{\partial F_{2}}{\partial y} + \frac{\partial F_{3}}{\hat{O z}}$

Compare the vectors provided. With the vector, $F (x, y, z) = x i + y j + z k$ .

$F (x, y, z) = F_{1} (x, y, z) + F_{2} (x, y, z) + F_{3} (x, y, z)$

So, $F_{1} (x, y, z) = x$

$F_{2} (x, y, z) = y$

$F_{3} (x, y, z) = z$

Explanation

Calculate $d i v F$

$div F = \frac{\partial F_{1}}{\partial x} + \frac{\partial F_{2}}{\partial y} + \frac{\partial F_{3}}{\partial z}$

$= \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial y} (y) + \frac{\partial}{\partial z} (z)$

$= 1 + 1 + 1$

$= 3$

Therefore,role="math" localid="1650784678183" $div F = 3$

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compute the divergence of the given vector field.
$F (x, y, z) = x i + y j + z k$

Short Answer

Step by step solution

Introduction

Explanation

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compute the divergence of the given vector field.F(x,y,z)=xi+yj+zk

Short Answer

Step by step solution

Introduction

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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compute the divergence of the given vector field.
$F (x, y, z) = x i + y j + z k$