Chapter 16.9, Problem 14E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use the Divergence Theorem to calculate the surface integral ∫∫_{s}**F** · *d*S; that is, calculate the flux of **F** across *S.*

**14. F** = |r|^{2}r, where **r** = *x* **i** + *y* **j**+ *z* **k**, *S* is the sphere with radius *R* and center the origin

To determine

**To calculate:** The flux of vector field

Explanation

**Given data:**

The vector field is given as follows.

Here,

The surface

**Formula used:**

Write the expression to find flux of the vector field

Here,

Write the expression to find divergence of vector field

Write the expression for spherical coordinate system.

Here,

**Calculation of vector field**
**:**

Substitute

**Calculation of**
**:**

Substitute

**Calculation of flux of vector field:**

Substitute

Parameterize the sphere with radius

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