Chapter 16.7, Problem 49E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Let **F** be an inverse square field, that is, |**F**(r) = *c*r/|r|^{3} for some constant *c,* where r = *x* **i** + *y* **j** *+ z* **k**. Show that the flux of **F** across a sphere *S* with center the origin is independent of the radius of *S.*

To determine

**To show:** The flux of

Explanation

**Given:**

The inverse square field is given by

The radius is given by

**Formula used:**

**Calculation:**

By using the spherical coordinates parameterize the sphere, consider

Find

Simplify the equation.

Thus, the inverse square field becomes,

To find

Substitute

To find

Substitute

Find

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