Chapter 16.8, Problem 19E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

If *S* is a sphere and **F** satisfies the hypotheses of Stokes’ Theorem, show that ∫∫* _{s}* curl F ·

To determine

**To show**: The surface integral of field

Explanation

**Formula Used:**

Write the expression for the Stokesâ€™ theorem for field

Here,

*S* is surface.

Consider the center of sphere *S* is located at origin with radius *a*. Consider the upper hemisphere of *S* is
*S* is

Consider the curve of upper hemisphere as

Re-modify equation (2) by using equation (1).

The curves

Sect-16.1 P-1ESect-16.1 P-2ESect-16.1 P-3ESect-16.1 P-4ESect-16.1 P-5ESect-16.1 P-6ESect-16.1 P-7ESect-16.1 P-8ESect-16.1 P-9ESect-16.1 P-10E

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