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Q. 16

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Calculus
Found in: Page 1119
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Use what you know about averages to propose a formula for the average rate of flux of a vector field F(x, y ,z) through a smooth surface S in the direction of n.

Hence, the average rate of flux of a vector field f(x,y,z) on a smooth surface S is,Fav(S)=∫S F(x,y,z)⋅ndS∫S 1dS

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Given

The given function is f(x, y, z) .

Step 2. Finding the average rate of flux of a vector field through smooth surface

Surface integrals of multivariate functions f(x,y,z) is,∫f(x, y, z)n. dS.The surface area of the smooth surface S is,∫S1dSHence, the average rate of flux of a vector field f(x,y,z) on a smooth surface S is,Fav(S)=∫S F(x,y,z)⋅ndS∫S 1dS

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