   Chapter 16, Problem 11RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If S is a sphere and F is a constant vector field, then ∬S F · dS = 0.

To determine

Whether the statement “If S is a sphere and F is a constant vector field, then SFdS ” is true or false.

Explanation

Given data:

F is a constant vector field.

Write the expression for Divergence Theorem.

EdivFdV=SFdS (1)

Write the expression for divergence.

divF=Px+Qy+Rz (2)

Consider the constant field vector F as follows.

F=K1i+K2j+K3k

Find the value of divF using equation (2)

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