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Chapter 14: Q. 8 (page 1150)

Recall from Section 14.4 that the divergence of a vector field is related to the expansion or compression of a gas whose motion is represented by that field. If a gas whose motion is represented by a vector field is expanding (or compressing) in a region of space, what effect should that have on the flux of the vector field out of (or into) a closed region $$W$$? Making some additional assumptions about the direction of the vectors in $$F$$ may help you to think about this situation.

Short Answer

Expert verified

If a gas whose motion is represented by a vector field is expanding (or compressing) in a region of space, the flux of the vector field will pointing outwards (or inwards) a closed region $$W$$.

Step by step solution

01

Step 1. Given Information

  • The divergence of a vector field is related to the expansion or compression of a gas whose motion is represented by that field.
  • A gas whose motion is represented by a vector field is expanding (or compressing) in a region of space.
02

Step 2. Explanation

When the gas is expanding, the vector field will be pointing outwards while when the gas is compressing, the vector field will be pointing inwards.

Therefore, if a gas whose motion is represented by a vector field is expanding (or compressing) in a region of space, the flux of the vector field will pointing outwards (or inwards) a closed region $$W$$.

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