Practice question · Put in order
Order the steps to apply the divergence theorem to compute flux.
- Compute
- Set up ∭_V dV with appropriate coordinates
- Evaluate the volume integral
- Verify S is a closed surface bounding volume V
- Result equals the outward flux through S
Hints
- The divergence must be computed before any volume integral can be set up.
- Converting the surface integral is what makes the calculation easier.
Show the answer
- Verify S is a closed surface bounding volume V
- Compute
- Set up ∭_V dV with appropriate coordinates
- Evaluate the volume integral
- Result equals the outward flux through S
Why
The divergence theorem converts a surface integral to a (often easier) volume integral.
Practise The Divergence Theorem
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