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ehrenfest
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I am trying to think of a non-constant function whose divergence and curl is 0. It seems like this is impossible to me. Any hints?
Divergence and Curl: Can a Non-Constant Function Have Both 0?
- Thread starter ehrenfest
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- Curl Divergence
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SUMMARY
A non-constant vector field cannot have both zero divergence and zero curl simultaneously. If the curl of a vector field is zero, it can be expressed as the gradient of a scalar function. When the divergence is also zero, this implies the field satisfies the Laplace equation, indicating that the only solutions are constant functions. Therefore, the existence of a non-constant function with both properties is impossible.
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- Investigate examples of vector fields with non-zero divergence and curl
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