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I'm having trouble with the following:

Does there exist in $R^3\setminus\{0\}$:

  1. a vector field F such that $div F = 0$, but is not solenoid (doesn't exist B such that F = ∇ × B)?
  2. vector field F which is not potential (doesn't exist function $f$ for which is $F = ∇f$), but for which holds $∇×F = 0$?

How to solve this? Can this be generalized on $R^n\setminus \{0\}?$

Any help is welcome. Thanks in advance.

0 Answers 0