# Div and Curl Identities

If $F$ is a vector field, I understand that the div(curl $F$) = 0. But would the curl(div $F$) have any interpretation?

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No. $\text{div}$ takes in vector fields and produces scalar fields; $\text{curl}$ takes in vector fields and produces vector fields. Thus, given a vector field $F$, it makes sense to write $$\text{div}(\text{curl}(F)),$$ but not to write $$\text{curl}(\text{div}(F)).$$ So there is no interpretation because it doesn't mean anything in the first place :)