for some scalar function ϕ. Now recall that a vector field is irrotational if and only if it admits a scalar potential. Put these two facts together and you get the answer.
for some scalar function ϕ. Now recall that a vector field is irrotational if and only if it admits a scalar potential. Put these two facts together and you get the answer.
You seem to have answered the inverse question, AFAICS: how many vector potentials does a certain vector field admit?
Ooh yes...could be. But is the inverse of this even a question?
It's a pretty boring one, I think, since differentiation isn't multivalued, but the OP answered my clarifying question with a yes. I've got a feeling that the setter or the OP posed the question incorrectly, and it's really meant to be the one that you asked.