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# Vector potentials watch

1. How many vector fields admit a certain vector potential?
2. (Original post by JrW13)
How many vector fields admit a certain vector potential?
Do you mean: given , for how many fields is it true that ?
3. Yes
4. (Original post by JrW13)
How many vector fields admit a certain vector potential?
Recall, as we saw in this thread, that

for some scalar function . 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.
5. (Original post by Gregorius)
Recall, as we saw in this thread, that

for some scalar function . 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?
6. (Original post by atsruser)
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?
7. (Original post by Gregorius)
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.

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