If you find the scalar potential of a conservative vector field

[schattenjaeger]

Should your answer include the constant of integration? I think it should but my book's answers don't, so I dunno.

Example, <2xy^3, 3y^2x^2>

answer is x^2y^3, but should I include the + C? (and yes I went through and made sure h(y) was in fact a constant

 

[robphy]

Technically, yes, you should include it.
Of course, a boundary condition might fix it to a specific constant.
From a (classical) physical point of view, it's the "difference in potential" that is physically relevant.

 

[Doc Al]

I would say yes. But it's OK to leave it out as long as you know that adding an arbitrary constant to the potential will produce the same vector field.

 

[quantumdude]

Should your answer include the constant of integration?

Did the question ask for "the" scalar potential? If so, then go to your teacher and toss a hot cup of coffee in his lap. Once you've got his attention, explain to him that scalar potentials for a given force field aren't unique.

Or did the question ask for "a" scalar potential? If so, then anyone will do.

 

[schattenjaeger]

Haha, hey, I like my teacher! It's actually outta the book, and it does say >A< scalar potential, had I been thinking it would've been clear, thanks though!