We have:
Now:
(constant function).
Regards.
Fernando Revilla
We're assuming that it has already been shown that the field is conservative.
I don't think I'm quite understanding how to do this.
So far, I have:
So, then I take the first one and integrate it with respect to x and get:
Then I find:
and set this equal to from above:
So I take the integral of this and get:
I'm not sure of what to do now.
The final answer to the problem is
We have:
Now:
(constant function).
Regards.
Fernando Revilla
Excellent! Now just continue what you were doing: since , so that by differentiating with respect to z,
but we know that
so we have and . Since h is a function of the single variable, z, h'(z)= 0 means that h(z) is, in fact, a constant, C.
The final answer to the problem is