Scalar potential and line integral of a vector field
1. The problem statement, all variables and given/known data
http://imgur.com/nSlbe.png 2. Relevant equations Given above. 3. The attempt at a solution I attempted this problem first without looking at the hint. I've defined F(r) as (B+A)/2 + t(BA)/2, with dr as (BA)/2 dt . Thus F(r)dr = ((B+A)/2)*((BA)/2)+((BA)/2)^2 dt When I integrate this from 1 to 1 I get 1/2*(B^2A^2). When I then looked at the hint, I saw it mentioned another (B^2+A^2)/2 term and another "c," neither of which I have, and my integrand has no "tau" squared element either. Is there a point where I went wrong here? 
Re: Scalar potential and line integral of a vector field
I'm guessing that you don't get to define F(r) but instead have to use the one given to you in problem 4.01, whatever that is.

Re: Scalar potential and line integral of a vector field
The idea is to used the derived formula to solve the next problem, which is find a scalar potential function phi(r) such that the line integral F(B,A) (as in 4.02) = phi(B)phi(A). So it's clear I need to solve this in terms of B and A.

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