Scalar potential and line integral of a vector field

  1. 1. The problem statement, all variables and given/known data


    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(B-A)/2, with dr as (B-A)/2 dt . Thus F(r)dr = ((B+A)/2)*((B-A)/2)+((B-A)/2)^2 dt

    When I integrate this from -1 to 1 I get 1/2*(B^2-A^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?
  2. jcsd
  3. LCKurtz

    LCKurtz 8,454
    Homework Helper
    Gold Member

    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.
  4. 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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