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Homework Help: Scalar potential and line integral of a vector field

  1. Feb 28, 2010 #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. Feb 28, 2010 #2


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    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. Feb 28, 2010 #3
    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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