I have spent a lot of time trying to understand potentials (gravitational and electrical) and I can't grasp it. I understand that it is the work in bringing a point mass (or charge) from infinity to a point in the gravitational (or electrical) field and I understand that I must integrate the force with respect to the displacement. But everytime I do it I seem to be coming out with the wrong sign. Boiled down, my questions are:

  1. For a gravitational field, is the work done in moving a point mass from infinity to a point at radius $R$ given by:

    $ -\int_\infty^R(-GMm/r^2)dr$

  2. Why is it a point mass or point charge, is this because if it was larger, it would have an affect on the other planet or charge?

  3. Between positive charges, is the electrostatic potential energy?: $+\int_\infty^R(kQq/r^2)dr$

  4. If so how would this change for positive and negative charges, or negative and negative?

  5. Is positive work if I have to "struggle" against something and negative work when I "give in", effectively going along with whatever the gravitational or electric field wants?