How am I to think about the potential difference between two objects? Non-point objects. I am reading a text that confuses me. It talks about the potential difference between two objects, yet it offers a calculation $$V=-\int^a_b \vec{E}\cdot d\vec{s}$$ of a line integral. A line (contour) goes between two points... It does not account for an entire object.
I thank you in advance, for any help. I am fluent in mathematics, and am now looking into physics out of interest.
Potential differences are measured between two points in space, not between two objects.
If you want to find the potential energy of an object, you look at all the charges in the object and multiply them by the potential at the point in space where they are located.
The potential difference $V$ between two points is the work per unit charge required to move the charge between the points in an electric field. These may be between single points, between a point and a line of charge, or between two parallel sheets of charge, as well as many other configurations.
For example, for two parallel plates one positively charged and one negatively charged separated by distance $d$ with a uniform (constant) electric field $E$ between them (so E comes out of the integral), the magnitude of the potential difference $V$ between them is:
$$V =Ed$$
Hope this helps
