13.6. Electric Field of a Parallel Plate Capacitor http://www.ck12.org
To address the first issue: when we dealt with gravitational potential energy we had to set some reference height
h=0 where it is equal tomg× 0 =0. In this sense, we were really talking about potential energy differences rather
than absolute levels then also: at any point, we compared the gravitational potential energy of an object to the energy
it would have had at the reference levelh=0. When we used the formula
Ug=mg∆hwe implicitly set the initial point as the zero: no free lunch! For the same reason, we use the concept of electric
potential difference between two points — or we need to set the potential at some point to 0, and use it as a reference.
This is not as easy in this case though; usually a point very far away ("infinitely" far) is considered to have 0 electric
potential.
Regarding the second issue: in the chapter on potential energy, we could have gravitational potential difference
between two points at different heights asg∆h. This, of course, is the work required to move an object of mass one
a height∆hagainst gravity. To find the work required for any other mass, we would multiply this by its magnitude.
In other words,
︸︷︷︸W
Work=︸︷︷︸m
Mass× g∆h
︸︷︷︸
Potential DifferenceWhich is exactly analogous to the equation above.