Peoples Physics Book Version-3

http://www.ck12.org Chapter 12. Electricity Version 2

More on Electric and Gravitational Potential

There are several differences between our approach to gravity and electricity that could cause confusion. First, with
gravity we usually used the concept of “energy”, rather than “energy difference”. Second, we spoke about it in
absolute terms, rather than “per unit mass”.

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∆h

we 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 Difference

Which is exactly analogous to the equation above.