Chapter 17
Electric Potential
17.1 Potential Energy
There is a potential energy associated with the electric force. Suppose, for example, that you have a positive
and negative charge right next to each other. Now separate the two charges by some distance; since the two
charges are attracted, they will “want” to come back together. You had to do work against the electric force
to separate the two charges, and now the system has a potential energy that will be released if you allow the
charges to come back together. The forceFand potential energyUare related by
FD
dU
dxU
x: (17.1)
The same thing happens with the gravitational force. If two masses are separated, the attractive gravitational
force will cause the two masses to want to come together again, so the system of separated masses contains
potential energy. This potential energy can be released by allowing the masses to come back together. In
the case of gravity, the potential energy of two point massesm 1 andm 2 separated by distancerisU D
Gm 1 m 2 =r(where we chooseUD 0 atrD1,soUis always negative). Similarly, with the electric force,
the potential energy of two pointchargesq 1 andq 2 separated by distanceris
UD
1
4" 0
q 1 q 2
r; (17.2)
where againU D 0 atr D1, andUis always negative for attracting charges and always positive for
repelling charges.
Another common situation is the potential energy in a uniform field. For gravity, the potential energy of
a massmin a uniform gravitational fieldgisUDmgh, wherehis the height above some arbitrarily-chosen
level for whichUis taken to be zero. Similarly, the potential energy of a chargeqin a uniform electric field
Eis
UDqEd; (17.3)wheredis the distance from some level at whichUis chosen to be zero.
17.2 Potential
Recall how the electric fieldEwas defined: by dividing the force on a small positive test charge by the
magnitude of the test charge, we get the electric field, which is a property of space. We can do something