similar with potential energy, and find a similar quantity that is a property of space only. This quantity is
called thepotential.
Let’s first look at how this would be done with gravity. As we’ve seen, the gravitational potential energy
of two point masses isU DGm 1 m 2 =r. By dividing by one of the masses, we can get thegravitational
potentialGdue to massmat distancerfrom the mass:GDGm=r. The gravitational potentialGhas units
of J/kg.
We can do something similar with the electric force. The electric potential energy between two point
charges isUDq 1 q 2 =.4" 0 r/; by dividing this by one of the charges, we get an expression for theelectric
potentialVdue to chargeqat distancerfrom the charge:
VD1
4" 0
q
r: (17.4)
The electric potential is measured in units ofvolts(V), named for the Italian physicist Alessandro Volta. One
volt is equal to one joule per coulomb (1 VD1 J/C). Electric potential is sometimes callvoltage.
As with potential energy, it is really onlydifferencesin potential that are physically meaningful. Equiva-
lently, we are free to choose what point in space (or a circuit) is chosen to have a potential of zero volts, and
all other potentials are measured with respect to that. In an electric circuit, there is usually a point called that
groundthat is connected to the Earth and/or to the negative terminal of a power source, and the ground is
taken to be 0 V by convention.
Another common situation is a uniform field. In a uniform gravitational fieldg, the potential energy is
UDmgh; dividing by the massmwe find the gravitational potential isGDgh. Similarly, in a uniform
electric fieldE, the potential energy isUDqEd; dividing by the chargeqwe find the electric potential is
VDEd: (17.5)Solving this forE, we can see that the electric field can be expressed in units of V/m as well as N/C. You
can check that these are equivalent by breaking everything down into base units (kg, m, s, A) with the help of
Table 2-2.
Because of the similarity between electric potential and gravitational potential, it can sometimes be help-
ful to think of potential as being analogous to height. Positive charge will tend to “fall” from high potential
to low potential.
Just as force and potential energy are related by Eq. (17.1), field strength and potential are similarly
related. The electric fieldEis related to the electric potentialVby
EDV
x: (17.6)
(The corresponding relation for gravity isgDG=x.)
17.3 Equipotential Surfaces
Imagine drawing a surface in space such that every point on the surface is at the same potential. Such a
surface is called anequipotential surface. An important property of equipotential surfaces is that they always
intersect electric field lines at right angles. (If this were not so, then there would be a component ofEin
the plane of the equipotential surface and thus a component of the net force in the plane of the surface, in
violation of the assumption that the surface is one of constant potential.)
17.4 Comparison between Gravity and Electricity.
The following table summarizes the formulæ for field strength, force, potential, and potential energy, both for
a uniform (constant) field and for a field due to a point particle.