electric potential. It is independent of the strength of the test charge. Any charge,
regardless of its magnitude, placed in an area of greater electric potential will create a
system with more electric potential energy than when it is placed in an area of lower
electric potential.
On the other hand, a location one centimeter from a highly charged plate with a
stronger electric field has more potential than a location the same distance from a less
charged plate. Again, this idea directly parallels the idea of gravitational potential. The
statement for charged plates is true no matter what test charge you might use to assess
the electric potential.
For the last idea, turn your attention to the illustration for the Concept 5 diagram. If you
want to calculate the potential difference between the 6th and 7th floors, subtract the
value of the potential at the 6th floor from its value at the 7th floor. Since we can treat the
Earth’s gravitational field as essentially uniform near its surface, the gravitational
potential difference between the 6th and 7th floors is the same as it is between the 12th
and 13th floors.
You should think of electric potential difference in a similar way. If you know the electric
potentials at two points, you can subtract them to calculate the potential difference. With
electric potential difference, the actual potentials at the points do not matter, only the
change in potential between two points. The concept of electric potential difference is
used frequently in everyday devices. For instance, if you are told you have a nine-volt
battery, you are being told the difference between the terminals, not the electric
potential of either terminal. This is analogous to how you might think if you were told to
run up the stairs of a skyscraper. It does not matter whether you run from the 5th floor to
the 15th, or from the 18th to the 28th. In either case, you have to run up 10 flights of
stairs.
Potential
Depends solely on location
Potential difference
Change in potential between two points
24.10 - Equipotential surfaces
Equipotential surface: A
surface with the same electric
potential everywhere.
As its name indicates, an equipotential surface is one
along which the electric potential of a field is
everywhere the same. The boundary of a sphere
centered about a point charge q is an equipotential
surface. All the points on this surface are the same
distancer from q. This means the electric potential,
which in this case can be calculated with the formula
kq/r, is the same at all points on the surface.
Such an equipotential surface is shown in the first diagram to the right. In the
illustration, we represent the equipotential surface around q with a circle instead of a
sphere for the sake of visual clarity.
No work is needed to move a charge from one resting place to another along an
equipotential surface, because the potential energy neither increases nor decreases as
the charge moves. If work were needed to change the charge’s position, its electric
potential energy would change, which means it would be in a location with a different
electric potential.
The second diagram shows a particular example of a relationship that holds true in
general: Electric field lines that intersect an equipotential surface are always
perpendicular to the surface where they intersect it.
This is true because any motion of a charged particle from one place to another along
such a surface must be in a direction perpendicular to the force exerted by the field.
Work equals the component of the force parallel to the motion, multiplied by the
displacement. No parallel component means no work occurs. In turn, no work means no change in potential energy, and no change in potential
energy means no change in potential.
You can explore equipotential surfaces in the simulations in the introduction to this chapter. If you move a test charge along an equipotential
surface, you will see that its electric potential energy stays the same.
The mountainous contour map above displays curves of constant altitude.
Its “equi-altitude” curves are like equipotential surfaces in an electric field.Equipotential surface
Surface with constant electric potential
No work to move charge along surface