24.13 - Gotchas
Electric potential energy and electric potential are the same. No, they are not even measured in the same units. Potential energy is a property
of a specific configuration of charges, while electric potential is a property of a point in space. Electric potential is measured by assessing the
potential energy with a test charge, and then dividing by the magnitude of that charge.
I quadrupled the strength of a test charge, but I think the electric potential at the location is unchanged. You are correct. Like an electric field,
electric potential is independent of the test charge.There is electric potential surrounding a single charge. Yes, there is. There is a field. Add a second charge, and you will have created a system
with electric potential energy.
Where does an electron go when it is free to move: to a location of higher or lower potential? Toward a location of higher potential. Electrons
tend to move toward positive charges and away from negative charges, which means they move toward regions of higher electric potential,
minimizing the electric potential energy. A positive test charge (or proton) would do the opposite, moving toward a region of lower potential,
which also minimizes the electric potential energy.
I calculated a negative potential difference between two points. Is that possible? Quite possible. If point A has an electric potential of 9.0 volts,
and point B an electric potential of 6.0 volts, the difference VBíVA is í3.0 volts. It is perhaps an unstated convention that when calculating a
potential difference, VA is subtracted from VB.24.14 - Summary
Electric potential energy is conceptually similar to gravitational potential energy. It is
determined by the configuration of a system of charges. As with gravitational
potential energy, external positive work that is done on a system results in a
positive change in the sum of the system’s PE and KE. On the other hand, positive
work done by the system on something outside the system results in a negative
change in the sum of the system’s PE and KE.
Since in this chapter we often assume that charges move from one stationary
configuration to another, there is no change in KE due to work, and positive work
done on a system increases its PE. Negative work done on a system, as when two
opposite charges are moved closer together, decreases its PE.
Electric potential is a scalar quantity defined throughout an electric field in a region
of three-dimensional space. It describes the electric potential energy that will be
possessed by an electric test charge í or more properly by the system of charges í
when the test charge is placed at various locations in the field. When a test charge
is introduced, its electric potential energy equals the electric potential at its location,
times its own charge value. The potential is measured in joules per coulomb, or
volts (V), where 1 V = 1 J/C.
Electric potential difference is more commonly measured and used than the electric
potential itself. It is the difference in electric potential between two points. Batteries
are categorized by the potential difference between their terminals, which is 1.5 V
for commonly sold small batteries.
The electric potential difference between two points also equals the work required to move a test charge from one point to the other, divided by
the value of the charge.
An equipotential surface in a field is a surface that has the same electric potential at all points. Because there is no potential difference
between any two points in the surface, no work is required to move a charge along the surface. The electric field is perpendicular to such a
surface at every point on the surface.Potential energy of 2-charge systemElectric potentialV = PEe/qtest
Potential difference in a uniform fieldǻV = –Eǻs
(^450) Copyright 2000-2007 Kinetic Books Co. Chapter 24