Electric Potential and Potential Difference
"The outcome of any serious research can
only be to make two questions grow where one question grew
Note that WAB
is the work done by the electric field in moving the charge.
The work done by the "external agent" is -WAB
- Units of potential difference are volts
1 Volt = 1 Joule/Coulomb (J/C)
- In a region of space where there is an electric field the work
done by the electric field, dW, when a positive point charge, q,
is displaced by ds is
For a uniform electric field we
where an arbitrary path can always be
split into sections along E and sections
perpendicular to E.
Note that this means that
the electric field can be expressed in the units
V/m. [ 1 N/C = 1V/m ]
electric field is a conservative field.
- This means that the potential difference between
two points is independent of the path taken.
Every point in space has a single value of V and E.
The gravitational field behaves in exactly the same
way. Changes in gravitational energy are
independent of the path taken. Climbing stairs
from one floor to another involve the same amount of
work against gravity as riding an elevator.
Note that in simple gravitational applications we
don't usually define a gravitational potential only
gravitational potential energy (mgh). In this
case the gravitational potential is defined as gh.
- Exactly equivalent to gravity, it
in potential difference, ,
which are defined. To obtain absolute values
of V physicists usually define V = 0 at
infinity. But this is an arbitary definition;
in engineering applications it is often convenient
to define the earth as V = 0.
- Potential due to a point
For a single point charge Q the potential difference
between A and B is given by,
E is the field due to a point charge and ds = dr ,
If we assume rB
= ∞ then VB
= 0 and,
Note that the
potential is inversely proportional to r,
rather than r2 as in the case of
the electric field.
In the period that Einstein was active as
a professor, one of his students came to him and said: "The
questions of this year's exam are the same as last years!"
"True," Einstein said, "but this year all answers are
Dr. C. L. Davis
University of Louisville