Electric Potential
Work must be done in moving a charge against an electric field. Here a positive charge is forced toward a positively charged sphere. It's being pushed against the E-field.
Definition of Electric Potential
The electric potential at any point in an E-field is the potential energy of a test charge at that location divided by the value of that test charge.
Units: J/C = volt, V
Example 16-1
Find the change in electric potential
energy, 
,
as a charge of (a) 
or (b) 
moves
from a point A to a point B, given that the change in electric potential
between these points is 
.
Definition of Potential Difference
The potential difference between any two points
A and B numerically equals the work done per unit charge, against the field
in moving a positive test charge 
from
A to B with no acceleration:
An electron volt is the amount of energy corresponding to an electron falling through a potential difference of one volt.
Potential in a Uniform Field
The potential difference is + (a voltage rise) when the displacement is opposite to the field and – (a voltage drop) when it is parallel to the field.
Example 16-2
A uniform electric field is established
by connecting the plates of a parallel-plate capacitor to a 12 V battery. (a) If
the plates are separated by 0.75 cm, what is the magnitude of the electric
field in the capacitor? (b) A charge of 
moves
from the positive plate to the negative plate. Find the change in electric
potential energy for this charge. (In elecrical systems we shall assume that
gravity can be ignored, unless specifically instructed otherwise.)
Example 16-3
The electric potential at point B in the parallel-plate capacitor shown below is less than the electric potential at point A by 4.50 V. The separation between points A and B is 0.120 cm, and the separation between the plates is 2.55 cm. Find (a) the electric field within the capacitor and (b) the potential difference between the plates.
Example 16-4
In a certain region of space the electric potential V is known to be constant. Is the electric field in this region (a) positive, (b) zero, or (c) negative?
Potential of a Point-Charge
The Electric Potential for a Point Charge:
Electric Potential Energy for Point
Charges q and Separated
by a Distance r:
Example 16-5
Find the electric potential produced by
a point charge of 
at
a distance of 2.60 m.
Example 16-6
A charge 
is
placed at the origin, and a second charge equal to -2q is placed on the x-axis
at the location x = 1.00 m. (a) Find the electric potential
midway between the two charges. (b) The electric potential
vanishes at some point between the charges; that is, for a value of x between
0 and 1.00 m. Find this value of x.
Example 16-7
Two point charges, each equal to +q, are placed on the x-axis at x = -1 m and x = 1 m. As one moves along the x-axis, does the potential look like a peak or a valley near the origin?
Example 16-8
Two charges, +q and +2q, are held in place on the x-axis at the locations x = -d and x = +d, respectively. A third charge, +3q, is released from rest on the y-axis at y = d. (a) Find the electric potential due to the first two charges at the initial location of the third charge. (b) Find the initial electric potential energy of the third charge. (c) What is the kinetic energy of the third charge when it has moved infinitely far away from the other two charges?
Equipotentials
Around a point charge there is a sphere that represents the same potential. If you put all of the spheres together in one figure you have an equipotential surface.
Field Lines and equipotentials for a small positive charge.
The equipotential surfaces are concentric spheres centered on the charge.
A continuous color representation of the potential.
The height of the peak corresponds to the size of the potential above the zero base level.
The electric fields and equipotentials.
After falling through a potential difference of 25 V, the charge has lost an amount of potential energy (25 V)q equal to its gain in kinetic energy.
The Potential of Several Charges
Two equal positive charges.
The equipotentials.
A color representation of the equipotentials.
A color representation with height.
The equipotentials and field lines for two opposite charges of equal magnitude (a dipole).
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