Electric Potential Energy - is energy stored in a system of charged particles due to their electrical interactions.

Electric Potential

**Example 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 .

An **electron
volt** is the amount of energy corresponding to an electron
falling through a potential difference of one volt.

**Example 2**

An electron has been accelerated from rest through a potential difference of 1000 V.

a. What is its kinetic energy, in electron volts?

b. What is its kinetic energy, in joules?

c. What is its speed?

**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 3**

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 electrical systems we shall assume
that gravity can be ignored, unless specifically instructed otherwise.)

**Example 4**

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.

**Potential of a Point Charge**

Electric potential energy for two point charges

Electric potential for a point charge

**Example 5**

Find the electric potential produced by a point charge of at a distance of 2.60 m.

**Example 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 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 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).

**Capacitors**

**Capacitance** is a measure of the ability
of a device to store charge.

Definition of Capacitance, C

Units: coulomb/volt = farad, F

**Example 9**

A capacitor of 0.75 µF is charged to a voltage of 16 V. What is the magnitude of the charge on each plate of the capacitor?

**Parallel-Plate Capacitor**

Capacitance of a Parallel-Plate Capacitor

is the permittivity of the substance between the parallel-plates. The chart 15-3 on page 550 in the book has the values needed. For air .

**Example 10**

A parallel-plate capacitor is constructed with plates of area and separation 0.550 mm. Find the magnitude of the charge on each plate of this capacitor when the potential difference between the plates is 20.1 V.

**Example 11**

A parallel-plate capacitor is connected
to a battery that maintains a constant potential difference V between the
plates. If the plates are pulled away from each other, increasing their
separation, does the magnitude on the plates **(a)** increase, **(b)** decrease,
or **(c)** remain the same?

Capacitance of a Parallel-Plate Capacitor Filled with a Dielectric:

where is the dielectric constant found also in table 21.2.

**Example 12**

A parallel-plate capacitor is constructed with plates of area and separation 0.550 mm. The space between the plates is filled with a dielectric with dielectric constant . When the capacitor is connected to a 12 V battery, each of the plates has a charge of magnitude . What is the value of the dielectric constant ?

**Electrical Energy Stored in a Capacitor**

The total energy storedin a capacitor with a charge Q and potential difference V can be written:

**Example 13**

A camera flash unit stores energy in a 150 µF capacitor at 200 V. How much electric energy can be stored?

**Example 14**

A parallel-plate capacitor has plates of dimension 2.0 cm X 3.0 cm separated by a 1.0 mm thickness of paper. (a) Find the capacitance of this device. (b) What is the maximum charge that can be placed on the capacitor? (Maximum voltage is .)