### – Electric Potential Chapter 18 and Capacitance Section 1

```Chapter 18 – Electric Potential
and Capacitance
Section 1
Electric Potential Energy
Electric Potential Energy
• Electric Potential Energy is a form of
mechanical energy, which is conserved
• Any time a charge moves within an electric
field, work is done on that charge
• If a positive charge moves in the direction
of the electric field, it will lose PEe; if a
negative charge moves in the direction of
the electric field, it will gain PEe….WHY?
What is a Uniform Electric Field?
+
+
+
+
+
+
+
+
+
-
• Exists where the
electric field lines are
parallel and evenly
spaced
• Direction of the field is
determined by which
way a small positive
test charge will move
if free to do so
• Compare a charge moving through a
uniform electric field and a ball moving
through a gravitational field:
(+)
positive
positive charge
The charge
loses
electrical
potential
energy as it
“falls” in a
uniform
electric field
ball
The ball loses
gravitational
potential
energy as it
falls toward
the Earth
What determines the
direction of an
electric field?
(-)
negative
Earth
Electric Potential Energy in a
Uniform Electric Field
PEelectric = -qEd
Electric Potential Energy = -(charge x
electric field strength x displacement from
a reference point in the direction of the
field)
Electric Potential Energy for a pair
of charges
PEelectric = kc q1q2
r
These energies can be added together
using algebraic summation – these are
scalar quantities!
Chapter 18 – Electric Potential
and Capacitance
Section 2
Potential Difference
Potential Difference
• Electric Potential Difference is a change in
electric potential – a change in the ability to do
work:
∆V = PEelectric
q
SI unit is the Volt = Joule/Coulomb
As a 1 coulomb charge moves through a potential
difference of 1 volt, the charge loses (or gains) 1
joule of energy
Examples
• Batteries: the difference
between the two
terminals on a battery
ranges from 1.5 volts to
12 volts – as charges
move from one terminal
to another, the energy
can be used for work, like
water falling over a water
mill is used to do work
• Household electrical
outlet is 120 volts
Potential Difference in a Uniform
Electric Field
∆V = -E∆d
∆d is the displacement in the direction of the
electric field; perpendicular movement in
an electric field does not change the
electric potential difference. Why is there
a negative sign here?
(Remember the equation for E? It’s from
chapter 17: E = kcq1/r2)
Potential difference between a
point at infinity and a point near a
point charge
• Huh? Don’t stress over this too much, look
at the explanation on pg. 672
∆V = kc q
r
Vectors in Electric Potential?
• No, these are scalar quantities!
• Simply add the Electrical Potentials,
paying attention to the signs, to get the
algebraic sum
A battery does work to move charges!
• Inside a 12 volt battery, the electric field does 12 joules
of work to move a 1 Coulomb charge from the (-)
terminal to the (+) terminal
• when you connect your device to this battery, the charge
moves from the (+) terminal, through the device toward
the (-) terminal, and gives up the 12 joules of energy to
• When it reaches the (-) terminal, the charge has an
electric potential of zero again, and the battery does 12
more joules of work on the charge to get it back to the
(+) terminal, ready for another round trip through your
device.
Chapter 18 – Electric
Potential and Capacitance
Section 3 - Capacitance
Capacitors and Charge Storage
• A parallel plate capacitor consists of two parallel
metal plates separated by a non-conducting
material, then rolled into a cylinder. One plate is
attached by a conducting wire to the (-) terminal
of a battery, the other plate is attached to the (+)
terminal of the battery
• The difference in potential energy in the battery
causes opposite charges to build up on the
plates, so that eventually the potential difference
between the plates is equal to the potential
difference between the battery terminals
• In this way, the capacitor can store
charges and their potential energy away
from the battery
• The “capacitance” of a conductor is its
ability to store energy in the form of
electrically separated charges
C = Q capacitance = charge on plate
∆V
potential difference
SI unit for capacitance is the farad (F) = Coulombs/volt
Typical values range from 1 µF to 1 pF
Capacitance for a parallel plate
capacitor in a vacuum
C = ε0 A
d
Capacitance = permittivity of a vacuum x area of one plate
distance between the plates
The capacitance of a sphere increases with its radius; for
example, earth has an extremely large capacitance, so it
can provide or accept a large amount of charge without
its electric potential changing very much; this is why the
earth is used as a ground in electric circuits.
The material between the plates of a
capacitor can change its capacitance
• A material called a “dielectric” is used to improve
capacitance
• A “dielectric” is an insulator (rubber, glass, etc)
that is inserted between the plates of a
capacitor, which allows charges to accumulate
on the surface of the plate. A vacuum can’t do
this. This allows the capacitor to store more
charge for a given potential difference,
increasing the conductor’s capacitance
Discharging capacitors rapidly
release their charge
• Once the capacitor is charged, the battery can
be removed from the circuit and the capacitor
will remain charged as long as it is not
connected to a conductor.
• Once the plates are connected to a conductor,
the capacitor will discharge – the charges move
back from one plate to the other until there is
zero potential difference between them
• This allows an instantaneous release of the
energy stored in the capacitor, which has many
applications – camera flashes for example.
Capacitor uses
• Also, the potential energy stored can be
manipulated by bringing the plates closer
to each other, which can be detected.
Some types of keyboards use this.
• Finally, since the area of the plates and
the distance between them can be
controlled, the capacitance, and thus the
electric field strength, can also be easily
controlled
Energy and Capacitors
• A capacitor stores electrical potential
energy because it requires work to move
charges through a circuit to the opposite
plates of a capacitor. The work done is a
measure of the transfer of energy
Equations for Electrical Potential
Energy stored in a capacitor
PEelectric = ½ Q∆V
PEelectric = ½ C(∆V)2
PEelectric = Q2
2C
PEelectric = electric potential energy
in Joules
Q = charge on one plate in
Coulombs
∆V = change in potential difference
in Volts
C = capacitance of the conductor