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Electrostatics: Capacitance
From Coulomb’s Law to charge storage
So what is capacitance?
Capacitance is basically the ability of an electric conductor to store an electric charge,
and is usually defined as the total electric charge placed on the object divided by the
potential of the object,
C=Q/V
with the capacitance “C” in Farads (F), the charge “Q” in Coulombs (C), and the
potential “V” in Volts (V).
A capacitor is a device designed to provide capacitance in an electric circuit by supplying
it with the ability to store energy in an electric field between two conducting bodies
(eg. two pieces of charged metal).
In its most basic form, a capacitor consists of two conducting plates separated by an
insulating layer called a dielectric. When a capacitor is connected across a voltage
source, such as a battery, the voltage forces electrons onto one plate resulting in a
negatively charged plate. The electrons of the other plate are pulled off by the battery
resulting in a positively charged plate. Because the dielectric between the plates is an
insulator, current cannot flow through it and a potential difference is created between
them. A capacitor has a finite amount of capacity to store charges. When a capacitor
reaches its capacity it is fully charged and will not store any more charge.
http://micro.magnet.fsu.edu/electromag/electricity/capacitance.html
Electrostatics: Capacitance
From Coulomb’s Law to charge storage
To the right is a list
of some everyday
objects and their
relative charges.
Rabbit fur
More
positive
Glass
Human hair
Polyamide (nylon)
Wool
Fur
Silk
Aluminum
Paper
Cotton
This chart provides an easy reference to
determine the ease with which rubbing
materials together will transfer charge.
The farther apart they are, the more
readily charge is separated. Balloons are
made of latex (rubber).
Steel
Wood
Rubber
Acetate rayon
Polyethylene (PE) and
polypropylene (PP)
PET
PVC
Polyurethane
PTFE
More
negative
Electrostatics: Capacitance
From Coulomb’s Law to charge storage
_
_
_
_
_
_
_
charged
surface
+ __
+
_
+
_
+
induced
dipole in
(neutral)
solid
conductor
Force
_
_
_
_
_
_
_
+ ___
+
__
+++
_
+
_
_
++
+
induced
dipole in
(neutral)
solid
conductor
charged
surface
Force
For a metal, charges move freely.
Capacitor battery: http://micro.magnet.fsu.edu/electromag/java/capacitor/index.html
Inductance applets: http://micro.magnet.fsu.edu/electromag/java/faraday/,
http://www.shep.net/resources/curricular/physics/P30/Unit2/electroscope.html
Electrostatics: Capacitance
From Coulomb’s Law to charge storage
_
_
_
_
_
_
_
_ _
+_ + _
+ _ +_
+ +
charged
surface
Force
induced
dipole in
(neutral)
solid
polar solution
or solid
_
_
_
_
_
_
_
_ _
+_ + _
+ _ +_
+ +
charged
surface
Force
induced
dipole in
(neutral)
solid
polar solution
or solid
For a polar material like water, charges are able to move short distances, but are
localized around the ‘donating’ atom. Solid polar materials are known as
dielectrics.
+
H
_
_
Electric dipole
O
+
+
H
Electrostatics: Capacitance
The untold story
_
_
_
_
_
_
_
charged
metal
surface
_ _
+_ + _
+ _ +_
+ +
induced
dipole in
(neutral)
solid
polar solution
or solid
_
_
__
__
_
charged
surface
_ _
+_ + _
+ _ +_
+ +
induced
dipole in
(neutral)
solid
polar solution
or solid
As the neutral, polarized material gets closer to the charged surface, the charges
on the charged surface redistribute (again, due to Coulomb’s forces). This
behavior is called induction. For an applet, see
http://www.shep.net/resources/curricular/physics/P30/Unit2/electroscope.html
Charging objects
By means of electrical induction
Charge by Induction
Charge by induction is simply charging a neutral object by bringing a
charged conductor close to it, which manipulates electrons, but never actually
making contact between the objects. Charge is not passed as with conduction,
it is “induced”. This principle is illustrated in the diagram below:
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/estatics/u8l2b.html
Electrostatics: Capacitance
The capacitor
_
_
_
_
_
_
_
_
_
_
_
_
_ _
+_ + _
+ _ +_
+ +
charged
metal
surface
+
+
+
+
+
+
+
+
+
+
+
+
charged
metal
surface
A dielectric is placed between the
charged plates because it helps the
capacitor to accumulate more
charge.
What characteristics does the
optimal dielectric have?
•High ‘polarizability’
•Highly insulating ability
•Thermal stability
•Water insolubility
Unit of measure for a capacitor is Farads, after Faraday.
1 Farad = 1 Coulomb/Volt or C = q/V = e0A/d, where e0 is
the permitivity constant
Charging Objects
Methods that do NOT involve induction
Charge Separation
All matter is composed of atoms, which are composed of
negative electrons and positive protons. These opposite charges attract
each other and require a force to separate. Rubbing your feet on the
carpet, combing your hair (both “charge by friction”), or passing a wire
through a magnetic field can provide such a force. Once the charges are
separated, they can be drawn back together in a way that the energy
produced can be harnessed for something like lighting a lamp.
Charge by Conduction
Also called charging by contact, charge by conduction is simply
taking a negatively or positively charged object, touching it to a neutral
object, and thus giving that neutral object a charge. This was the method
used by Coulomb to charge his pith balls in his famous torsion balance
experiment.
http://www.shep.net/resources/curricular/physics/P30/Unit2/electroscope.html
Electrostatics: Capacitance
Lightning
Moisture accumulates in the atmosphere as a
cloud containing millions upon millions of
suspended water droplets and ice.
These ice droplets collide with each other as the
moisture rises. The importance of these
collisions is that electrons are transferred
between particles. The larger ones accumulate
electrons and fall toward earth from gravity.
The smaller ones have a positive potential and
rise to the top of the clouds.
+++++++
___
earth
This mimics a capacitor. When the voltage
becomes high enough, lightning strikes by
ionizing the air and creating a conductive
path to ground.
_____
Lightning/capacitor: http://micro.magnet.fsu.edu/electromag/java/lightning/index.html
Electrostatics: Capacitance
Lightning
•Voltage: 10-100 MV
•Peak current: 5-20 kA
•Power per stroke: P = VI = 50-2000 GW
•Same website: A moderate
thunderstorm generates several hundred
megawatts of electrical power. FALSE
(You do the math…)
•The Discovery Channel in Canada put
this in layman's terms, explaining that
one lightning strike has enough energy to
light 150,000,000 light bulbs
MISLEADING
•Energy: E = PT = 3.5 to 140 MJ
•An Atlanta Journal article states that
one storm can discharge enough energy
to supply the entire U.S. with electricity
for 20 minutes FALSE
Power company: One lightning
strike can carry enough electricity to
power 10 million homes for one
month. FALSE
One 100 W light bulb operating for
The key is understanding the duration of a bolt.
one month = 260 MJ
Electrodynamics: Ohm
The MAN: Georg Simon Ohm
Ohm sought a connection
between voltage and current.
Unfortunately, Ohm's law
was met with ‘resistance.’
Many of his countrymen
were used to experimenting
with voltage and current, but
they considered these to be
entirely separate
phenomena.
Electrodynamics: Ohm
The MAN: Charles Augustin de Coulomb
In his experiments, Ohm
used thin resistive wire of
various lengths in simple
circuits. He found that V =
IR (voltage = current ×
resistance). Voltage was
supplied to the circuit by a
thermocouple and current
was measured by
measuring the deflection of
a thin magnet near the
wire.