Electric Fields and Forces
The magnitude of an electric field can be
determined by measuring the force experienced
by a charge placed in the field:
q
E=F÷q
Therefore, the charge placed in an electric field will
experience an electric force,
F = Eq
This force will make the charge accelerate
(according to Newton’s Second Law, F = ma)
Electric Fields
What direction will a charge accelerate?
+
+
+
+
+
+
+
+
+
-
Positive charges will
accelerate in the same
direction as the
electric field.
Negative charges will
accelerate in the
opposite direction of
the electric field.
Conversion of energy
Moving a mass or
moving a charge
takes
work energy
that is transformed to
potential energy
and/or to
Kinetic energy
If you pick up an object in a
gravitational field, you have
supplied work energy.
The object now has
potential energy.
If you release the object,
That potential energy is
converted to kinetic energy.
Work energy = potential energy = kinetic energy
If you move a charge in an electric field, it requires
work energy.
That work energy is converted to potential energy.
When the charge is released, its electric potential
energy, is converted to kinetic energy!
Work energy = potential energy = kinetic energy
E
-
Move a mass, m
Through a gravitational field, g
A distance, h
Gravitational Potential Energy, mgh
Move a charge, q
Through an electrical field, E
A distance, d
Electrical Potential Energy, qEd
The work energy required to move a charge through
an electric field is given by
+++
+++
+++
W = qEd
Electric “Pressure”
Voltage
Voltage can be thought of as a kind of
pressure- Electrical Pressure
Voltage is also called Electric Potential
Think of the water supply at your housesometimes you have high water
pressure-water flows quickly- and
sometimes low water pressure- water
flows slowly.
With Higher Voltage (pressure), charges are
able to flow more quickly
Voltage and Pressure
You may have more PRESSURE in a shower
nozzle than in a slow moving river, but does the
pressure alone tell you how much total water is
actually moving?
No! The pressure alone does not tell you how
much total water was actually flowing.
The flow of water is called the “current”.
Rub a balloon on your hair and it
becomes negatively charged, perhaps to
several thousand volts.
Does this mean that there’s a lot of
electrical energy?
Well, the charge transferred to the
balloon is typically less than a millionth of
a Coulomb (Remember, one Coulomb is charge is
a HUGE amount of charge)
There’s a LOT of difference
Voltage = Energy / charge
between Voltage and Energy!
Energy = Voltage x charge
Energy = 3000 V x 0.000001 C
Energy = 0.003 J
That’s not much energy!
High Voltage does not
necessarily mean that there’s a
lot of useful energy or that
something is dangerous.
High Voltage is not necessarily
dangerous- a Van de Graaff
generator can have more than
400,000 V, but there’s not much
charge that is transferred to you
from the globe.
Low Voltage is not necessarily safe.
Our houses are wired with 120V
and you can be killed from that
electricity.
Voltage (potential) is not the
dangerous part of electricity. The
dangerous part is how many
charges are flowing- the “current”.
The Electric Potential (Voltage), V, changes
as you move from one place to another
within an electric field
The change in Potential (“pressure”), called
the “Potential Difference” is given by
DV = Ed
Electric Field
3 meters
For example, the potential
difference between two
locations separated by 3
meters in a 4000 N/C electric
field is given by
DV = Ed = 4000 N/C x 3 m =
12,000 V
DV = Ed
4. If the potential changes by 100 V
between two locations separated by 5
meters, what is the strength of the electric
field?
Electric Potential Energy = qEd
Electric Potential difference, DV = Ed
5. How much work energy was required to
move a 0.8 C charge a distance of 3 meters
through a 1200 N/C electric field?
6. What is the potential difference between
those two locations?
#7 Which image shows the correct electric field lines
drawn around two positive charges?
A
B
C
#8 A positive charge is released in the electric
field as shown below. To which direction will the
positive charge accelerate?
A. Straight up
B. Straight down
C. right
D. left
E. The charge will not move
+
Electric Potential Energy
d
Energy stored up
between 2 charges
separated by a
distance d:
q1q 2
UE  k
d
Unit: Joules
Changing the Electric Potential
Energy
If you raise or lower a mass in a
gravitational field, you change the
gravitational potential energy, UG.
If you move a charge in an electric field,
you change the
electric potential energy, UE.
Two Ways to Find Electric Potential
Energy ?
q1q 2
UE  k
d
OR
Are these the same thing???
Which equation should be used??
qEd
If you RELEASE a charge in an electrical
field, its potential energy is converted to
kinetic energy!
Work enery = potential energy = ½ mv2
E
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Examples
What is the potential
energy stored
between 2 charges of
3 C and 4 C
separated by 2 m?
5.4 x 1010 J
q1q 2
UE  k
d
It takes 2.43 x 10-15 J of work to move an
electron as distance of 2 m in an electric
field. What is the strength of the field?
W = qEd
E = 7600 N/C
The electron is then released. What is the
maximum velocity it will achieve?
2.43 x 10-15 J = W = qEd = ½ mv2
v = 7.3 x 107 m/s
If two charges are placed close to each
other and held in place, there is an electric
potential energy stored between them.
+
+
Two charges in an electric
field at the same location
will have twice as much
electric potential energy as
one charge;
Five charges will have five
time the potential energy,
and so on…
It is often convenient to
consider the
electric potential energy per
charge.
+
+
+
+
+
Electric potential energy
charge
The concept of the electric potential energy
per charge has a special nameElectric Potential
Unit: Joule/coulomb.
However, it gets its own unit called a volt.
1 volt = 1 joule / coulomb
Since electric potential is measured in volts,
it is commonly called Voltage.
Electric Potential = Voltage
The work energy required to move a charge, q,
through an electric field, E, a distance d, is given by
+++
+++
+++
W = qEd = qDV
Sometimes, a charge is said to be located “at
ground”.
The potential (voltage) at “ground” is zero.
Vground = 0 Volts
There is another unit for very tiny amounts of
energy associated with atoms and sub-atomic
particles. It is called an “electron-Volt” or eV.
One electron-Volt is the amount of work energy
required to move one electron through 1 Volt of
potential difference.
In other words, 1 eV = W = qDV
= 1.6 x 10-19 C x 1V
So the conversion between eV’s and Joules is
1 eV = 1.6 x 10-19 J
V = ??
q
The Electric Potential, V, due to a point
charge, q, is given by
q
Vk
d
The potential will have the same sign
as the charge- there can be a large
positive and a large negative potential
At very great distances away from a charge…
d is very large…
q
Vk
d
The Potential, V, due to that charge is virtually ZERO.
Potential due to more than one
charge
Potential is NOT a vector…. (yea!!!)….So
The potential due to a group of point
charges is given by
q
V  k
d
Example
What is the potential halfway
between 2 charges of 3mC
and 4mC located 16 cm
apart?
787500V
What would be the potential
if the 4mC charge were
negative?
-112500 V
q
V  k
d
+
Higher V
Lower V
-
The potential near a positive charge will
be higher (it’s positive!) than the
potential near a negative charge (it’s
negative!).
• Therefore a positive charge will
accelerate from high to low V
• A negative charge will accelerate from
low to high V