We said last time that charged particles give rise to an electric field.
If a positively charged particle is placed in an electric field and then let go, the particle
will accelerate in the direction of the field. If the particle is charged negatively, it will
accelerate toward the field (in the opposite direction of the positive charged particle).
The units for electric field are Volts per meter, or Volts/meter, which is usually
abbreviated by V/m. What does this mean? It means that if a charge of one Coulomb is
allowed to accelerate is held fixed, and then let go so it accelerates for one meter, it will
obtain an energy equal to one Coulomb-Volt. Another name for one Coulomb-Volt is
one Joule.
1 Joule = 1 Coulomb-Volt
This is still hard to get a feeling for in terms of things that we are accustomed to, so lets
talk a little about charge. First of all, a Coulomb is the fundamental unit of charge, which
is a rather large charge. There are about 6 x 10**18 electrons in a Coulomb of negative
charge. Now let’s go back to the energy that a field transfers to a charge by accelerating
it. But this time, let’s take our charged particle to be one electron. The charge on one
electron is 1.6 X 10**-19 Coulombs. Now, if the electron is placed in the electric field,
and the electron is accelerated by the field for one meter, then the energy the electron gets
from the field is
Energy = 1.6 X 10**Coulomb-Volt = 1.6 X 10**-19 Joule = 1 electron-Volt or 1 eV.
Now, suppose the electron accelerates for 2 meters, then it will have 2 eV of energy, etc.
How much energy is 1 eV?
There are all types of energy, but we often think of the energy of motion, which is called
kinetic energy. The kinetic energy is a measure of how fast something is moving, and the
formula for kinetic energy is
Kinetic Energy = ½ mv2
Where m is in KG, v is in meters/sec.
Using this formula, we can find how fast an electron goes after it attains 1 eV of kinetic
energy from the electric field
1.6 X 10**-19 Joule = (½)9.1X10-31 v2
v=6 X 10**5 m/sec
Potential
This leads to the idea of potential energy and voltage. The potential energy is a measure
of how fast the electron would go if we were to let is accelerate in the field, but have not
done it yet.
In other words, we say an electron has 1eV of potential energy, if we are holding it
stationary at one an electric field of one V/m that has a spatial extent of one meter.
Picture
Other examples
2eV PE for field 2 V/m in one meter of extent. Etc.
So, voltage is the ability to impart energy onto a charged particle, but it has not happened
yet.
Let’s go back to our electron.