Is Static Electricity Static?
Static electricity is often considered to be the effect of electric charges at rest on insulators or insulated
conductors. And this is surely true in part.
When a nylon slip clings to the body, or when you have problems leafing through the pages of a magazine, you are witnessing a static effect of electric charges. But the buildup of charge distributions in a thundercloud or on a person
walking along a hotel corridor are dynamic processes, and the
possible resulting discharges can hardly be called static. Let's
look a little closer at some such examples.
Charging by Walking
The charging of a person walking
on an insulating floor covering is described here in a simplified
The contact and friction between
a person's shoe soles and the floor separate a charge q
for each step. If she walks with a rate of n steps per unit of
time, this corresponds to a charging current, ic, where
ic = nq.
In this way she achieves a voltage V that at first will increase
with an average rate of
where C is her capacitance. The voltage does not
increase smoothly with the constant rate just given, but literally
as a step function. This is further complicated by the fact that
the capacitance decreases when her foot is lifted and increases
again when her foot is put back down on the floor. The voltage,
V, will keep increasing, but not infinitely, because the effect
of the charging current will be counteracted by a decay current,
id, given by
where R is the resistance from the person to ground
through or across the floor covering. The voltage has reached
its maximum value, Vm, when the two currents
balance each other, which is shown as
play a little with this equation. It is easy enough to determine
R, the decay resistance for a given floor and shoe combination.
The step rate, n, is, according to an ISO standard, two steps
per second, that is, n = 2 s1. The charge transferred
per step, q,
looks more difficult to handle, but we can estimate a reasonable
upper limit in the following way.
If the breakdown field strength
in the space between an elevated sole and the floor is Eb,
then the maximum charge density, m,
on the sole is m
= 8.85 1012 F m1 is
the permittivity of vacuum and approximately that of air (see
|Figure 1. Maximum charge density (m)
on the sole where Eb is the breakdown field strength
between the sole and the floor.
Hence if the area of the shoe sole is A,
then the maximum charge transferred per step is qmax
and the maximum voltage will be Vm = nAoEbR.
Assuming we can consider the
combination of an elevated foot and the floor's surface a pair
of planar, parallel electrodes, Eb ~ 3 ~ 106
V m1. The sole's area may be about 150
cm2, depending on the shoe size of course. Entering
these values into the equation for Vm (and considering
their uncertainties), we find that Vm ~ 106
R when Vm is measured in volts and R in ohms.
Now suppose we want to be sure that our person
does not get charged to more than 100 V by walking. The equation
for Vm tells us that the decay resistance
has to fulfill the condition
The same equation further suggests
that the maximum charging current a person may produce by walking
on an insulating floor is on the order of 1 µA. Although
the capacitance, C , of the person has no influence on the maximum
voltage, it does, in cooperation with the decay resistance, determine
the rate with which the voltage increases.
After a time,
= RC, the voltage will have reached (approximately) 63% of the
maximum value. It can also be mentioned that the energy, W, stored
electrostatically in the field of the charged person is given
However, the effect this energy will
have if discharged into the environment, on an electronic component,
for instance, also depends upon the person's resistance, Rp,
which may be described more or less as the resistance through
the person from the location of the charge to the point of discharge.
Charging of Liquids
A process somewhat similar to
the one we've just described above is the flow of an insulating
liquid through a tube.
Suppose a liquid is flowing with
a volume flow rate of u(m3 s1)
and has a specific mass (kg
m3) and specific charge density of µ(C
kg1). The flow constitutes a current ic
given by ic = uµ.
If the liquid is collected in a conductive, semiinsulated container
(Figure 2) with a resistance R to ground and a capacitance C,
the voltage of the container will increase toward a maximum value
Vm, given by Vm = icR = uµR,
and the energy stored will approach a maximum value Wm,
Assuming u = 103 m3
s1 (1 liter per second or 16 gallons
= 103 kg m3, µ = 106
C kg1, R = 1010 ,
and C = 200 pF, we then have
ic = 106A
= 1 µA,
Vm = 104
Wm = 102
J = 10 mJ.
The maximum values of voltage will,
in practice, have been reached within 10 seconds.
An essential difference between
this process and the one of a person being charged by walking
is that with the flowing liquid there is a much wider range of
charging currents. While we're not going to go into the questions
of how or why the liquid gets charged in the first place, or how
the charging may be affected by whether the pipe is conductive
or insulative, it should be noted that the liquid must have a
volume resistivity higher than approximately 107 m
for any appreciable charging to take place.
|Figure 2. Liquid collected in a conductive,
semiinsulated container with a resistance, R, to ground and
a capacitance, C.
This means (among other things) that
water cannot charge. Mind you, it cannot charge because of flowing.
If spraying is involved, the situation is completely different.
In such circumstances, probably all liquids may charge.
The Electrofilter and Spray Painting
Now let's turn to something completely
The two examples we've just discussed
are both cases of what you might call "unwanted static electricity,"
possible causes of production problems or even explosion risks.
But we must remember that static electricity has many applications,
as we'll see by looking at a couple of examples that also involve
a certain degree of nonstatic behavior.
Possibly the most important device
based on static electric principles is the electrostatic filter
(or simply, electrofilter) without which, for example, it would
be impossible to clean the smoke from traditional power plants.
In an electrofilter (Figure 3),
the air is passed through a region where air ions are being produced
by a corona discharge. Some of the ions will attach to particles
in the passing air. This passing air is then brought into an electric
field where the particles may plate out on one of the electrodes.
|Figure 3. Air passes through
a region of an electrofilter where air ions are being produced
by a corona discharge.
Whether a particle actually lands on
the collector electrode depends upon the magnitude of the airflow,
the field strength, and the charge on and the mass of the particle.
Obviously the larger and heavier
the particle is, the more difficult it will be to pull it out
of the airflow. On the other hand, the larger the particle is,
the more ions may attach to it, making the deflecting force larger.
An electrofilter should not be mistaken for an electret filter
where the electric part of the filtering process depends primarily
upon polarization forces.
Another important application
of electrostatic principles is spray painting.
If a liquid is vaporized from
a grounded spray gun some of the droplets formed are likely to
be charged, but not in a predictable way.
If, however, the gun is held
at a voltage, for example a positive one as shown in Figure 4,
the droplets will leave the gun with a positive charge proportional
to the field strength at the nozzle, and hence to the voltage
of the gun. The charge will also be proportional (approximately)
to the square of the radius of the droplet. If a grounded, conductive
object is placed in front of the gun, the droplets will be deflected
toward the object because of the field from the gun. By adjusting
the airflow rate and the voltage of the gun, it is possible to
ensure that practically all the droplets will land on the object.
|Figure 4. Droplets leave a spray gun with
a positive charge proport ional to the gun's voltage.
Although there will be field lines "ending"
on any part of the object, obviously the part facing the gun where
the field is strongest will get most of the paint. However, by
rotating the object to be covered, it is possible to make the
covering very uniform. It should be mentioned that the method
described here is only one of a variety of surface treatments
I hope these simple examples
have helped demonstrate that static electric processes often involve
dynamic features. So how then can we define a static electric
process? I don't believe there is a simple definition. Or rather
I think there are two different types of static processes.
Obviously static electricity
as traditionally defined encompasses a lot of processes that we
call static, although they may have some dynamic features, like
decay currents and discharges. But as the examples of the electrofilter
and spray painting have shown, we sometimes call processes electrostatic
even though there are no charged insulators or insulated conductors
involved because the necessary fields are provided by generators
with an electromotive force.
And it seems to me that what
makes both types of processes static is the fact that the charge
carriers are created by the process itself, like corona ions attaching
to the smoke particles in the electrofilter or paint droplets
being surface-charged in the electrostatic spray gun.
I'm sure somebody will consider
these distinctions too elaborate, but then let's hear a better
one. Of course, we could just settle for the old saying from the
high school student that static is what your dad gives you a lot
of, when you don't come home until three o'clock on Saturday morning.
Niels Jonassen, MS, DSc, is retired
from the Technical University of Denmark, where he has conducted
classes on static electricity, ions, and indoor climate. After retiring, he divided his time among the
laboratory, his home, and Thailand, writing on static
electricity topics and pursuing cooking classes. He passed away in 2006.
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