Air is normally an insulator, but under certain conditions, it can suddenly and temporarily
change into a conductor, and we end up with a spark. In this video, we'll use the related
concepts of electric fields and electric potential to explain how insulators can suddenly, dramatically
and temporarily become conductors.
This video is part of the Derivatives and Integrals video series.
Hello. My name is John McGreevy. I am a professor in the physics department at MIT, and today
I'll be talking with you about the electric field and electrical potential.
To get the most out of this video you should already have some exposure to the electric
field and electric potential. You should be able to take a mathematical expression for
the field and obtain the potential, and vice versa. You should also know how to draw equipotential
surfaces and electric field vectors.
Throughout this video our goal is to help you gain a clearer picture of the electric
field and the electric potential. By the end of the video you should also be able to describe
the process of electrical breakdown by using either the field or the potential.
Let's start with a review of electric field and electric potential. First we'll describe
them conceptually. Then we'll show the mathematical relationship between them, and show some of
their typical visual representations.
First, let's see what you remember. Take out a piece of paper and write down everything
you remember about the electric field and the electric potential. Try to concentrate
on their similarities and differences. Pause the video to do this.
Now you can compare the list you made to our list.
The electric field is generated by electric charges, and extends an infinite distance
from them.
If you bring a second electric charge into a region of electric field, there will be
a force exerted on it. Like all forces, that force has magnitude and direction. The stronger
the charge is, the more force will be applied to it.
The electric field is a vector quantity. It has a vector value at every point in space,
measured in Newtons per Coulomb or Volts per Meter.
Much like the electric field, electric potentials are created by charges and extend an infinite
distance from them.
If you bring a second charge into a region of electrical potential, that second charge
will gain or lose potential energy. The stronger that charge, the more its potential energy
will change.
Unlike the electric field, the electric potential is a scalar quantity, which means that everywhere
you look you can find a number that represents the potential, measured in Joules per Coulomb.
Let's look at two ways to envision an electric potential for a positively charged line near
the origin. We're going to look at this in two dimensions to make things easier to see.
We can also draw the level curves for the electric potential function. These are called
"equipotential lines," because the value of the potential is equal at every point on a
given line. For instance, we might draw lines every ten volts.
If we plot the potential on the vertical axis, we end up with this mountain-like shape. We
can imagine positive charges rolling down the mountain as they are pushed away from
our line charge.
We can also sketch the electric field around a line charge. If we pick regularly spaced
points at which to draw our electric field vectors, we end up with a picture like this
one. Each vector shows the direction and strength of the electric field at that point. The longer
the arrow, the stronger the field is. Here you might imagine the arrows pushing a positive
charge away from our line
Displaying both the equipotential lines and the field vectors at once, we get this picture.
You can see that the equipotential lines are always perpendicular to the field.
Since charges create both fields and potentials, both will be present all the time, though
we might only draw one or the other.
The field and the potential are related mathematically through the gradient operator. As a vector
operator, the gradient turns the scalar potential into a vector field. To go in the other direction,
a line integral of the electric field turns that vector field into the scalar electric
potential.
The negative sign that appears in both equations is important—the electric field points in
the opposite direction from any changes in the potential. If the electric potential increases
in a particular direction, the electric field points in the opposite direction.
We're going to use something called "electrical breakdown" to illustrate our concepts today.
We'll start with an example, give a definition, then go into an explanation of the phenomenon.
Here is a clip from the Boston Museum of Science to demonstrate
the phenomenon.
Quite a dramatic demonstration! Let's look at this in a little more depth.
Electrical breakdown is defined as the process by which an insulating material in a strong
electric field becomes electrically conductive. The material actually changes from being an
insulator to being a conductor. In the clip you saw, this happened in the air near the
Van de Graaff generator, and a large electric spark resulted.
You may sometimes hear this referred to as breakdown potential, or breakdown voltage,
which is the same thing.
The exact value of the electric field needed depends on many factors, including distance,
humidity, temperature, and the material itself.
Here is a simplified explanation of how electrical breakdown works in air. Consider this house
in a thunderstorm.
If we zoom in on the air above the house, we can see the molecules of gas in the air.
Thunderstorms involve strong electric fields and high electric potential differences. We
can represent those on our diagram.
Imagine that one electron is pulled from its atom by the strong electric field. Because
the electron is negatively charged, it will accelerate against the electric field, and
will eventually collide with another atom. That collision might knock another electron
loose. Now there will be two electrons accelerating.
A single electron can thus create a chain reaction, where many atoms lose their electrons.
This creates a region of ionized air. Air is normally a good insulator, but the presence
of ions allows it to conduct electricity.
...resulting in a lightning bolt!
Let's use the electric field and electric potential to investigate this situation further.
Here are the Van de Graaff generators from the video, charged up, with a metal ball as
a target.
Let's take a simplified version of the situation shown. Draw the equipotential surfaces around
these two objects, and then draw in the electric field arrows as well. You can ignore the presence
of the support pillars.
Here are two hints. First, the small metal ball is grounded, or "earthed," with an electrical
potential of zero. Second, the electrical charge on the generator will spread itself
equally over the surface of the conducting spheres.
Pause the video here to draw the equipotential lines and the field vectors.
Here's another picture of the generator with the target ball nearby.
This picture is too complex. Let's create a simpler version of the picture. That's
Now we can draw in the lines. Our equipotential lines will "hug" the surface of the conductors
when they are nearby. Because the charge is spread evenly across the surface of the conductor,
the whole surface will be at the same electric potential. The equipotential lines will tend
to be smoother when farther away from the conductors.
Because the electric potential of the Van de Graaff generator gets up to about one million
volts (or 1000 kilovolts), and we have drawn eight lines in the picture, each line must
represent a difference of about 125 kilovolts.
In this view we have colored in the regions where the equipotential lines are more closely
packed, or less closely packed.
In the blue area, with the close-packed lines, the gradient of the potential is larger. Because
the electric field is proportional to the gradient of the potential, the places where
our lines are more closely packed will have a stronger electric field.
In the red areas, where equipotential lines are far apart, the gradient of the potential
is smaller. Therefore, the electric field will be weaker.
We can use this as a guide when drawing our field vectors.
Let's draw in those electric field vectors now. We have assumed here that the generator
becomes positively charged, but if it were negatively charged, we could simply reverse
the direction of our arrows.
Look carefully: our field arrows are perpendicular to the equipotential surfaces at all points.
Check your own diagram - is this true on yours as well?
Our field arrows are longer where the equipotential lines are more closely packed—is this true
on your diagram?
If you need to revise your diagram or draw a new one, do so now. If you have questions
for your teacher, here is a chance to ask them.
Pause the video here.
Some of you may be confused by the terminology that is used for this phenomenon. Many people
refer to the "breakdown potential" required to create a spark. However, but you may have
noticed that the sparks in the video were produced where the electric field was the
strongest, not where the electric potential was the highest. Turn to a friend and discuss
why this is the case. Pause the video here to discuss.
If we return to the equations that relate the field and the potential, we can improve
our understanding. You can see that we have a gradient term—a derivative with respect
to distance.
If our potential changes slowly over distance, the field is weak, and no spark is generated.
On the other hand, if the potential changes quickly over distance, the field is strong.
A stronger field is more likely to remove an electron from an atom.
In fact, when numerical values are given for the breakdown potential, they are most often
given in "volts per meter," which is a measurement of the electric field. The term "breakdown
potential" is a little misleading, but it is still the standard terminology.
To review, the gradient connects the electric field to the electric potential. A steeper
change in the potential results in a stronger electric field. We also saw that electrical
breakdowns happen in areas of strong electric field, or of steep change in electrical potential.
We hope you enjoyed this clip from the Theatre of Electricity at the Boston Museum of Science.
Good luck in your future studies of electricity.