Electric Potential Video Lecture - Electronics and Communication Engineering (ECE)

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
derivatives and integrals are used to
analyze the properties of a system
derivatives describe local properties of
systems and integrals quantify their
cumulative properties hello my name is
John McGreevy I'm a professor in the
physics department at MIT and today I'll
be talking with you about the electric
field and electric potential to get the
most out of this video you should
already have some exposure to the
electric field an 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 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 fields 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 a magnitude and a direction
the stronger the charges 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 Newton's 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 one 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 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 10 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're 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 you
end up with the picture like this one
each vector shows the direction and
strength of the electric field at that
point the longer the arrow stronger the
field is here you might imagine the
arrow is pushing a positive charge away
from our line charge 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 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 a 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's a clip from the
Boston Museum of Science to demonstrate
the phenomenon
a Van de Graaff generator it is actually
the world's largest air insulated Van de
Graaff generator it was built by dr.
Robert Van de Graaff himself
you
that's 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
so a single electron can 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 those ions
allows it to conduct electricity
resulting in a lightning bulb let's use
the electric field an electric potential
to investigate the 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 earth with an electrical
potential
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
better now we can draw in the lines our
equipotential lines will hug the surface
of the conductor's when they're 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 their conductors
because the electric potential of the
vandegraaff generator gets up to about 1
million volts or a thousand 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 either
more closely packed or less closely
packed in the blue area with the close
packed lines 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 or
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 in 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's a
chance to ask them pause the video here
some of you may be confused by the
terminology that's used for this
phenomenon many people are refer to the
breakdown potential required to create a
spark however 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're often given in volt per meter
which is actually a measurement of the
electric field the term breakdown
potential is a little misleading but
it's 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
happened in areas of strong electric
field or a steep change in the
electrical potential we hope you enjoyed
this clip from the Theater of
electricity at the Boston Museum of
Science good luck in your future studies
of electricity