This video is about electrostatic fields.
The expression electrostatic field simply means that the electric field in question
is produced by stationery as opposed to moving charge.
When talking about fields in this video, I will use the words electric and electrostatic
interchangeably.
We'll learn about electric fields in subtopic 5.1.
Here we discussed general electric field concepts, electric field patterns, electric
field strength and electrical potential difference.
I will refer to some of these concepts in this video without discussing them again in
detail so feel free to refresh your knowledge and go back to watch some of the videos in
subtopic 5.1.
Here we'll start by looking at electric potential at a point and then move on to electric
equipotentials.
Let's begin with electric potential at a point.
So far we have used the expressions electric potential and electric potential difference
interchangeably.
These two concepts are closely connected but they mean different things.
Let's explore this difference.
We'll begin by refreshing the definition of electrical potential difference which is
the work done when moving a unit charge between two points in an electric field.
Based on this definition we can write that delta VE, so change in electrical potential
or in other words electrical potential difference, is equal to W divided by Q.
Rearranging leads to the formula that's given in the IB physics data booklet and here are
the variables that are present in this formula.
So far we dealt with potential difference between two points.
If a potential difference exists between two points, it also makes sense to have specific
potential values at each point.
However, in order to define electric potential at a point as opposed to the potential difference
between two points, we need a system with a zero reference point.
Similarly to gravitational potential, the zero reference point for electric potential
is defined to be at infinity.
This is consistent with Coulomb's law which tells us that the force between two charges
is inversely proportional to the square of the distance between these charges.
As r the distance is increased and approaches infinity, 1 over r squared approaches zero
which means that when two charges are at an infinite distance, the force between the
charges is zero.
As a result, the electric potential of the system is also zero.
By system we mean the two charges.
Now imagine that the charges are moved closer to each other, so the distance between them
becomes finite.
With a finite distance, if the charges have the same sign they repel, in other words when
released they move back towards infinity, which means that when the charges were brought
closer to each other, energy was stored in the system, therefore the electric potential
is positive.
If the charges have opposite signs and they are moved to a finite distance from each other,
they attract and move towards each other when released.
This means that in order to move the charges back to an infinite distance from each other,
energy must be supplied to the system, so it follows that electric potential is negative.
You can also think about this situation in the following way.
Electric potential at infinity is always zero.
When charges of the same sign are moved closer to each other from an infinite distance, energy
must be supplied to the system, so electric potential increases and becomes positive.
When the charges have opposite signs, energy must be supplied to move the charges from
a finite to an infinite distance.
So as the charges are moved towards each other from infinity, electric potential decreases
and becomes negative.
Based on this discussion, now we can define electric potential at a point, which is the
work done per unit charge when moving a positive test charge from infinity to the point.
We'll further discuss electric potential in subtopic 10.2.
Now let's move on to electric equipotentials.
We already covered electric field line patterns in subtopic 5.1.
We saw how field line patterns look like around the point charge, between two point
charges, between two parallel plates, and between a charged plate and the point charge.
Here we'll discuss how electric equipotentials look like around the point charge and between
two parallel plates.
As you can see, these diagrams already include electric field lines as we learned in subtopic
5.1.
Let's begin with the point charge.
Here I chose to work with a positive charge, but the concepts are exactly the same for
a negative charge.
One way to define equipotentials is that they represent points where the potential is the
same.
We learned in the previous video that gravitational equipotentials and gravitational field lines
are perpendicular to each other.
This is also true for electric fields.
So now we can draw the equipotentials around the point charge.
Using the same concepts, we can also do this for the parallel plates.
In the general definition of electric potential, we use the idea that the zero reference point
is at infinity.
However, just as for gravitational potential, in a given situation, we can choose the ground
as our zero potential reference point.
When working with electric potential in specific situations, we can also decide to choose an
arbitrary zero reference point to make working with the given situation a bit easier.
For example, I can choose the positive plate to be at a zero volt potential.
Let's assume that the potential difference between the plates is 12 volts.
When a positive charge is released in the electric field between the plates, it moves
towards the negative plate.
To move this charge back towards the zero volt position, so towards the positive plate,
we would need to do work on the charge.
In other words, we would need to supply energy to the system.
This tells us that as we move from the positive towards the negative plate, electric potential
decreases and becomes negative.
As a result, the potential on the negative plate is negative 12 volts.
It logically follows that the potential values on the equipotential lines would be negative
3 volts, negative 6 volts and negative 9 volts.
Of course, we can choose a different zero reference point, for example the negative plate.
This means potential increases as we move from the negative towards the positive plate.
The potential values on the equipotentials would be positive 3 volts, positive 6 volts
and positive 9 volts.
The potential of the positive plate would be positive 12 volts.
Let's summarize what we have learned in this video.
We started by refreshing the definition and the formula for electrical potential difference.
Then we began discussing electrical potential and said that it is defined to be zero at
infinity.
We added that this is consistent with Coulomb's law and concluded that when two charges are
at an infinite distance, the force between the charges is zero, so the electric potential
of the system is also zero.
Then we learned what happens when the charges are moved closer to each other to a finite
distance.
If the charges have the same sign, then the electric potential of the system is positive
and if they have different signs, the electric potential is negative.
Finally, based on these concepts, we defined electric potential at a point.
Next, we moved on to discuss equipotentials and said that these represent points where
the potential is the same.
We added that equipotentials are perpendicular to field lines and based on these ideas, we
drew equipotentials around a point charge and between two parallel plates.
Finally, we looked at possible equipotential values between the plates by taking the negative
or the positive plate as our zero reference point.
This wraps up our discussion of electrostatic fields and completes the final video of subtopic
10.1.
In the first video of subtopic 10.2, we'll start learning in more detail how fields work.