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This video is about electrostatic fields.

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The expression electrostatic field simply means that the electric field in question

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is produced by stationery as opposed to moving charge.

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When talking about fields in this video, I will use the words electric and electrostatic

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interchangeably.

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We'll learn about electric fields in subtopic 5.1.

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Here we discussed general electric field concepts, electric field patterns, electric

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field strength and electrical potential difference.

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I will refer to some of these concepts in this video without discussing them again in

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detail so feel free to refresh your knowledge and go back to watch some of the videos in

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subtopic 5.1.

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Here we'll start by looking at electric potential at a point and then move on to electric

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equipotentials.

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Let's begin with electric potential at a point.

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So far we have used the expressions electric potential and electric potential difference

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interchangeably.

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These two concepts are closely connected but they mean different things.

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Let's explore this difference.

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We'll begin by refreshing the definition of electrical potential difference which is

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the work done when moving a unit charge between two points in an electric field.

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Based on this definition we can write that delta VE, so change in electrical potential

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or in other words electrical potential difference, is equal to W divided by Q.

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Rearranging leads to the formula that's given in the IB physics data booklet and here are

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the variables that are present in this formula.

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So far we dealt with potential difference between two points.

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If a potential difference exists between two points, it also makes sense to have specific

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potential values at each point.

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However, in order to define electric potential at a point as opposed to the potential difference

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between two points, we need a system with a zero reference point.

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Similarly to gravitational potential, the zero reference point for electric potential

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is defined to be at infinity.

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This is consistent with Coulomb's law which tells us that the force between two charges

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is inversely proportional to the square of the distance between these charges.

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As r the distance is increased and approaches infinity, 1 over r squared approaches zero

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which means that when two charges are at an infinite distance, the force between the

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charges is zero.

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As a result, the electric potential of the system is also zero.

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By system we mean the two charges.

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Now imagine that the charges are moved closer to each other, so the distance between them

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becomes finite.

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With a finite distance, if the charges have the same sign they repel, in other words when

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released they move back towards infinity, which means that when the charges were brought

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closer to each other, energy was stored in the system, therefore the electric potential

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is positive.

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If the charges have opposite signs and they are moved to a finite distance from each other,

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they attract and move towards each other when released.

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This means that in order to move the charges back to an infinite distance from each other,

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energy must be supplied to the system, so it follows that electric potential is negative.

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You can also think about this situation in the following way.

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Electric potential at infinity is always zero.

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When charges of the same sign are moved closer to each other from an infinite distance, energy

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must be supplied to the system, so electric potential increases and becomes positive.

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When the charges have opposite signs, energy must be supplied to move the charges from

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a finite to an infinite distance.

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So as the charges are moved towards each other from infinity, electric potential decreases

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and becomes negative.

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Based on this discussion, now we can define electric potential at a point, which is the

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work done per unit charge when moving a positive test charge from infinity to the point.

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We'll further discuss electric potential in subtopic 10.2.

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Now let's move on to electric equipotentials.

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We already covered electric field line patterns in subtopic 5.1.

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We saw how field line patterns look like around the point charge, between two point

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charges, between two parallel plates, and between a charged plate and the point charge.

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Here we'll discuss how electric equipotentials look like around the point charge and between

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two parallel plates.

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As you can see, these diagrams already include electric field lines as we learned in subtopic

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5.1.

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Let's begin with the point charge.

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Here I chose to work with a positive charge, but the concepts are exactly the same for

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a negative charge.

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One way to define equipotentials is that they represent points where the potential is the

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same.

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We learned in the previous video that gravitational equipotentials and gravitational field lines

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are perpendicular to each other.

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This is also true for electric fields.

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So now we can draw the equipotentials around the point charge.

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Using the same concepts, we can also do this for the parallel plates.

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In the general definition of electric potential, we use the idea that the zero reference point

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is at infinity.

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However, just as for gravitational potential, in a given situation, we can choose the ground

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as our zero potential reference point.

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When working with electric potential in specific situations, we can also decide to choose an

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arbitrary zero reference point to make working with the given situation a bit easier.

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For example, I can choose the positive plate to be at a zero volt potential.

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Let's assume that the potential difference between the plates is 12 volts.

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When a positive charge is released in the electric field between the plates, it moves

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towards the negative plate.

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To move this charge back towards the zero volt position, so towards the positive plate,

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we would need to do work on the charge.

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In other words, we would need to supply energy to the system.

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This tells us that as we move from the positive towards the negative plate, electric potential

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decreases and becomes negative.

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As a result, the potential on the negative plate is negative 12 volts.

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It logically follows that the potential values on the equipotential lines would be negative

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3 volts, negative 6 volts and negative 9 volts.

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Of course, we can choose a different zero reference point, for example the negative plate.

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This means potential increases as we move from the negative towards the positive plate.

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The potential values on the equipotentials would be positive 3 volts, positive 6 volts

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and positive 9 volts.

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The potential of the positive plate would be positive 12 volts.

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Let's summarize what we have learned in this video.

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We started by refreshing the definition and the formula for electrical potential difference.

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Then we began discussing electrical potential and said that it is defined to be zero at

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infinity.

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We added that this is consistent with Coulomb's law and concluded that when two charges are

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at an infinite distance, the force between the charges is zero, so the electric potential

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of the system is also zero.

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Then we learned what happens when the charges are moved closer to each other to a finite

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distance.

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If the charges have the same sign, then the electric potential of the system is positive

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and if they have different signs, the electric potential is negative.

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Finally, based on these concepts, we defined electric potential at a point.

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Next, we moved on to discuss equipotentials and said that these represent points where

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the potential is the same.

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We added that equipotentials are perpendicular to field lines and based on these ideas, we

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drew equipotentials around a point charge and between two parallel plates.

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Finally, we looked at possible equipotential values between the plates by taking the negative

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or the positive plate as our zero reference point.

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This wraps up our discussion of electrostatic fields and completes the final video of subtopic

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10.1.

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In the first video of subtopic 10.2, we'll start learning in more detail how fields work.