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Welcome to our Physics lesson on Displacement Current, this is the third lesson of our suite of physics lessons covering the topic of Maxwell Equations, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
When analysing the equation derived from the Ampere-Maxwell Law
it is obvious that the expression
must have the dimension of current. This current is known as the "displacement current, id", despite no current is really being displaced. Thus, the above equation becomes
Let's consider again the charging capacitor of the previous section, shown in the figure below.
Let's find a way to relate the real current I that is used to charge the capacitor plates to the fictitious displacement current Id which is associated to the change in the electric field between the plates.
From the Gauss Law for electric field
we obtain for the charge Q on the plates at any time:
where E is the magnitude of electric field between the plates at that time.
Differentiating the above equation with respect to time, we obtain for the real current I which charges the capacitor:
As for the displacement current Id, we have
As you see, we obtained the same expression for the displacement current to the expression obtained for the real current. Thus, we can consider the fictitious displacement current Id simply as a continuation of the real current I from one plate of capacitor to the other plate flowing through the gap between plates. Although no charge actually moves across the gap between the plates, the idea of the fictitious current Id can help us to quickly find the direction and magnitude of an induced magnetic field as we will see in the next paragraph.
You have reached the end of Physics lesson 16.18.3 Displacement Current. There are 5 lessons in this physics tutorial covering Maxwell Equations, you can access all the lessons from this tutorial below.
|Tutorial ID||Physics Tutorial Title||Tutorial||Video|
|Lesson ID||Physics Lesson Title||Lesson||Video|
|16.18.1||Gauss Law for Magnetic Field|
|16.18.2||Induced Magnetic Fields|
|16.18.4||How to Find the Induced Magnetic Field?|
|16.18.5||Maxwell Equations Explained|
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