Physics Lesson 16.18.3 - Displacement Current

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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.

Displacement Current

When analysing the equation derived from the Ampere-Maxwell Law

B dL = μ0 ∙ ε0e/dt + μ0 ∙ iencl

it is obvious that the expression

ε0e/dt

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

B dL = μ0 ∙ id,encl + μ0 ∙ iencl

Let's consider again the charging capacitor of the previous section, shown in the figure below.

Physics Tutorials: This image provides visual information for the physics tutorial Maxwell Equations

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

Φe = E ∙ dA = Q/ε0

we obtain for the charge Q on the plates at any time:

Q(t) = ε0 ∙ E(t) ∙ A

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:

dQ(t)/dt = I = ε0 ∙ A ∙ dE(t)/dt

As for the displacement current Id, we have

id (t) = ε0e/dt
= ε0d(E ∙ A)/dt
= ε0 ∙ A ∙ dE(t)/dt

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.

More Maxwell Equations Lessons and Learning Resources

Magnetism Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
16.18Maxwell Equations
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
16.18.1Gauss Law for Magnetic Field
16.18.2Induced Magnetic Fields
16.18.3Displacement Current
16.18.4How to Find the Induced Magnetic Field?
16.18.5Maxwell Equations Explained

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  6. Continuing learning magnetism - read our next physics tutorial: Introduction to Magnetism

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