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

∮B⃗ dL⃗ = μ₀ ∙ ε₀ ∙ dΦ_e/dt + μ₀ ∙ i_encl

it is obvious that the expression

ε₀ ∙ dΦ_e/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

∮B⃗ dL⃗ = μ₀ ∙ i_d,encl + μ₀ ∙ i_encl

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

Φ_e = ∮E⃗ ∙ dA⃗ = 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 I_d, we have

i_d (t) = ε₀ ∙ dΦ_e/dt
= ε₀ ∙ d(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 I_d 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 I_d 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 ID	Physics Tutorial Title	Revision Notes	Revision Questions
16.18	Maxwell Equations
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
16.18.1	Gauss Law for Magnetic Field
16.18.2	Induced Magnetic Fields
16.18.3	Displacement Current
16.18.4	How to Find the Induced Magnetic Field?
16.18.5	Maxwell Equations Explained

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Displacement Current Feedback. Helps other - Leave a rating for this displacement current (see below)
Magnetism Physics tutorial: Maxwell Equations. Read the Maxwell Equations physics tutorial and build your physics knowledge of Magnetism
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Magnetism Practice Questions: Maxwell Equations. Test and improve your knowledge of Maxwell Equations with example questins and answers
Check your calculations for Magnetism questions with our excellent Magnetism calculators which contain full equations and calculations clearly displayed line by line. See the Magnetism Calculators by iCalculator™ below.
Continuing learning magnetism - read our next physics tutorial: Introduction to Magnetism

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