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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

ε_{0} ∙ *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

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

Φ_{e} = __∮__E*⃗* ∙ dA*⃗* = *Q**/**ε*_{0}

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

Q(t) = ε_{0} ∙ 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:

As for the **displacement current** I_{d}, we have

i_{d} (t) = ε_{0} ∙ *dΦ*_{e}*/**dt*

= ε_{0} ∙ *d(E ∙ A)**/**dt*

= ε_{0} ∙ A ∙ *dE(t)**/**dt*

= ε

= ε

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.

Enjoy the "Displacement Current" physics lesson? People who liked the "Maxwell Equations lesson found the following resources useful:

- 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
- Magnetism Revision Notes: Maxwell Equations. Print the notes so you can revise the key points covered in the physics tutorial for Maxwell Equations
- 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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