Displacement Current: Definition & Function

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  • 0:04 Electric Current and…
  • 0:54 The Maxwell-Ampere Law
  • 2:30 Displacement Current
  • 3:24 Electromagnetic Wave…
  • 4:24 Lesson Summary
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Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Discover what displacement current is and how its theory was developed. Then, explore how the structure of electromagnetic waves and how they propagate through space are related to displacement current.

Electric Current and Magnetic Field

Introductory physics courses are split into several main topics, and one of the largest of those topics is electricity and magnetism. Electricity and magnetism are put together on a single topic because they are intrinsically related to each other. The first hint physics students see of this relationship is when working with current carrying wires. As electric current travels through a wire, it creates magnetic field lines around the wire.

The type of current we've been talking about so far is called conduction current, which is the current created by the movement of electrons through a conductor such as an electrical wire. This is the type of current you're probably most familiar with, but there's also another type of current you may not know about called displacement current. In this lesson, you're going to learn how displacement current differs from conduction current, and how it's important in the propagation of electromagnetic waves.

The Maxwell-Ampere Law

The development of the theory of displacement current can be traced back to a famous physicist named James Clerk Maxwell. Maxwell is most well-known for what are simply called Maxwell's equations. Together, the four equations form an elegant way to state the fundamentals of electricity and magnetism. For displacement current, we will be most concerned with one of these equations known as the Maxwell-Ampere law.

Before Maxwell, Andre-Marie Ampere had developed the famous equation known as Ampere's law. Ampere's law relates the magnetic field (B) surrounding a closed loop to the conduction current (I) traveling through that loop multiplied by a constant known as the permeability of free space (μ0).

amperes law

Ampere's law as it was originally written holds true whenever you have a continuous conduction current, but there are cases when problems arise in the law as it's written. The classical example of this is a circuit with a capacitor in it. The diagram below depicts a voltage source at the bottom charging a capacitor at the top. You can see positive charge (+Q) and negative charge (-Q) gather on opposite plates of the capacitor.

basic circuit with a capacitor

When the capacitor is charging and discharging, current flows through the wires creating a magnetic field, but between the plates of the capacitor, there is no current flowing. According to Ampere's law there can be no magnetic field created by the current here, but we know that magnetic field does in fact exist. Maxwell realized this discrepancy in Ampere's law, and added an additional term to Ampere's law to resolve the issue.

maxwell ampere law

This final form of the equation is known as the Maxwell-Ampere law.

Displacement Current

The part Maxwell added to it is what we call the displacement current (Id), but what is it? To understand this, let's look at its formula.

displacement current

This equation consists of two terms multiplied together. The first is known as the permittivity of free space (ε0), and the second is the derivative with respect to time of electric flux (ΦE). Electric flux is the rate of flow of an electric field through a given area. By taking its derivative with respect to time, we're looking at the change in that rate of flow over time.

The addition of the displacement current term in Maxwell-Ampere law tells us that this change in an electric field's rate of flow over time can act like a current and generate a magnetic field. This law is then the natural pair to Faraday's law, which tells us that a changing magnetic field (B/dt) can create an electric field (E).

faradays law

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