Displacement Current and Maxwell Ampere - Introduction
The rate of change of the electric displacement field is known as the displacement current. It is calculated in the same way as electric current density is calculated.
Maxwell's Equation includes a term called displacement current. It was created to bring the Ampere circuit law into line with logic. Ampere (Amp) is the SI unit for displacement current.
This dimension can be measured in length units, which can be maximum, minimum, or equivalent to the actual distance traveled from start to finish.
Displacement current is an electric current created by a time-varying electric field rather than by moving charges.
Characteristics of Displacement Current
Displacement current is another type of current apart from conduction current.
As with conduction current, it does not appear from the actual movement of electric charge.
It is a vector quantity.
It is vital for electromagnetic wave propagation.
Maxwell's Equation is a good way to explain displacement current.
Maxwell-Ampere Law and Equation
Electricity and magnetism are important aspects of physics. Because electricity and magnetism are intrinsically related, they are grouped as electromagnetism.
A current-carrying wire provides insight into electromagnetism. When an electric current flows via a wire, it creates a magnetic field around the wire or conductor.
This current, which travels through a conductor, is known as the conduction current. It is caused by electrons moving through a conductor.
Since we learned about displacement current earlier, it is now important to note that displacement current is distinct from conduction current. Because displacement current does not carry electrons.
Now let’s understand the relationship between displacement and Maxwell Ampere law.
1. Ampere's law was developed by Andre-Marie Ampere. It states that :
When conduction current (I) passes through a closed-loop, a magnetic field (B) is formed around the closed-loop.
Here Maxwell gave an addition to Ampere’s law which resulted in Maxwell-Ampere Law.
2. James Clerk Maxwell, a famous physicist, well known for his work on Maxwell's equations gave addition to Ampère's law which stated that:
Magnetic fields can be generated in two ways: by electric current (already stated by Ampere Law) and by changing electric fields (Maxwell's addition, which he called displacement current).
Equation of Maxwell-Ampere Law
Maxwell predicted that a time-varying electric field in a vacuum/free space (or in a dielectric) produces a magnetic field.
It indicates that a changing electric field causes a current to flow across a region. Maxwell also predicted that this current produces a magnetic field similar to that of a conducting current. "Displacement current" (ID) was the name given to this current.
The equation is:
\[I_{D}=\epsilon _{o}\frac{d\phi E}{dt}\]
Where \[\phi E\] is the Electric Flux
Maxwell also stated that when conduction current (I) and displacement current (ID), are combined, they have the property of continuity, even though they are not continuous individually.
Maxell was inspired by this idea and modified Ampere's circuital law to make it logically consistent. Thereafter he stated revised Ampere circuital law which now is known as Ampere-Maxwell law.
From
\[\oint _{C}\vec{B}.\vec{dl}=\mu _{o}(I+I_{D})\]
\[\mu _{o}(I+\epsilon _{o}\frac{d\phi E}{dt})\]
FAQs on Displacement Current
1. What is displacement current and how does it differ from conduction current in the context of electromagnetic theory?
Displacement current refers to the current produced by a time-varying electric field, as opposed to conduction current, which is caused by the actual flow of electric charges (electrons) in a conductor. Displacement current becomes significant in situations like a charging capacitor, where the electric field is changing but no free electrons cross the dielectric. This current was introduced by Maxwell to maintain the continuity of current and satisfy Ampere-Maxwell law in electromagnetic theory.
2. What is the mathematical expression for displacement current and what do its terms represent?
The mathematical expression for displacement current (ID) is:
- ID = ε0 (dΦE/dt)
3. Why did Maxwell introduce displacement current to Ampere’s law, and what problem did it resolve in classical electromagnetism?
Maxwell introduced displacement current to Ampere’s law to address the inconsistency observed when applying Ampere’s law to cases like a charging capacitor, where the conduction current seemed to stop at the dielectric. By adding displacement current, the modified law ensures the continuity of magnetic fields even in regions where no conduction current exists, thus unifying the treatment of both electric and magnetic fields in electromagnetic wave propagation.
4. How does displacement current contribute to the propagation of electromagnetic waves?
Displacement current is essential for electromagnetic wave propagation. A time-varying electric field creates a displacement current, which generates a changing magnetic field. This changing magnetic field, in turn, produces a changing electric field, resulting in the self-sustaining propagation of electromagnetic waves even through free space where conduction current cannot flow.
5. Describe the key differences between displacement current and conduction current in both origin and physical meaning.
- Origin: Conduction current arises from the actual movement of electrons (charges) in a conductor, while displacement current is due to a changing electric field.
- Physical meaning: Conduction current exists only in conductive materials; displacement current can exist wherever the electric field changes, even in vacuum or dielectrics.
- In a charging capacitor: Displacement current flows between the plates, where no electrons move across the dielectric.
6. In what real-world contexts is displacement current especially important, and what are its applications?
Displacement current plays a significant role in the operation of capacitors in AC circuits, the generation and transmission of electromagnetic waves (such as radio and light waves), and in understanding the behavior of alternating current in non-conducting regions. It is fundamental in wireless communication, microwave technology, and electromagnetic field theory.
7. What are Maxwell's equations and how does displacement current fit within them?
Maxwell's equations are a set of four fundamental laws describing electric and magnetic fields and their interplay:
- Gauss's law for electricity
- Gauss's law for magnetism
- Faraday's law of induction
- Ampere-Maxwell law (Ampere's law with displacement current addition)
8. How can students distinguish between questions that require understanding of displacement current and those focused only on conduction current, especially for CBSE Board exams?
For CBSE Board exams, questions on displacement current typically involve situations with changing electric fields or capacitors (e.g., "Explain why current appears between capacitor plates during charging"). In contrast, conduction current questions focus on electric current through conductors with steady fields. It's important to identify whether the scenario involves changing electric fields or steady current flows to choose the correct concept.
9. What misconceptions do students commonly have about displacement current in capacitor circuits?
A common misconception is that no current flows between the plates of a capacitor because there is no movement of electrons through the dielectric. In reality, displacement current ensures that the current appears continuous when a capacitor is charging or discharging, as the electric field changes between the plates, even though no charge physically passes through the dielectric material.
10. How do examiners expect students to approach derivations related to the displacement current for full marks in CBSE 2025–26 Physics exams?
For full marks, students should:
- Clearly state Maxwell-Ampere law and show the addition of displacement current term.
- Define each term and specify their units.
- Explain the physical situation (such as charging a capacitor) where displacement current is significant.
- Use correct mathematical steps and annotate diagrams if required.
