Displacement Current vs Conduction Current: Key Differences for Students
Displacement current is a fundamental concept in electromagnetism. It describes a phenomenon analogous to ordinary electric current, but instead of being caused by the direct flow of charges like electrons, it is linked to changing electric fields. Understanding displacement current helps to explain how magnetic fields can be generated even when there is no actual movement of electric charge in certain regions, such as between the plates of a charging capacitor.
What is Displacement Current?
In simple terms, displacement current refers to an effect where a changing electric field produces a magnetic field similar to how a conduction current (the flow of electrons) would do. This concept was introduced to account for situations where the traditional notion of current does not explain the presence of a magnetic field, especially when electric fields are changing with time.
In practical terms, displacement current is significant in cases like the space between the plates of a capacitor. When the capacitor is charging or discharging, the electric field between its plates changes over time. Although no electrons physically cross the gap, a magnetic field is still observed, which is explained using the idea of displacement current.
Key Differences: Displacement Current vs Conduction Current
| Aspect | Conduction Current | Displacement Current |
|---|---|---|
| Physical Origin | Due to the actual flow of charges (such as electrons in a wire) | Due to the changing electric field over time (no physical charge movement) |
| Medium | Requires a material conductor | Can exist in vacuum, air, or any dielectric |
| Example | Current through a metallic wire | Current effect between capacitor plates during charging |
| Relation to Charges | Movement of free charges | Variation in electric field, not charges |
| Magnetic Field Production | Produces magnetic field according to Ampère's law | Produces magnetic field in similar way, especially in non-conducting regions |
Mathematical Expression of Displacement Current
The displacement current is mathematically expressed as:
Here, Id is the displacement current, ε0 is the permittivity of free space, and dΦE/dt represents the rate of change of the electric flux through a surface.
| Formula | Explanation | SI Units |
|---|---|---|
| Id = ε0 × (dΦE/dt) | Displacement current due to changing electric field | Ampere (A) |
Application Example: Displacement Current in a Capacitor
Consider a parallel plate capacitor connected to a circuit and being charged. As the charges build up on the plates, the electric field in the gap between the plates changes with time. Although no actual charge passes through the dielectric, a magnetic field is observed near the capacitor.
This scenario demonstrates displacement current. The changing electric field between the plates acts as a source of magnetic field just like a real current. Displacement current ensures that Ampère’s law remains valid in regions with time-varying fields but no physical charge movement.
Step-by-Step Approach to Solve Displacement Current Problems
- Identify whether the problem involves a changing electric field (for example, a charging capacitor).
- Calculate the rate of change of electric flux (dΦE/dt), or find how fast the electric field is changing.
- Multiply this value by the permittivity of free space (ε0) to find the displacement current using the formula.
- Present the answer with appropriate units. For current, use Ampere (A).
Key Formulas and Concepts
| Formula | Description | Application |
|---|---|---|
| Id = ε0 × (dΦE/dt) | Displacement Current | Used to calculate magnetic field due to changing electric field |
| ΦE = ∫ E · dA | Electric Flux | Calculate rate of field change in region of interest |
Quick Example
Suppose the electric field between capacitor plates is increasing at a rate of 2 × 1011 V/m·s, and the area of the plates is 0.01 m². To find the displacement current:
Id = ε0 × (dΦE/dt) = (8.85 × 10-12 C²/N·m²) × (2 × 109 V·m/s) = 1.77 × 10-2 A
Practice and Next Steps
- Read more detailed explanations and solved examples on Displacement Current.
- Practice numerical questions involving both conduction and displacement current in capacitors and other devices with time-varying electric fields.
- Revise the relationship of displacement current to the creation of magnetic fields in electromagnetic theory.
For structured learning and further practice, review relevant lessons and problem sets on the Vedantu Physics pages. Explore other key topics in electricity and magnetism to see how displacement current integrates with concepts like electromagnetic induction and capacitor behavior.
Understanding displacement current builds a solid foundation for advanced topics in electromagnetism and prepares you for conceptual and numerical questions in your Physics studies.
FAQs on Displacement Current in Physics: Definition, Formula & Examples
1. What is displacement current?
Displacement current is the current that arises due to a changing electric field in a region, even if no actual movement of free charges occurs. This concept, introduced by Maxwell, helps explain how current continuity is maintained in situations like a charging capacitor. Displacement current allows magnetic fields to be produced in regions where conduction current is absent, ensuring the symmetry of Maxwell's equations.
2. What is the formula for displacement current?
The displacement current formula is:
Id = ε0 (dΦE/dt)
where:
• Id is the displacement current (Ampere)
• ε0 is the permittivity of free space (8.85 × 10-12 C2/N·m2)
• dΦE/dt is the rate of change of electric flux
This formula is directly given in NCERT and JEE Main syllabus.
3. How is displacement current produced?
Displacement current is produced whenever there is a time-varying electric field. This typically occurs in the gap between the plates of a charging or discharging capacitor, or in any dielectric medium where the electric field changes with time. The changing electric field creates a displacement current equal to the conduction current in the circuit, ensuring current continuity.
4. What is the physical meaning of displacement current?
The physical meaning of displacement current is that it represents the effect of a changing electric field, which can generate magnetic fields just like a real (conduction) current. Even though no actual charges flow between, for example, capacitor plates, the rapidly changing electric field behaves as if a current flows there, preserving the validity of Maxwell’s equations.
5. What is the difference between displacement current and conduction current?
Key differences between conduction and displacement current:
• Conduction current is due to actual movement of free charges (e.g., electrons in a wire).
• Displacement current arises from a changing electric field, not from actual movement of charges.
• Conduction current requires a conducting medium; displacement current exists even in vacuum.
• Conduction current: I = nqVA; Displacement current: Id = ε0 (dΦE/dt).
6. Why did Maxwell introduce the concept of displacement current?
Maxwell introduced displacement current to resolve the inconsistency in Ampere’s law, specifically in scenarios like a charging capacitor where there is no conduction current through the dielectric. The concept completes Maxwell’s equations, ensures current continuity, and explains how changing electric fields can generate magnetic fields, facilitating the propagation of electromagnetic waves.
7. Does displacement current actually exist physically?
Displacement current does not represent actual movement of charge but is a real physical phenomenon because its effects, such as producing a magnetic field and enabling electromagnetic waves, can be observed and measured. It is essential for the proper description of electromagnetic fields, especially in capacitors and free space.
8. What is the displacement current in a charging capacitor?
In a charging capacitor, the displacement current between the plates is equal in magnitude to the conduction current in the connecting wires. This equality ensures continuity of current throughout the entire circuit, even where no free charges move between the plates.
9. How does displacement current help in the propagation of electromagnetic waves?
Displacement current allows a time-varying electric field to generate a magnetic field, just like conduction current does. This interaction enables self-sustaining electromagnetic waves to propagate through vacuum or any medium, as described by Maxwell’s equations. The mutual generation of changing electric and magnetic fields allows EM waves such as light and radio waves to travel through empty space.
10. What is the formula for displacement current density?
Displacement current density (Jd) is given by:
Jd = ε0 (dE/dt)
where:
• ε0 is the permittivity of free space
• dE/dt is the rate of change of the electric field
Units: Ampere per square meter (A/m2)
11. Can displacement current flow through a vacuum?
Yes, displacement current can flow through a vacuum. Since it is caused by a changing electric field and not by moving charges, displacement current is present even where there are no physical charge carriers, such as in empty space. This property enables propagation of electromagnetic waves through vacuum.
12. In what types of questions is the concept of displacement current commonly applied in exams?
Displacement current is frequently tested in:
• Problems involving charging or discharging capacitors
• Multiple-choice questions (MCQs) comparing conduction and displacement current
• Numerical calculations of current or current density between capacitor plates
• Conceptual questions on electromagnetic wave propagation and Maxwell’s equations
Understanding its formula and difference with conduction current is crucial for scoring in Physics board and entrance exams.
