30.16
Significance of Displacement Current
A displacement current is analogous to a real current in Ampère's law, participating in Ampère's law the same way as the usual conduction current. How…
Displacement current is defined in terms of a time-varying electric field and has an associated displacement current density.
To understand the significance, consider a circular-shaped parallel capacitor.
A conduction current flows throughout the wires, but there is no conduction current in the region between the capacitor plates as there is no charge flow.
If a compass needle is placed between the capacitor plates, deflection is observed, confirming the presence of a magnetic field.
Displacement current accounts for this continuity of magnetic field in the region between the capacitor plates.
Applying generalized Ampere's law to find the magnetic field between the plates.
For this, consider an Amperian loop with a radius less than that of the capacitor.
The line integral of the magnetic field along this loop equals the magnetic field times the circumference.
The current enclosed by the loop equals the product of current density and the enclosed area.
Thus, the magnetic field between the plates of the capacitor is obtained, which is zero at the axis and increases linearly with increasing distance from the axis.
View the full transcript and gain access to JoVE Core videos
Q1: Why is displacement current significant in regions between capacitor plates?
Displacement current accounts for magnetic field continuity in capacitor regions where no conduction current flows. Although charges don't move between the plates, a time-varying electric field produces displacement current, which generates a magnetic field detectable by a compass needle. This ensures the magnetic field remains continuous throughout the circuit.
Q2: How does displacement current differ from conduction current?
Conduction current results from charge flow through wires, while displacement current is produced by a changing electric field without charge movement. Displacement current is defined in terms of a time-varying electric field and has an associated displacement current density. Both participate in Ampère's law identically, making displacement current analogous to real current.
Q3: What modification did Maxwell make to Ampère's law?
Maxwell added a term accounting for displacement current to the existing Ampère's law, creating the generalized Ampère's law. This modification allows the law to apply in regions where no conduction current exists, such as between capacitor plates. The generalized form ensures consistency with electromagnetic field behavior throughout all regions.
Q4: How does the magnetic field vary between capacitor plates?
The magnetic field between capacitor plates is zero at the axis and increases linearly with distance from the axis. Using an Amperian loop with radius less than the capacitor, the magnetic field can be calculated from the displacement current density and enclosed area. This linear relationship demonstrates how displacement current generates the observed magnetic field.
Q5: How can you experimentally detect displacement current between capacitor plates?
Placing a compass needle between the capacitor plates reveals magnetic field deflection, confirming displacement current presence. Although no charge flows in this region, the time-varying electric field produces displacement current that generates a measurable magnetic field. This experimental observation validates the theoretical concept of displacement current.
Q6: What role does displacement current density play in calculating magnetic fields?
Displacement current density is the product of the time-varying electric field and a proportionality constant. When applying the generalized Ampère's law, the current enclosed by an Amperian loop equals displacement current density multiplied by the enclosed area. This relationship allows precise calculation of magnetic field strength in regions lacking conduction current.
Q7: Why does conduction current not flow between capacitor plates?
No conduction current flows between capacitor plates because there is no charge movement in that region. The dielectric material between plates prevents charge flow, yet the changing electric field during charging produces displacement current. This displacement current maintains magnetic field continuity despite the absence of moving charges.