A dielectric of permittivity 3.5 ×10^-11 F / m completely fills the volume between two capacito

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A dielectric of permittivity 3.5 ×10^-11 F / m completely...

A dielectric of permittivity $3.5 \times 10^{-11} \mathrm{~F} / \mathrm{m}$ completely fills the volume between two capacitor plates. For $t>0$ the electric flux through the dielectric is $\left(8.0 \times 10^{3} \mathrm{~V} \cdot \mathrm{m} / \mathrm{s}^{3}\right) t^{3} .$ The dielectric is ideal and nonmagnetic; the conduction current in the dielectric is zero. At what time does the displacement current in the dielectric equal $21 \mu \mathrm{A} ?$

Key Concepts

Time-varying Electric Fields

Time-varying electric fields are central to many dynamic electromagnetic phenomena. They give rise to displacement currents even in the absence of conventional conduction currents, ensuring the continuity of electromagnetic effects as described by Maxwell's equations. Understanding the rate of change of these fields is key to analyzing transient behaviors in capacitive systems.

Displacement Current

Displacement current is a term added by Maxwell to Ampère’s law to account for the changing electric field in situations where conduction current is absent, such as in dielectrics. It is defined as the time derivative of the electric displacement field times the area and is crucial for maintaining continuity in current flow in circuits with time-varying fields.

Maxwell's Correction to Ampère's Law

Maxwell's correction to Ampère's law introduces the displacement current, allowing the law to apply in situations where the electric field changes with time. This correction ensures that the modified law correctly predicts the generation of magnetic fields by time-varying electric fields in both conducting and non-conducting regions.

Dielectric Materials

Dielectric materials are insulators that can be polarized by an electric field. When placed between the plates of a capacitor, they increase the capacitance by reducing the effective electric field, and they affect how energy is stored in the system. Their behavior under time-varying fields is critical to understanding non-conductive current contributions.

Electric Permittivity

Electric permittivity is a measure of a material's ability to permit an electric field. It determines how much electric field is reduced within a medium compared to a vacuum. This property is essential in quantifying the polarization of dielectrics and influences both the capacitance and the behavior of displacement currents in the material.

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