A parallel-plate capacitor has square plates 10 cm on a side...

A parallel-plate capacitor has square plates $10 \mathrm{cm}$ on a side and $0.50 \mathrm{cm}$ apart. The voltage across the plates is increasing at 220 V/ms. What's the displacement current in the capacitor?

Key Concepts

Displacement Current

Displacement current is a concept introduced by Maxwell to modify Ampere's Law in situations where the electric field changes with time. It represents an effective current generated by a time-varying electric field, even in regions where no charge carriers are moving, and is given by the product of the vacuum permittivity and the rate of change of electric flux through a surface.

Maxwell's Correction to Ampere's Law

Maxwell extended Ampere's Law by adding the displacement current term, ensuring that the law holds even in cases of non-steady currents. This correction reconciles the law with the principle of charge conservation and is fundamental in the derivation of electromagnetic wave equations.

Time-Varying Electric Field

A time-varying electric field arises when the voltage across components, such as a capacitor, changes with time. The rate at which this field changes is directly related to the rate of voltage change and plays a crucial role in the creation of displacement current in the system.

Capacitor Geometry

The geometry of a capacitor, defined by the area of its plates and the separation distance between them, is essential in determining the electric field and the resulting flux within the capacitor. This geometric relationship influences both the capacitance and the magnitude of the displacement current when the electric field varies over time.

Transcript

Please give Ace some feedback