A 1 -megabit computer memory chip contains many 60.0-fF capacitors. Fach capacitor has a plate a

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A 1 -megabit computer memory chip contains many 60.0-fF...

A 1 -megabit computer memory chip contains many $60.0-\mathrm{fF}$ capacitors. Fach capacitor has a plate area of $21.0 \times 10^{-12} \mathrm{m}^{2} .$ Determine the plate separation of such a capacitor (assume a parallel-plate configuration). The order of magnitude of the diameter of an atom is $10^{-10} \mathrm{m}=0.1 \mathrm{nm} .$ Express the plate separation in nanometers.

Key Concepts

Unit Conversion and Dimensional Analysis

Dimensional analysis and unit conversion are crucial in physics to ensure that equations are consistent and that calculated values are expressed in appropriate units. This involves converting between units such as farads, meters, and nanometers to match the scale of the phenomenon being analyzed.

Capacitance

Capacitance is a measure of a capacitor's ability to store electric charge per unit voltage. It is a fundamental concept in electromagnetism and electronics that underpins the design and function of various circuits and devices.

Parallel?Plate Capacitor Configuration

A parallel-plate capacitor consists of two conductive plates separated by a small distance and possibly a dielectric material. Its capacitance is given by the formula C = ??A/d, where A is the area of the plates, d is the separation, and ?? is the permittivity of free space. This idealized model is widely used for theoretical and practical calculations in electronics.

Permittivity of Free Space

The permittivity of free space, denoted as ??, is a constant that characterizes the ability of a vacuum to support electric field lines. It is a key parameter in the equations governing electromagnetic phenomena, including the determination of capacitance in a parallel-plate capacitor.

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