A researcher needs a compact energy-storage device for a portable sensor

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A researcher needs a compact energy-storage device for a portable sensor. She decides to build a parallel-plate capacitor that can store

0.50\,\text{J}

of energy when charged to a maximum potential difference of

2.0\,\text{kV}

. The plates will be separated by

0.50\,\text{mm}

and completely filled with mica, which has a dielectric constant of

\kappa = 5.4

. Edge effects can be neglected. (a) Determine the minimum plate area required to meet the energy-storage specification. (b) Calculate the magnitude of charge that must reside on each plate when the capacitor holds the stated energy. (c) Qualitatively discuss how the required plate area would change if the capacitor were built without any dielectric, keeping all other design goals the same.

Related theory

Energy Stored in Capacitors
Capacitance
Parallel-Plate Capacitor
Electrostatic Potential and Capacitance

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