Not all dielectrics that separate the plates of a

Chapter , Problem 94

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Not all dielectrics that separate the plates of a capacitor are rigid. For example, the membrane of a nerve axon is a lipid bilayer that has a finite compressibility. Consider a parallel-plate capacitor whose plate separation is maintained by a material that has a dielectric constant of 3.00, a dielectric strength of and a Youngs modulus for compressive stress of When the potential difference between the capacitor plates is zero, the thickness of the dielectric is equal to and the capacitance of the capacitor is given by (a) Derive an expression for the capacitance as a function of the potential difference between the capacitor plates. (b) What is the maximum value of this potential difference? (Assume that the dielectric constant and the dielectric strength do not change under compression.)