A laboratory has parallel-plate capacitors of fixed plate area A=250cm2 and fixed separation d=3mm. The air-filled capacitance is found to be too small for a particular experiment, which requires at least a 60% increase over the air value without changing A or d. The store room offers four dielectric materials with relative permittivities as follows:
Material P: κ=2.1
Material Q: κ=3.4
Material R: κ=4.5
Material S: κ=5.2
Only one slab, completely filling the space between the plates, can be used.
a. (i) Determine which of the four materials can individually satisfy the experimental requirement.
b. (ii) For the material(s) identified in part (i), calculate the new capacitance value.
c. (iii) Explain, with quantitative support, why the other materials do not meet the requirement.