Final answer:
To find the dielectric constant of material B in a capacitor configuration, analyze the overall capacitance using the series combination of capacitors and the known dielectric constant of material A, the plate area, and the layer thicknesses. Apply the capacitance formula for parallel-plate capacitors adjusted for dielectric materials to obtain material B's dielectric constant.
Step-by-step explanation:
To determine the dielectric constant of material B in a three-layer A-B-A parallel-plate capacitor with an electric field E = 9.3 × 10^4 V/m and a stored charge of 25 × 10^(-6) C on each plate, we first find the overall capacitance of the system using the charge and electric field. For each material layer A and B, we use the capacitance in series formula ℓ = ℓ1 + ℓ2 + ℓ3 where C1 and C3 are the capacitances of layers A, and C2 is the capacitance of layer B. The thicknesses of the layers are given as 4.3 mm for A and 2.8 mm for B.
The capacitance for a parallel-plate capacitor is given by C = κε₀A/d, where κ is the dielectric constant, ε₀ is the permittivity of free space (ε₀ = 8.85 × 10^-12 F/m), A is the plate area, and d is the separation between plates. For material A, κ is 2.3.
By knowing that E = V/d and rearranging the capacitance formula to find the dielectric constant as κ = Cd/ε₀A and using the given values, we can solve for the dielectric constant of material B.