Chapter 25, Problem 48CP

A parallel-plate capacitor with plates of area LW and plate separation t has the region between its plates filled with wedges of two dielectric materials as shown in Figure P25.48. Assume t is much less than both L and W. (a) Determine its capacitance. (b) Should the capacitance be the same if the labels κ₁ and κ₂ are interchanged? Demonstrate that your expression does or does not have this property. (c) Show that if κ₁ and κ₂ approach equality to a common value κ, your result becomes the same as the capacitance of a capacitor containing a single dielectric: C = κϵ₀LW/t.

Figure P25.48