A parallel-plate capacitor is made of two square plates of side a separated by distance d (d ≪ a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown. The capacitance is:

Question

G1 Physics · Accepted Answer

Treat vertical strips of width dx as parallel capacitors. Each strip has air and dielectric portions in series along the field; integrating dC over the plate gives C = [Kε₀a²/(d(K-1))] ln K. Hence C.