Let's say we have a parallel plate capacitor, and a solid dielectric that partially fills the space between the plates.
If the dielectric is just a slab of material, with sides parallel to the plates, then I can calculate the capacitance easily. What happens if instead it is slightly tilted? Does the capacitance stay the same? And what if instead of a slab of material, the dielectric has a completely irregular shape, but occupies the same volume as before? Is the capacitance different?