How Does a Multi-Dielectric Parallel Plate Capacitor Calculate Its Capacitance?

[meth_90]

We have got a parallel plate capacitor . The distance between the plates is 2*h and each plate's dimensions are a,b . Between the plates there exists dielectric e1 in the volume 0<z<h and e2 in the volume h<z<2*h (out of the plates e0 ) , with e1,e2>>e0 . At z=h we place another plate with dimensions l,b (l<a) like the figure . The potential of the plates at z=0 , z=h is 0 and at z=2*h is V . What is the capacity of the whole system?




figure :
____ z=2*h
e1
__ z=h e0
e2
____ z=0

 

[Nate810]

The capacitance of the whole system can be calculated using the formula C=εA/d, where A is the area of each plate, d is the distance between them and ε is the dielectric constant of the material between them. For the parallel plate capacitor, the capacitance can be calculated as: C = (e1*a*b + e2*l*b)/(2h), where a and b are the dimensions of each plate and l is the dimension of the additional plate.