We have a case of a parallel-plate capacitor that has plate area A with a plate separation of d filled with dielectric strontium titanate up to half depth, similar to the figure as shown above. The remaining depth is empty and therefore has air as dielectric. It is clear that both dielectrics cover half the areaA2 of the parallel plates.
Capacitance C=kε0Ad ......(1)
where k is relative permittivity of dieletric material, and ε0 is permittivity of free space =8.854×10−12Fm−1
k=1 for free space, k>1 for all media and k≈1 for air.
Both dielectrics k1(air)andk2(strontium titanate) experience the same potential difference as both are connected to the same parallel plates on either sides. This is exactly the same situation as two capacitors connected in parallel where
Total capacitance Ctotal=Cair+Cdielectric .....(2)
Using (1) and information given above
Ctotal=ε0A2d+kε0A2d
⇒Ctotal=ε0A2d(1+k)
Taking the relative permittivity of strontium titanate as 310 we get
Ctotal=311ε0A2d
Inserting given values in SI units we get
Ctotal=311×8.854×10−12×2001042×4103
⇒Ctotal=6.88×10−9F, rounded to two decimal places.
