Question

A capacitor is made of two oppositely charged circular parallel conducting plates with side-length of 1.00m and separation distance 2.00mm. A circular dielectric of side-length is 0.05m and with a dielectric constant, K is 2.4 and thickness of 2.00mm is inserted in the center of the capacitor.

1. Find the capacitance.

Answer 1

Given

d = 2 mm

circular capacitors

the capacitance C0 = epsilon not *A /d

with dielectric fully inserted between the plates then capacitance is C' = k*C0

side length of the circular plate is 1m = circumferance of the circle = 2pi*r

so the radius of the plate is r = 1/2pi m = 0.1592 m

the area of the circle is pi*r^2 = pi*0.1592^2 m^ = 0.079623 m^2

the area covered by the dielectric is A2 = pi(0.05/(2pi))^2 m^2 = 0.000198944 m^2

the capacitance of the capacitor with dielectric region is C' = k*epsilon not *A2 /d

C' = 2.4(8.854*10^-12*0.000198944)/(2*10^-3) F = 2.1137*10^-12 F

now without dielectric material the capacitance is  

C0 = epsilon not *A0 /d

C0 = (8.854*10^-12*(0.079623-0.000198944)/(2*10^-3) F = 351.6103*10^-12 F

now these two are in parallel the net capacitance is C = C0+C' = 2.1137*10^-12 +351.6103*10^-12

C = 0.353724*10^-9 F