two circular metal plates each of radius 10 cm are kept parallel to each other at a distance of 1 - Physics - Electrostatic Potential And Capacitance

Question

two circular metal plates each of radius 10 cm are kept parallel
to each other at a distance of 1 mm what kind of capacitor do they
make? mention one application of this capacitor if the radius of
each of the plates is increased by a factor of 21/2and
their distance of separation is decreased to half of its
initialvalue, calculate the ratio of capacitance in the two
cases

Abhay Kumar · Accepted Answer

They form a parallel plate capacitor C=εA/d Where A is the
Area of the circular plate d= 1mm A = πr2So we can write ,C
initial C
final=επr2/dεπr'2/d'=επr2/dεπr'2/d'=επr2/dεπ(r+2r)2/d/2=r22(r+2r)2
=1/2(1+2)2
The are used in ceiling fans to provide the initial startup energy