Question

linear dimensions of parallel plate capacitor of length l*l and distance between them is d much smaller than l.half of the space between them is filled with mica sheet of thickness d/2 and dielectric constant E1.the plates are connected across an ideal battery of resistance r.the mica sheet is pulled slowly out of the capacitor with constant velocity v.find the heat developed in the capacitor.permittivutyof free space is e0
​

Answer 1

Answer:

Capacitance of the vacuum capacitor  Co=dAϵo

where A is the area of the plates of capacitor.

Dielectric constant of the medium at a distance x from first plate is given by  K(x)=Ko+λx

Capacitance of capacitor of thickness dx,   dC=dxK(x)Aϵo=dxAϵo(Ko+λx)

Total capacitance  C1=∫odAϵo(Ko+λx)dx

Or   C1=Aϵo1×λln(Ko+λx)∣∣∣∣∣od

Or   C1=Aϵoλ1ln(1+λd/K