there is capacitor which square plates ,each side has length L

distance between the plates is d.

we insert a dialectric plate. with dielectric constant

our capacitor is connected to ressistor and in a row

and a contant voltage sourse .

we how one loop

battery ressistor and cappacitor.

find the work need to be done in the dielectric plate to move it with some x distance forward.

how i tried to solve it:

work is integral of force by distantace

but we were not given force.

so our work is the sum of two things

1.difference netween energys of the capacitor

2.work of the corrent on the ressistor

the problem is that that

the integral is over time but our cappacitace dependant on distace

and i cant put capacitace as a constant because it canging

and i dont have the kink betweeb distance and time

there is no speed

and

i searched google for days abour a similar problem

and i cant find one