A glass plate totally fills up the gap between the electrodes of a prallel-plate capacitor whose capacitance in the absence of that glass plate is equal to `C = 20 nF`. The capacitor is connected that glass voltage source `V = 100 V`. The plate is slowly, and without friction, extracted from the gap. Find teh capacitor energy increment and the mechanical work perfomed in the process of plate extraction.

Explanation

Initailly, capacitance of the system `= C epsilon`
So, initial energy of the system : `U_(i) = (1)/(2) (C epsilon) V^(2)`
and finally, energy of the capacitor : `U_(f) = (1)/(2) C V^(2)`
Hence capacitance energy increment,
`Delta U = (1)/(2) CV^(2) - (1)/(2) (C epsilon) V^(2) = - (1)/(2) CV^(2) (epsilon - 1) = 0.5 mJ`
From enerfgy conservation
`Delta U = A_("cell") + A_("agent")`
(as there is no heat liberation)
But `A_(cell) = (C_(f) - C_(i)) V^(2) = (C - C epsilon)V^(2)`
Hence `A_("agent") = Delta U - A_(cell)`
`= (1)/(2) C (1 - epsilon) V^(2) = 0.5 m J`