Question

A dielectric-filled parallel-plate capacitor has plate area A = 20.0 cm2 , plate separation d = 8.00 mm and dielectric constant k = 3.00. The capacitor is connected to a battery that creates a constant voltage V = 15.0 V . Throughout the problem, use ϵ0 = 8.85×10⁻¹² C2/N⋅m2

A) Find the energy U1 of the dielectric-filled capacitor

B) The dielectric plate is now slowly pulled out of the capacitor, which remains connected to the battery. Find the energy U2 of the capacitor at the moment when the capacitor is half-filled with the dielectric.

c) The capacitor is now disconnected from the battery, and the dielectric plate is slowly removed the rest of the way out of the capacitor. Find the new energy of the capacitor, U3

D) In the process of removing the remaining portion of the dielectric from the disconnected capacitor, how much work W is done by the external agent acting on the dielectric?

Answer 1

Ans PART-A enery ill 1know that enery Stored capacitor is iven y we Here c Ca pacrtme fcapachtor or voltge V Batheny aceros ca paejte /2 K:3.D b b cm2 A= bf Parellel plate hiven ana 3.009mm seprationn betueen plate (c) -la ciketnie ems tant -12 8.85X10 -2 permi tuity of air -re, lb The capadtne af Parallel Plate Cpactor with diclectie k is gnen yC kE Thus

3 x 8 85 16 Ck - 8 X163 -2 - 26.55 X16 Ck -12 6.63 X10 6-63 PF C1K -3 1 12 enes 11 ui7.46x10u par T3 - Halt HIled Half Filled capacitor work as X tuo parallel Capacitor one lled with dieketc and other one is aiy 7 dielectic aiy inthi's Case area ef capacitor plate divide

pally two parts so capacitence new will be 2. Cair apriv gulent capacltane f perellr Combination will Ge Cle t Cair 1 A d will be gjuen by . 11 d (3+) 8.8sx o 8 763 XIs 2 42 4 137.8 x12 0.497 x10 J Part- capacitor dus connecded m the battery and clieleetic plate sowty emoned h this proces plate emains 7 charge on the ttar Constant

iially nersy 4- let ass4me Here a is ch asye on plate and (2 - u The final enersy u3 Can be In terms of the capacitance charge Curiten l dieletic fre capactne) Hene CE A Thus Eo A u talee ram part- Hent ( ) &s A 2X0.45771b 8-85 12XPox6 152 +13 24X 0.045IX16 g, 75 X10 0.44 x1017

PART D hemoviny the pemaihing Portton of dis conneetecl capacitor dane the dielectic from work W wll be By uting ener consenvationy Rule work done wit be equal to but ween fhiti enery States at thu fined Capacttor M2 +W W =ua-2 W: 0.440110 O.497 x10 43.7x1611 0.440x1011 - 49.26X10J