Aula 15

$8/$  &$3$&,725(6 &20 ',(/e75,&26

Cd =
3RGHPRV FDOFXODU V d GD VHJXLQWH PDQHLUD

Q . Vd



2%-(7,926 '(7(50,1$5 $ ,1)/8Ç1&,$ '( ',(/e75,&26 (0 &$3$&,725(6

Cd =

Q Q V0 = , Vd V0 Vd

 ,1)/8Ç1&,$ '2 ',(/e75,&2

RQGH V0 p D GLIHUHQoD GH SRWHQFLDO GR FDSDFLWRU VHP GLHOpWULFR FXMD FDSDFLWkQFLD p

C 0  0DV VDEHPRV TXH
$ FDSDFLWkQFLD GH XP FDSDFLWRU SRGH VHU DXPHQWDGD VH SUHHQFKHUPRV D UHJLmR HQWUH DV SODFDV FRP XP GLHOpWULFR $V SODFDV FRQGXWRUDV SRGHP VHU IL[DGDV QR GLHOpWULFR 2 FDPSR HOpWULFR HQWUH DV SODFDV FRP R GLHOpWULFR p GDGR SRU

Q = C0  (QWmR WHPRV V0
C d = C0 V0 . Vd 

E=
RQGH

Q εA

8VDQGR DJRUD D HTXDomR  WHPRV TXH

ε

p D SHUPLVVLYLGDGH GR PDWHULDO GR GLHOpWULFR &RPR

ε > ε 0 SDUD RV PDWHULDLV
RX

KC 0 = C 0

V0 Vd

XVXDOPHQWH XWLOL]DGRV R FDPSR HOpWULFR GLPLQXL ,VVR SURYRFD DXWRPDWLFDPHQWH XPD GLPLQXLomR QD GLIHUHQoD GH SRWHQFLDO HQWUH DV SODFDV H DVVLP XP DXPHQWR QD FDSDFLWkQFLD 3RU H[HPSOR D FDSDFLWkQFLD GH XP FDSDFLWRU GH SODFDV SODQR SDUDOHODV QR YiFXR FRPR YLPRV p GDGD SRU

V0 =K Vd



C0 =

ε0 A
L

,VWR p D GLIHUHQoD GH SRWHQFLDO GLPLQXL SHOR PHVPR IDWRU K TXDQGR SUHHQFKHPRV

.

R FDSDFLWRU FRP XP GLHOpWULFR 7RGD HVVD GLVFXVVmR TXH IL]HPRV p YiOLGD SRUTXH R FDSDFLWRU HVWi LVRODGR GR PHLR H[WHUQR H DV FDUJDV HVWmR IL[DV QDV SODFDV

1HVVDV FRQGLo}HV VXSRQKDPRV TXH HVWH FDSDFLWRU VHMD GHVFRQHFWDGR GRV ILRV H[WHUQRV H VHMD PDQWLGR LVRODGR $JRUD WRPHPRV XP GLHOpWULFR GH SHUPLVVLYLGDGH

ε

0DV R TXH DFRQWHFHULD VH IL[iVVHPRV R SRWHQFLDO DR LQYpV GDV FDUJDV" $V FDSDFLWkQFLDV C 0 H C d VmR DV PHVPDV TXH DQWHV SRLV FRPR YLPRV Vy GHSHQGHP GH IDWRUHV JHRPpWULFRV H GD SHUPLVVLYLGDGH GR PHLR

H R FRORTXHPRV HP VHX LQWHULRU SUHHQFKHQGR WRGR R VHX YROXPH $ FDSDFLWkQFLD YDL PXGDU SDUD

ε 0 H ε  3RUWDQWR FRQWLQXD

Cd =
( D UD]mR HQWUH DV GXDV FDSDFLWkQFLDV p

εA
L

VHQGR YHUGDGH TXH D FDSDFLWkQFLD QD SUHVHQoD GR GLHOpWULFR