$a=3,22cm,b=10,54cm$

$R=310k,a=0\mathrm{.}0322m,R=310K$

radius $a=1(1)$

ECE $3320-$ Electromagnetic Field Theorys $b=0\mathrm{.}1054m$

Test #$3$ Tuesday, November $26,2024$

Analysis of Resistof: STEp $1$ & CHOOSE CONVENFEUT coor. SYs$.$

STEP $2$: Assume $V_0$ as the potential diff.

STEP $3$: Colculate the Electric Potental V by using Laplaces Eq$.gra{d}^{2}V=0$

STEP $4$ : Colculate vec$(E)$ using vec$(E)=-$graddarr$=-\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{r}}$hat$(a{)}_r+\frac{1}{r}\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}}$hat$(a{)}_{}+\frac{1}{rsin}\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{x}}{}_0$

Step $5$ : Calculate I from $I={}_{}vec(E)*dvec(s)={}_s(-\frac{V_0}{d}(hat(a_z)))*dvec(s)$

$I=-\frac{V_0}{d}s$

Step $6$: Caleulate $R_{ressingy}R=\frac{V_0}{\text{I}}$~~$[\frac{d}{s}]$

$R={\displaystyle \underset{a}{\overset{b}{}}}dR={\displaystyle \underset{a}{\overset{b}{}}}\frac{dr}{(4r^2)}=R=\frac{1}{4}[\frac{1}{a}-\frac{1}{b}]$

$($b$)$ Calculate the $$ Conductivity in S$/$mater $a$:$0322,b=0\mathrm{.}1054$